European Mathematical Society - 00b15
https://euro-math-soc.eu/msc-full/00b15
enThe Best Writing on Mathematics 2019
https://euro-math-soc.eu/review/best-writing-mathematics-2019
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the 10th volume in this series reprinting every year a collection of diverse texts on mathematics (i.e., not necessarily mathematical papers) that are accessible to a broad public. I have been reviewing these books since 2012, and I have repeatedly explained the idea behind the concept and the kind of papers that are selected in my reviews. These ideas have not changed in this anniversary volume, so I will not repeat them here. If you are not familiar with the concept of the series, you can look it up and read all about it in the previous reviews <a href="/review/best-writing-mathematics-2012">2012</a>, <a href="/review/best-writing-mathematics-2013">2013</a>, <a href="/review/best-writing-mathematics-2014">2014</a>, <a href="/review/best-writing-mathematics-2015">2015</a>, <a href="/review/best-writing-mathematics-2016">2016</a>, <a href="/review/best-writing-mathematics-2017">2017</a>, <a href="/review/best-writing-mathematics-2018">2018</a>.</p>
<p>
This volume reprints 18 papers almost all originally published in 2018. The fact that the subjects of the papers are usually crossing the boundary between two or more domains is one of their interesting features. It is remarkable how smoothly the sequence of papers in this book migrates from one subject into the next, due to a careful selection and collation strategy of the editor.</p>
<p>
For example the first paper links geometry to gerrymandering. The latter is a manipulative subdivision of the sets of voters in a the-winner-takes-it-all system to enforce some outcome of the voting. Finding a fair subdivision is a combinatorial problem that can only be solved in a feasible time using Markov Chain Monte Carlo techniques. This smoothly connects to the next paper about a problem from the <em>Scottish Book</em>, a legendary diary from Polish mathematicians meeting in Lviv (Poland) in the 1930's. The problem posed by Hugo Steinhaus in there gave rise to the ham-sandwich theorem, which is also about a problem of fair partitioning. In two dimensions the problem reduces to cutting a pizza and all of its ingredients distributed on top into fair parts.</p>
<p>
Politicians may be interested in gerrymandering and perhaps even in fair distribution, but they may also have something to say on the educational system, and in how to distribute different subjects that children have to learn over a limited education time. In that respect it is important to know if mathematics learns children how to think. Some claim that this can also be learned by studying languages (like Greek and Latin), computer science, or even by solving brain teasers and puzzles. After a careful analysis of this question in relation with different mathematical subjects, the authors of the next paper, conclude with some recommendations on how to teach calculus.</p>
<p>
Speaking of puzzles, the next paper deals with the Rubik's cube and all its generalizations that were realized practically or that were studied on an abstract mathematical basis. Three-dimensional geometry of the cubes brings the reader to the next paper discussing 3D objects that when viewed from different viewpoints create some optical illusions. This optical paradox is geometrically analysed and ingeniously illustrated using a picture of the object simultaneously with its reflection in a mirror representing the alternative viewpoint. The mirror is a perfect link to the detection of mirror symmetry in string theory, which became an important subject in both theoretical physics and algebraic geometry.</p>
<p>
The illustrations in the texts are grey-scale, but when in the original text they were in colour, then sometimes the caption of a grey-scale image refers a line or area of a certain colour. To mitigate this, colour versions of the illustrations of all the papers are collected at this point of the book. This somewhat hides the abrupt switch to more computer related papers that now follow. The first of these more computational type texts is about the application of a so called probabilistic abacus to find the probability that some event will happen. This computational mechanism was invented by A. Engel in 1975. It simulates a finite game played on a graph based on chip-firing. This computational technique is now known as Engel's algorithm.</p>
<p>
Computers play also an increasing role in the analysis and classification of integer sequences. The on-line encyclopedia (<a href="https://oeis.org/" target="_blank">OEIS</a>) started by Neil Sloane in 1996 had 100k entries in 2004. Sloane's paper in this collection is listing some fascinating examples among which an (in 2018) recent entry 250000. At the time of writing this review (Jan 2020) the OEIS has 331811 entries and counting. If anything is related to computers nowadays, then it is certainly big data. That topic made a bliz career in research funding and was promptly turned into a buzz word. The next paper briefly discusses examples of well known big date problems: from search engines to health care to recommender systems to farming, and I am sure we haven't seen the last of it</p>
<p>
What can be computed or even what can be decided is a fundamental question to ask in computer science as well as in mathematics (cfr. the halting problem and Gödel's incompleteness theorem). The next paper explains that deciding whether all materials have a spectral gap (i.e. the gap between the energy of the ground state and the first excited state) is proved to be impossible, using Turing machines and ideas from plane tilings. Computer generated proofs and verifying proofs by computers become more and more common practice. That is illustrated with some historical examples in a paper that is wondering how we should proceed for the future.</p>
<p>
Quantum physics and the quest for a theory of everything has divided physics research. The pure mathematical labyrinth in which theoretical physics has evolved as opposed to the classical empirical physics is not completely unrelated to mathematical models that have been designed for other scientific disciplines. The phenomena one wants to study are simplified to models that isolate some interesting characteristics. Given such a model (as a set of equations and constraints), also solving the models analytically or computationally, may require further simplifications to become feasible. Computed results are validated and when not matching with reality, the model may need adaptation. Is not mathematics of modelling here a kind of empirical science. This brings us on the verge of philosophy about mathematics. More philosophy is in a paper asking what it means that 2+3=5 (what is meant is adding of numbers, not counting quantities), Do the numbers 2 and 3 actually exist? We assume they do, since it is so obvious. But why then prove Fermat's last theorem while it is so obvious that it must hold? More on philosophy, in particular about the link to the history of mathematics is illustrated in a paper about Gregory's notion of infinitesimals and continuity as compared to the Weierstrass approach of epsilon-delta definitions. Some purists think infinitesimals are evil, others consider it a blessing to work with. The authors however conclude that eventually, after closer analysis, the two historical approaches are not that different.</p>
<p>
We humans do not like chaos. We try to make sense of things and are constantly looking for patterns. The Kolmogorov complexity corresponds to finding the shortest program that can describe some (mathematical) object like for example a sequence. This links back to the previously discussed problem of computability or decidability. The seemingly complex problem to describe "the smallest number that cannot be described by less that 15 words" is trivial and yet impossible to grasp. Just like an infinitesimal, something smaller than anything finite and yet not zero is difficult to conceive, and still easy to describe and work with.</p>
<p>
What we believe to be true and what actually is true is, with the constant exposure to information, an important issue in an epoch of fake news. Statistics is in this respect a seemingly scientific tool to sustain some fact, but unfortunately, it is easily misused. A paper discussing this ethical issue gives some recommendations about this like: be open about data and methods, be aware of the limitations of statistics, be open for criticism, etc. and I would like to add to that: be careful about causality claims.</p>
<p>
The two remaining contributions are diverse. One is a plea to return to the original idea of Fields when he installed the Fields Medal. Should one recognize brilliant mathematicians who accomplished something big in mathematics and thus are already "established", or should one celebrate a mathematician who is pioneering a new field in mathematics? The original idea was to stimulate (international) collaboration, not competition. Since the Fields Medal got the status of a mathematical Nobel Prize around the 1960's, that original idea is violated and it became the subject of competition. The last paper is about an Eulogy delivered by Melvyn Nathanson for Paul Erdős in 1996 shortly after Erdős passed away, and some considerations Nathanson has to add now (in 2018). The paradox of Erdős is that he was enormously prolific and versatile, even creating new fields and yet he never embraced the new mathematical domains of the twentieth century. How could he publish such important theorems and yet know relatively little?</p>
<p>
I should also mention the list of interesting books that appeared in 2018 and that get some recommendation from Pitici. As in previous volumes there is also a long list of papers that could have been selected as well for this collection (but they were not) and of other writings such as reviews of books and essays, teaching notes, and special journal issues. Thus this book is again a most interesting collection of mathematics related papers of the usual quality.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is volume 10 of Picici's annual harvest of papers on diverse topics related to mathematics that are collected from different journals and books. The contributions relate mathematics to philosophy, history, education, communication, computer science, games, puzzles, statistics, etc. Most of them were published in 2018 and are written for a generally interested readership.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691198675 (hbk), 9780691198354 (pbk), 9780691197944 (ebk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even"> £ 66.00 (hbk), £ 20.00 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">287</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://press.princeton.edu/books/hardcover/9780691198675/the-best-writing-on-mathematics-2019" title="Link to web page">https://press.princeton.edu/books/hardcover/9780691198675/the-best-writing-on-mathematics-2019</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Fri, 31 Jan 2020 10:37:23 +0000Adhemar Bultheel50361 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2019#commentsMathematics for Planet Earth
https://euro-math-soc.eu/review/mathematics-planet-earth
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Since 2018 Springer has started publishing this book series Mathematics of Planet Earth (MPE), and there are already six volumes by the end of 2019. The present book is volume 5 and is somewhat representative for the idea behind the whole book series.</p>
<p>The idea of the series is to describe and model several global problems that can be in any area, like climate change, epidemics, biodiversity, food security, urban societies, the Internet of Things, and many more. The list of topics is very broad and often require a multidisciplinary approach. A major objective in creating this book series is to raise interest and stimulate interdisciplinary collaboration. Therefore the papers of the books in this series are intended to be written and to be read by a broad range of pure or applied mathematicians, engineers, scientists, and other researchers. They are at a level that is not elementary but neither too technical so that it can be understood even by a beginning researcher from a different discipline. Solutions need not, or are only partially provided. The chapters are both introductions to the topic discussed and invitations to work on it.</p>
<p>While other volumes in the series were dealing with a specific topic like modeling of infectious diseases, tropical climate dynamics, energy transfer in atmosphere and oceans, and dynamics of biological systems, this volume has the generic MPE title of the series. Its subtitle Protecting Our Planet, Learning from the Past, Safeguarding for the Future can refer to anything and is not really enlightening the contents either. The reason is that this volume covers several different topics. There are thirteen papers divided over four parts: (1) Geo- and Physical sciences, (2) Life Sciences, (3) Ecology and Evolution, and (4) Socio-Economics and Infrastructure. Each part of almost a hundred pages consists of three or four papers. All of the papers were invited and refereed and can be read independently as an introduction to the problem discussed. Discussing each paper in some detail would be too much for this review, so what follows is just a birds eye view of the topics.</p>
<p>Learning from the past is applicable to the first paper in part 1. It takes data from glacial cycles in the Pleistocene Epoch to investigate the influence of CO2 by proposing different models that take care of the eccentricity of the Earth's orbit, precession, and inclination of its axis. This allows to predict the corresponding exposure to sunshine, the melting of ice, the volume of Northern Atlantic Deep Water, and other parameters. The resulting dynamical systems with bifurcation and limit cycles is investigated to make predictions about our future. The second paper is somewhat related and investigates the effect of melting of polar ice over the last 700 Kyears which changes the volume of solid land and the volume of water on the surface. Finding patterns in the evolution of precipitation of the third paper is more difficult since this has much more variable dynamics, both in time and in space.</p>
<p>In the Life Science part, we find a paper on the relation between malaria and climate change. The latter influences air-water temperature differences which influences the survival of the mosquito, and hence the spreading of malaria. Another paper models the spread of Buruli ulcer disease in Ghana and how the human-human and human-environment interactions influence that. These two papers obviously focus on problems of the African continent. A much more general view is taken in a paper that analyses the massive amount of data in the health sector that is becoming available. The purpose is to use this to obtain probabilistic data-driven models for some phenomena like food poisoning, transmission of avian influenza etc.</p>
<p>Ecology and Environment is represented by three papers. It is known that ecosystems are highly nonlinear and have several stable and unstable states to which it evolves under different circumstances. Extreme climate events or human intervention can result in a malfunctioning ecosystem. If we have proper models and can find the regions in parameter space in which some of these local states are embedded, perhaps we can we make these changes more gradual or partially prevent them. Dryland ecosystems are used as a case study. A paper about biodiversity is stressing the importance of having parameters for the number of different species, but also for how evenly they are distributed. In another paper several models for population dynamics at different scales are proposed to calculate an extinction risk.</p>
<p>The last part has contributions about Socio-economic Systems like the modelling of food systems, which, at a global scale, involves production, distribution, and consumption with complex network interactions. Bad management may lead to malnutrition and overweight existing simultaneously in different regions. A second paper models how the ecosystem can benefit from natural capital. Optimal management can be obtained from a dynamical optimization problem. For example what should be the optimal fishing quota for a steady state equilibrium? The Infrastructure is the subject of the remaining two papers. Network and scheduling analysis is used to obtain quantitative models to manage the restoration of infrastructure after extreme events. With the Internet of Things a massive network is created that should be managed to optimize urban societies. Transportation and municipal water services are used as case studies.</p>
<p>This quick survey illustrates the general set-up. It definitely illustrates the diversity of problems and methods that we have to deal with to cope with the enormous challenges that result from an increasing globalisation. Problems become very large scale, involve large networks, and become highly nonlinear. The parameters are changing drastically faster and the systems become very sensitive to small changes when they approach unstable states. If we ever want to control and manage all these effects, it will need substantial scientific research. And time is pressing. Here we meet several examples of research in action, trying to solve practical problems. Let's hope this is a wake-up call and that this will result in joining forces worldwide and across specialisations, instead of driving researchers away from each others into their own abstract unworldly niches with the only purpose to publishing papers.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is volume five of the book series Mathematics of Planet Earth in which mathematicians pure and applied describe mathematical methods and techniques to model global problems and describe them at a level that is not too technical and not too elementary. Hence it is hoped that they will raise the interest to work on these problems.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/hans-kaper" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Hans Kaper</a></li><li class="vocabulary-links field-item odd"><a href="/author/fred-roberts" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Fred Roberts</a></li><li class="vocabulary-links field-item even"><a href="/author/eds-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(eds.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-nature" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Springer Nature</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-3-030-22043-3 (hbk); 978-3-030-22044-0 (ebk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">€ 103.99 (hbk); € 84.99 (ebk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">394</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/dynamical-systems-and-ordinary-differential-equations" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dynamical Systems and Ordinary Differential Equations</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://www.springer.com/gp/book/9783030220433" title="Link to web page">https://www.springer.com/gp/book/9783030220433</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/86-geophysics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">86 Geophysics</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/86-06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">86-06</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/86axx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">86Axx</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Mon, 25 Nov 2019 09:35:01 +0000Adhemar Bultheel49949 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/mathematics-planet-earth#commentsThe Best Writing on Mathematics 2018
https://euro-math-soc.eu/review/best-writing-mathematics-2018
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Here is number nine in this series in which Pitici collects previously published papers about mathematics and how it relates to society. See also the reviews of the previous volumes on this EMS site. As usual the papers are harvested from magazines and journals that are not in the mainstream of specialised mathematical research journals. Although they are about mathematics, they do not really involve new mathematical results as such. They are rather about mathematicians and the way they do mathematics. The topics are familiar for those who know (some of the) previous volumes. The papers deal with for example the teaching and the history of mathematics, or things that inspire(d) mathematicians. Others are about paradoxes, games, or recreational aspects. Eighteen papers were reprinted in a uniform way for this volume, all published originally in 2017. What follows is a quick survey.</p>
<p>
The first paper is a contribution by <strong>Francis Edward Su</strong>, past president of the MAA and strongly involved in methods to transfer mathematics to students. His paper is a plea arguing that practising mathematics cultivates virtues that bring humans to completion (he uses the term "human flourishing") because mathematics answers to five basic human desires: play, beauty, truth, justice, and love.</p>
<p>
<strong>Margaret Wertheim</strong> argues that people often think of mathematics as being formulas and abstractions, i.e., fabrications of human intelligence. However, much of our mathematical inspiration comes from nature. Nature does not have the advanced human intelligence, but it is just <em>"living the mathematics"</em>. It does expose all the juicy mathematical charateristics such as patterns, fractals, hyperbolic geometry, etc.<br />
On a more philosophical level is a contribution by <strong>Robert Thomas</strong> who explains that the aesthetics of mathematics is not only beauty. Just being <em>interesting</em> is also an important aesthetic category. If your paper is not interesting, it will not get published.</p>
<p>
Computers certainly have influenced the way we do mathematics. <em>Satisfiability</em> (or SAT) is a concept of computer science. A Boolean formula is satisfiable if it is possible to find a model or interpretation of the variables that makes the formula true. Here computers can come to the rescue giving automated proofs that recently solved open problems where traditional proofs are infeasible because too many cases have to be considered separately. <strong>Marijn Heule and Oliver Kullmann</strong> give an introduction to SAT and make a point of the fact that this may give insight in the complexity of a problem and it may open some perspectives for Ramsey theory. So, what is needed is that the proofs themselves should become objects of investigation. Also in the realm of computer science is the paper by <strong>Peter Denning</strong> who gives his definition of the recent paradigm of <em>computational thinking</em> and discusses its advantages and limitations.</p>
<p>
Mathematics can be inspired by physics, as <strong>Robbert Dijkgraaf</strong> illustrates with quantum physics. The concept of <em>mirror symmetry</em> such as particle and wave interpretations of the same (quantum) mechanical phenomenon may have consequences for mathematics. These different interpretations require different mathematical tools and methods. So perhaps mirror symmetry also connects different mathematical disciplines as two sides of the same reality.<br />
But also the playfulness of mathematicians can lead to interesting problems. Three examples can be found here. <strong>Erik Demaine et al.</strong> discuss planar configurations that can be produced in <em>Tangle toy</em> by joining quarter circle pieces together to form a closed loop. Like in other papers in which father and son Demaine are involved, there are some interesting mathematical questions that can be asked about something that starts from playful amusement. And these are just the planar problems, predicting much more involved questions since the loops can also be constructed in 3D. <strong>James Grimm</strong> describes the design of dice to play a game where the winning strategy is nontransitive, meaning that one state winning over another may lead to circular arrangements like in rock, paper, scissors. And <strong>Arthur Benjamin et al.</strong> analyse the statistics of a kind of Bingo game to explain a paradoxical outcome. In the same vein but less straightforward is the analysis of the <em>Sleeping Beauty problem</em> by <strong>Peter Winkler</strong>. The problem was formulated around mid 1980's and has caused a lot of controversy since. The Sleeping Beauty has to undergo a sleeping experiment, with a final result that depends on a coin toss. She has to estimate the probability of the outcome of a coin toss when she wakes up at the end of the experiment (the details can be looked up on the web). Winkler does not favour one solution but he gives arguments to support the different possible probabilities that have been proposed in the past.</p>
<p>
There are also papers of a more historical nature. <strong>José Ferreiros</strong> discusses the paper by E. Wigner in which he introduces his often quoted "unreasonable effectiveness of mathematics in natural sciences".<br />
<strong>Daniel Mansfield and N. Wildberger</strong> show that the Babylonians knew Pythagoras' theorem long before Pythagoras (which is probably not a surprise), but also that their study of (rectangular) triangles was based on ratios of the sides of the triangle. Since they used a number system in base sixty, they were able to produce some rather accurate tables that we now call goniometric tables, but the surprise is that they did it independently of the angles.<br />
Isidore of Seville (560-636 CE) was a Spanish bishop and scholar. He authored the encyclopedic <em>Etymology</em>. In his time mathematics was part of the priesthood education. It is via sources like this that classical Greek mathematics was passed on to the Middle Ages. <strong>Isabel Serrano et al.</strong> discuss what sources he may have used for his description of the classical <em>Quadrivium</em>.<br />
<strong>Michael Barany</strong> shows how after World War II <em>mathematical awareness</em> became an issue (and it still is today) and that Mina Rees has been instrumental as the first president of the <em>American Association for the Advancement of Science</em> (AAAS) to promote the idea.</p>
<p>
In the vein of education and teaching, there are four papers: Methods, concepts, and techniques of <em>interdisciplinary teaching</em> is discussed by <strong>Chris Arney</strong>. <strong>Nancy Emmerson Kres</strong> goes through a list of essential questions to ask when solving a problem. <strong>Benjamin Braun et al.</strong> explain what <em>active learning</em> means when teaching mathematics. And finally <strong>Caroline Yoon</strong> wants to remove the dichotomy between mathematics and languages (sometimes almost considered to be opposites of each other) by illustrating that there is a clear parallel between them: writing a text can be seen as a task of modelling (getting insight), of problem solving (reorganizing the text), and even of giving a proof (convincing your reader).</p>
<p>
Pitici gives also a list of around sixty interesting books, and a long list of "notable writings" (journal papers, or special issues, book reviews, teaching tips, interviews, biographies, obituaries). The selection from this vast amount of the eighteen papers included here is obviously a personal choice made by Pitici. If you are interested in just one of the broad set of topics that were touched upon in this volume and you want to know more, then you will certainly find a lot of inspiration to read. There is certainly enough material to keep you reading till the next volume of "The Best Writing in Mathematics" to which I am already looking forward to now.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
For the ninth time, Pitici has collected papers about mathematics and its relation to society. This volume contains the harvest of 2017. As in previous anthologies, the papers do not really contain mathematics but they discuss topics such as history, philosophy, education, games, and recreational mathematics.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici-ed" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">mircea pitici (ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-691-18276-6 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 24.95</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">270</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://press.princeton.edu/titles/14178.html" title="Link to web page">https://press.princeton.edu/titles/14178.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Fri, 30 Nov 2018 15:21:17 +0000Adhemar Bultheel48887 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2018#commentsThe Best Writing on Mathematics 2017
https://euro-math-soc.eu/review/best-writing-mathematics-2017
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
In the eight volume of this successful series, Pitici has collected 19 papers on mathematics published in 2016, reprinted and typeset in a uniform way. Six of the previous volumes (2011-2016) were reviewed in this EMS review database, which you can recover by searching for "Pitici" with the search tool. The general concept and the practical realisation has not been changed in this volume.</p>
<p>
It may be useful to recall that the papers here, like in the previous anthologies, are not mathematical research papers in the usual sense, but they are papers about mathematics and mathematicians and how their work relates to society. Here again we thus find papers about history, philosophy, art and culture, education, economics, and many other aspects of society. Sometimes it are these factors that influence mathematics, sometimes it is the other way around, but it illustrates that mathematics is an integral part of society and hence deserves general interest.</p>
<p>
Some examples of these relations: Mathematics seen as a system producing products that have economic, legal, and social effects (Ph.J.Davis), just realize how mind-blowingly large the largest known prime number is (E. Lamb), how to describe random growth in nature (K. Hartnett), Richard Guy, the man who knows everything and who was a friend of Paul Erdős turned 100 in 2016 (S. Roberts), inverse yogiisms are mathematical statements that are literally true but hide or suggest something untrue, and thus are prone to misinterpretation (L.N. Trefethen), how I acquired a bronze statue of Ramanujan (G.L. Alexaderson), who would have won the Fields Medal if it had existed 150 years ago (J. Gray), what arguments are used in the ongoing debate about the human brain being Bayesian or not (R. Bain), what is and is not possible in prediction and forecasting (G. Southorn). These are just a few of the general subjects.</p>
<p>
Somewhat more mathematical are contributions about the creation of symmetric fractals (L. Riddle) and another one about the use of projective` geometry to explain the tilt illusion of the moon (M. Frantz). Mathematics and art are walking side by side in an analysis of the painting of Luca Pacioli (ca. 1500) where the artist wants to show his craftsmanship by painting a glass rhombicuboctahedron half filled with water in a corner of the painting. A careful analysis of the angles and the perspective of this object allows to conclude that it was almost certainly added by a different painter and even the size and the position of the object with respect to the painter can be estimated (C.H. Sequin, R Shiau). More applied art in an analysis of Islamic girih decoration, not in the plane this time but on the curved surfaces of domes (M. Kasraei et al).</p>
<p>
In the realm of mathematics education we have a contribution where it is advised that we should let children use their fingers for counting (J. Boaler, L. Chen). Other papers dealing with the subject are discussing how to explain the logarithm with a piece of string and using the catenary curve (v. Blåsjö), why one should be careful and not apply a simple mechanical cause-effect analysis when researching educational processes (J. Mason), what are the threshold concepts in undergraduate mathematics teaching, that are the hurdles, the crucial concepts to be understood properly before one should continue with subsequent material (S. Breen, A. O'Shea).</p>
<p>
A problematic characteristic of mathematics, at least in an educational context, is its abstraction. On a more philosophical level the method of abstraction applied in mathematics and how this is different from an axiomatic approach is also discussed in a longer paper (J.-P. Marquis). The limits of mathematics and science in general is revealed in paradoxes and contradictions (N.S. Yanofsky). The latter is basically a summary of what is more elaborated in this author's book <a href="/review/outer-limits-reason"><em>The Outer Limits of Reason</em></a> (MIT Press, 2016).</p>
<p>
This very brief enumeration does not give proper credit to the deeper contents, but it at least illustrates the breadth of the subjects covered. The number of papers in each volume of the series is usually between 20 to 24, with a peak in the 2015 and 2016 issues of about 30 papers. This 2017 volume is back to 19 and is about half the number of pages of 2016. This does not necessarily mean that the number of papers in this particular area has reduced. Pitici introduces the topics of the issue in his editorial, but, as usual, this introduction also mentions in a paragraph `More Writings on Mathematics' a number of books (a list of 68 books) whose contents perfectly blends with the subjects that are selected in this series. Moreover at the end if this collection 14 more pages list references to papers that could also have been selected, but were not, and 6 pages listing references to interesting book reviews, to notable interviews, memorial notes, obituaries, and to special journal issues. Thus there is so much more to be explored.</p>
<p>
What is found on all these writings on mathematics is an illustration of what Pitici describes in in his introduction as follows: "Mathematics is a domain of clarity <em>and</em> obscurity, of enchantment <em>and</em> boredom, of unperturbed neatness <em>and</em> of puzzling paradox, of apodictic truth <em>and</em> arguable interpretation. The pieces in this volume once again demonstrate the dynamic coexistence of opposite characteristics of mathematics — and show that mathematics is anything but the dull subject serviced by an increasing powerful but stultifying educational bureaucracy unable to grasp, appreciate, promote, and teach the creative and imaginative sides of mathematics".</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Mircea Pitici has selected once more a series of papers on mathematical subjects that are not so easily found in the literature and that will enjoy mathematicians as well as non-mathematicians with interest in science. It is the eight volume in this wonderful series.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691178639 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£ 19.95 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">248</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://press.princeton.edu/titles/11102.html" title="Link to web page">https://press.princeton.edu/titles/11102.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Mon, 08 Jan 2018 21:24:43 +0000Adhemar Bultheel48156 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2017#commentsThe Best Writing on Mathematics 2016
https://euro-math-soc.eu/review/best-writing-mathematics-2016
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the seventh volume in the series for which Mircea Pitici selects every year a set of papers that discuss popular mathematics-related topics. This genre, if it can be called so, has gained an increasing interest, and the number of pages in each volume seems to be a nondecreasing sequence. Pitici's task may become more difficult every year in making some selection within the scope of the book taking into account the limitations of space and copyright restrictions. On the other hand, with a larger supply to choose from, the quality of the eventual selection is easily kept as high as in previous years.</p>
<p>
In the first four volumes some <em>big shot</em> wrote an introduction, but since the 2014 volume, the series has established a reputation of its own and Pitici writes his own introduction with a long list of books that fall into the same class as the papers in the collection. As usual, there is also a long enumeration at the end of the book with other publications that were not included but that are still highly interesting. That list also has references to notable book reviews, interviews, and special issues of journals. Pitici stresses in his introduction that each volume is an integral part of the whole series. He announces the compilation of an index over all volumes to be produced in the near future. That would indeed be a nice tool to browse through the whole series more easily.</p>
<p>
There are 30 papers selected for this book, all published in 2015. The numbering is indeed a bit misleading, yet reasonable and correct if you think of it practically. This collection is published in 2017, with the title <em>Best writing on Mathematics 2016</em>, since 2016 is the year in which the papers of 2015 are harvested and the book is being prepared. It takes indeed some time to deal with copyright and to typeset the papers in a uniform format.</p>
<p>
What exactly should be understood by fitting under the umbrella of <em>popular mathematics</em>? The last contribution by Ian Stewart, who is a prolific writer of this kind of books, gives a possible answer. Besides children's books, topics treated can be philosophy, history and biography, fun and games, big problems, pure versus applied, or links with arts and culture. He also gives a lot of good advice for anyone who feels the urge to write a book in this class. We find papers in this collection that represent most of the topics that Stewart enumerates, to which we should probably add education and teaching. Not exactly a "popular" topic, but it certainly addresses a public much broader than just mathematicians. Therefore also this topic has in the collections of this series found a settled place.</p>
<p>
Remarkable in the current collection are the three contributions that debunk or at least place in proper perspective what has been a firm folk belief: Wigner's "the unreasonable effectiveness of mathematics in physics" and Hardy's "defense of pure mathematics" and Leibniz's formulation of "the fundamental theorem of calculus". The authors if these papers show that these statements seem not to be as accurate as generally accepted. Another historical contribution is about the most illustrious constant in mathematics. The constant <em>π</em></p>
<p>
is often defined as the ratio of the circumference of a circle over its diameter, but if we consider this as a theorem, then its origin is surprisingly very fuzzy. One more generally accepted expression is to say that a theorem is "deep". It is used lightly by many, but difficult to define. What exactly does it mean when a theorem is called deep? You can find some answers to all these puzzling issues in this book.</p>
<p>
Of course the other topics mentioned are also represented: games and recreation (design of a card deck for Spot It!, stacking wine bottles, billiards), art (mathematics in the collection of the Metropolitan Museum of Arts in NY), and the big problems (The monster group, and Mochizuli's "proof" of the abc conjecture). And there is much more of course. Each paper is selected among the best papers that were published. Not only are the subjects teasing, but the stories are told with vivacity that just gets you hooked after reading the first paragraph. If you do not know where to start, you can find a 3 page survey of all contributions in Pitici's introduction. It is clear that each paper can be read independently, but there is some loose logical ordering. For example the five papers with a statistical flavor are placed together.</p>
<p>
Once again a highly recommended collection that saves you the time to search for the papers yourself and finding out whether it is top quality or not. You do not need to be a mathematician. Mathematical technicalities are totally avoided. These are papers <em>on</em> mathematics, not mathematical papers. It also aims at politicians, managers, philosophers, and whoever has a broader interest in science or society. It presents mathematics in its broadest cultural and social context.</p>
<p>
For reviews of previous volumes see <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2012" target="_blank">2012</a>, <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2013" target="_blank">2013</a>, <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2014" target="_blank">2014</a>, and <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2015" target="_blank">2015</a>.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the seventh volume in the series for which Mircea Pitici selects every year a set of papers that discuss popular mathematics-related topics. As previous volumes we get a high quality selection of papers originally published in 2015 discussing mathematics and its relation to education, history, philosophy, games and recreation, and art. Once more a marvelous selection.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691175294 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">27.95 £ (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">408</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10953.html" title="Link to web page">http://press.princeton.edu/titles/10953.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Mon, 10 Apr 2017 07:21:29 +0000Adhemar Bultheel47611 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2016#commentsThe Best Writing on Mathematics 2015
https://euro-math-soc.eu/review/best-writing-mathematics-2015
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the sixth anthology of math related papers in this series of <em>Best Writing on Mathematics</em>. For the review of four previous volumes in this EMS database see <a href="/review/best-writing-mathematics-2011">2011</a>, <a href="/review/best-writing-mathematics-2012">2012</a>, <a href="/review/best-writing-mathematics-2013">2013</a>, and <a href="/review/best-writing-mathematics-2014">2014</a>.</p>
<p>
The concept has not changed since the previous edition. This time, we get 29 contributions which, as you may recall from previous volumes, are not per se mathematical, but reflect on mathematics. The writings are <em>on</em> mathematics, not <em>of</em> mathematics. They are addressing mathematicians as well as non-mathematicians. The book is copyright 2016, and from the title, one could expect reprints of papers that were published in 2015. However, all the papers are re-formatted in a uniform lay-out and that takes some time, so the papers that are collected in this volume are all from 2014. In that sense the title is a bit misleading.</p>
<p>
The topics are covering again mathematical games and recreation, mathematical education, some history and some geometry, in short mathematics (also, and most prominently so) for the non-mathematician. Let me pick some items that caught my attention, implying that this is a personal selection, and other readers may have a totally different choice.</p>
<p>
M. Barany and Donald McKenzie emphasize the importance of the blackboard in mathematical education and research. There may be some benefits in using PowerPoint or other digital presentation tools, but abandoning chalk and blackboard has definitely a great impact on the organization of our thoughts in mathematics communication. P. Mutalik points to the psychological impact of an Aha! experience when solving a puzzle or a mathematical problem and hence moulds our minds and shapes our development as humans. The reform of mathematical education is a permanent struggle, if not war, worldwide. Strong emotions, political, economic, and emotional forces tear in all directions. J. Fey and S. Garfunkel give five tenets that should be taken into account to reform math education in high schools (in the US). Highly instructive is the paper by G. Zhang and M. Padilla who compare the mathematical education in China and the US which are almost opposites, yet with a result that is favorable for the Chinese.</p>
<p>
In the realm of puzzles and games, I mention yet another celebration of Martin Gardner (C. Mulcahy and D. Richards), the morphing game needed when juggling (R. Tou), billiards of all possible shapes (M. Freiberger), the generation of magic squares (A. Benjamin, E. Brown), the mathematics behind candy crush (T. Walsh), and the historical roots of the game Nim (L. Rougetet).</p>
<p>
Some of the papers can be classified as related to geometry. Several of the classical curves such as spirals, (epi-)cycloids, etc. are discussed by E. Maori and E. Jost. A quite remarkable study is B. Polster's paper about non-circular shapes of constant width and how they have been applied. J. Conway and A. Ryha give an amusing discussion of different proofs for an old geometric problem in triangular geometry. The perspective used by Dürer in his drawings duscussed by A. Cranell, M. Frantz, and F. Futamura, and unseen visualizations of symmetry groups such as the quaterion group by V. Hart, and H. Segerman.</p>
<p>
But as I am enumerating the papers that I found personally interesting, I realize that I will end up with most of the content, if not all of it. There are the ones that relate mathematics and art, philosophy, biology, the papers with a statistical aspect, etc. Certainly, I have to mention the introduction by the editor Mircea Pitici explicitly. As before, he does not only summarize the contributions, but since there are only papers in the book, he also gives a list of books recently published that have a similar content and are intended for a broad readership. New is that he started a Twitter account (@mpitici) and supplementary material is available on the website of this book at Princeton University Press that can be found elsewhere on this review page. This extra material consists e.g. of an extended version of the introduction of the book –—so you can also find there his summary of the contents of all the papers in the book which is more complete than mine—– and there are many links to extra online information. This is provided in pdf form, so it is a bit disappointing that the links have to be copy-pasted since they are not directly clickable. Everyone is invited to make suggestions and contribute to future volumes.</p>
<p>
Every year I look forward to the new volume of <em>Best writing on mathematics</em> and just like the previous volumes, this one, even thicker than the previous, fulfills all the expectations.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the sixth anthology of math related papers in this series that collects diverse essays on mathematics that are accessible for a broad audience. The papers appearing in different books and journals in the year 2014 and are reprinted here in a uniform format. </p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2016</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691169651 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£16.95 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">336</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10558.html" title="Link to web page">http://press.princeton.edu/titles/10558.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Tue, 09 Feb 2016 08:02:58 +0000Adhemar Bultheel46707 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2015#commentsThe Best Writing on Mathematics 2014
https://euro-math-soc.eu/review/best-writing-mathematics-2014
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the fifth anthology of math related papers in this series of <em>Best Writing on Mathematics</em>. For the review of three previous volumes in this EMS database see <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2011">2011</a>, <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2012">2012</a> and <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2013">2013</a></p>
<p>
The harvest this time consists of 25 papers. The subjects are again very diverse, always about mathematics, but not necessarily just mathematical results. Some examples of what questions were discussed in the contributions: Will the massive digital information available today (big data) change the way we look at the world? Is it true that logarithmic scaling is natural for our senses to perceive the environment? How to knit a Klein bottle cap or scarf? One of the topics that is well represented by several of the contributions is (math) education. For example does gaming influence math education? Should we introduce more engineering applications in our math teaching? Is it more important to <em>do</em> things rather than think or reason about it? Can fruit that is brought to the classroom be an incentive to learn (mathematics)? Etc. Some recreational and true mathematical subjects are represented by the solution of a puzzle formulated by John Conway, and Conway himself showing that some statements can not be proved mathematically. Can we teach generic proofs for building blocks of more complex proofs? Many proofs can lead to the same result by different approaches, for example proofs to show that √2 is irrational. How can mathematics help to assign room mates or match couples in stable marriage? Can statistics be used to analyze or create art? What is the shape of our universe? How about the dichotomy between the continuity of real numbers and the finite, hence discrete, computations in our models for real phenomena? This is just an enumeration of randomly selected samples because there is so much more to read in this book.</p>
<p>
Unlike the previous volumes, where someone (some "big shot") was invited to write an introduction and give a discussion of the content (these went well beyond some sympathizing phrases), this time there is an introduction by the editor M. Pitici himself. That does not only include a survey of the contributions, but it also mentions a list of books, that have some affiliation with the kind of papers that were included here. That results in a bibliography of 79 books published mostly in 2013 (with few exceptions from 2012). And that is just a selection. It is a fact that there is a growing interest in popular science books, and several professional mathematicians and science communicators, sooner or later come up with such a volume. Sometimes it is the result of a derailed interest for a subject and written during the free time, while others are actually making a living out of it. Thus if you are looking for some more substantial material to read, there are a lot of suggestions here. Pitici ends his introduction as usual with some references to online material. Websites which colorful math images, with blueprints to construct 3D objects, origami algorithms, mathematics and art, etc. More interesting papers that did not make it into this volume are given as an (uncommented) bibliography at the end of the book.</p>
<p>
So all in all, if your are not (but of course also if you are) a professional mathematician, but you are for example a journalist, a politician, or if you are interested in education (of mathematics), these volumes carefully assembled each year, keep you informed about what is happening in the margin of mathematical research. You do not have to be afraid that it will be too technical, there is indeed hardly any "hard" mathematics involved. If you are (as a mathematician) interested in new results or breakthroughs in mathematics that do not belong to your own backyard, then perhaps, this will not be the kind of collection you are looking for.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the fifth book in the successful series of <em>The Best Writing on Mathematics</em>. As before, M. Pitici collected a number of generally accessible math related (i.e., not necessarily mathematical) papers that were published in 2013, and that are reprinted in this volume.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691164175 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£16.95 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">360</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10316.html" title="Link to web page">http://press.princeton.edu/titles/10316.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Mon, 22 Dec 2014 11:54:02 +0000Adhemar Bultheel45922 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2014#commentsThe great mathematical problems
https://euro-math-soc.eu/review/great-mathematical-problems
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The popular science writer Ian Stewart tackles the <em>Great Problems of Mathematics</em>, i.e., the conjectures that gained fame because they remained unsolved for many years or that are still unsolved. They are important since they often generate a whole new body of mathematics so that prestigious prizes are rewarded for their solution. Stewart describes the origin, the history, and the development of some of these. It is not easy, but Stewart at least tries, with some success I must say, Stewart largely succeeds in transferring the ideas without the plethora of formulas and difficult mathematical concepts that one would expect. He also illustrates that often a breakthrough is triggered by the development in a seemingly unrelated piece of mathematics.</p>
<p>
The first topic is the <em>Goldbach conjecture</em> (1742): every integer larger than 2 is the sum of 2 primes. Stewart takes his time to introduce prime numbers, their history and their computation. This pays because several of the subsequent problems are related to prime numbers as well. He explains what has been shown and what is not, how it has been linked to the Riemann conjecture and the open problems left for the present and future generations.</p>
<p>
<em>Squaring the circle</em> is a problem that dates back to the Greeks and is clearly linked to $\pi$. This is a nice illustration how an obviously geometric problem, is reformulated as an algebraic one, solving polynomial equations, leading to real and later complex analysis (to prove that $\pi$ is irrational and transcendental). Much more recent is the <em>four colour problem</em> (1852) Again, the solution is not important for cartography because there are many other reasons to choose a colour for the map, but it started research is networks and graphs, and it has been generalized to colour problems on much more complex topological surfaces. It was finally proved in 1976 by Appel and Haken and it revolutionized the concept of a proof, since it was the first time that a proof relied on the verification by a computer of many cases to which the problem was reduced. Too many to be checked by humans.</p>
<p>
Although the original 1611 version of <em>Kepler's conjecture</em> appeared in his booklet on 6-pointed snowflakes, it is asking how dense spheres can be packed. Every grocer knows how to mount oranges in a pyramid, but it took 387 years for a proof to be found. Again, a computer was needed to solve the global optimization problem. A formal proof avoiding the computer is still an ongoing project. The <em>Mordell conjecture</em> (1922) was proved by Faltings in 1983. It is about Diophantine equations but has a geometric formulation stating that a curve of genus $g>1$ over $\mathbb{Q}$ has only finitely many rational points. Stewart uses this on his path towards <em>Fermat's last theorem</em>, since one may start from Pythagoras equation $x^2+y^2=z^2$ with integers to the equation of a circle $(x/z)^2+(y/z)^2=1$ with rational numbers and subsequently to a generalization where the circle is replaced by an elliptic curve.</p>
<p>
Although Poincaré got the award of the Swedish King Oscar II in 1887, he did tot really solve the originally posed <em>three body problem</em> that was suggested by Mittag-Leffler. Nowadays there are numerical techniques to solve equations with a chaotic solution approximately, rigorous proofs and many questions remain unanswered. The answers are directly related to fundamental questions about the stability of our solar system.</p>
<p>
Back to prime number distribution with the <em>Riemann hypothesis</em> (1859). Again number theory is lifted to complex analysis in the study of the ζ-function (Stewart needs quite some pages to come to this point). It is explained how this leads to the conjecture that the zeros of the ζ-function are on the critical line $x=1/2$ in the complex plane. This is one of the most famous open problem in mathematics today. It survived Hilbert's 1900 unsolved problems and it is reformulated as one of the Clay millennium problems. Most mathematicians believe it to be true as numerics seem to indicate but a proof is still missing.</p>
<p>
The other six millennium problems are the subject of the following 6 chapters, in which the mathematics that Stewart needs become tougher. The <em>Poincaré conjecture</em> (1904) was solved by Perelman in 2002, but because it took 8 years for the math community to verify his proof, the introvert and eccentric Perelman, totally disappointed with that situation, has withdrawn from mathematics and refuses all contact with the media. He declined the EMS prize (1996), Fields Medal (2006), and the Clay millennium prize (2010).</p>
<p>
The <em>P/NP problem</em> is still open and the outcome is uncertain: are hard problems such as the traveling salesman problem solvable with polynomial time algorithms? The answer to this question seems to be NP-hard itself.</p>
<p>
Solving the <em>Navier-Stokes equation</em> is a problem from applied mathematics. Can one verify that the small changes made by numerical procedures don't miss some turbulent solution because the approximation is not fine enough. In January 2014, Otelbaev claims to have solved this problem. The proof is still under review. The <em>mass gap hypothesis</em> relates to quantum field theory of elementary particles. These quantum particles have a nonzero lower bound for their mass even though the waves travel at the speed of light. In relativity theory, the mass would be zero. The <em>Birch-Swinnerton-Dyer conjecture</em> is another millennium problem about rational solutions of certain elliptic curve equations. Finally the <em>Hodge conjecture</em> connects topology, algebra, geometry and analysis to be able to say something about algebraic cycles on projective algebraic varieties.</p>
<p>
</p>
<p>
Although Stewart tries very hard to introduce the unprepared reader to the problems and the techniques for the latter four problems, the much more advanced mathematical needs make these chapters definitely harder to read than the earlier ones. As a conclusion, he gives his own opinion of what will and what will not be proved in the (near) future. Just in case the reader gave up on the Riemann hypothesis and is looking for inspiration to find another really challenging problem, Stewart provides a list of 12 somewhat less known open questions that are as yet unsolved.</p>
<p>
Stewart's entertaining style, his meticulous sketching of the historical context, his sharp analysis of the importance and consequences, his broad insight in the wide spectrum of mathematics and, being a mathematician himself, his understanding of the human behind the mathematician, struggling for solutions and recognition, makes this book a very interesting and highly recommendable read.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Ian Stewart, in his well known style, guides us through the history and the developments of the great conjectures of mathematics, the approaches undertaken and the kinds of mathematics that were developed in the attempts (and successes) to solve them. Not only the Goldbach and Riemann conjectures and Fermat's last theorem, but also several others, including the Clay Mathematical Institute millennium prize problems.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/ian-stewart" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">ian stewart</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/profile-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">profile books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-84668-1998 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£9.99 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">352</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.profilebooks.com/isbn/9781846683374/" title="Link to web page">http://www.profilebooks.com/isbn/9781846683374/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Fri, 07 Feb 2014 07:53:40 +0000Adhemar Bultheel45551 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/great-mathematical-problems#commentsThe Best Writing on Mathematics 2013
https://euro-math-soc.eu/review/best-writing-mathematics-2013
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This collection, the fourth in a row, was brilliantly selected once more by the editor Mircea Pitici. Mind you, the papers were selected, not published in 2013. The current selection has papers published in the period 2009-2012. As usual, the foreword is provided by a mathematical celebrity. This time it's written by Roger Penrose. Reviews of the two previous collections can be found in this EMS database: see <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2011">2011</a> and <a href="http://www.euro-math-soc.eu/review/best-writing-mathematics-2012">2012</a>.</p>
<p>
As in the previous collections we find here a diversity of generally accessible papers that report on issues from mathematics or about mathematics that not only professional mathematicians will (or should be) interested in, also politicians or anybody responsible for science and education are advised to read some of the 20 contributions.</p>
<p>
There is an enlightening paper by <em>Ph.J. Davis</em> on the drastically changed landscape dominated by computers and multimedia in which mathematics has to operate nowadays. <em>I. Stewart</em> in a tribute to A. Turing explains how stripes on animals appear as a consequence of waves, while spots are the result of interfering waves. <em>T. Tao</em> illustrates how universal or global laws may result from unpredictable behaviour of a great many individuals. The small world phenomenon discussed by <em>G. Goth</em> is a counter-intuitive property of the many individuals populating e.g. social networks. This concept is by now fairly well known by the general public. To find the shortest path visiting several nodes in such a graph is known as a traveling salesman problem, and is hard to solve. It is NP-complete. The problem whether the class of NP problems equals its subclass of easier problems of class P is one of the big open problems in computer science and it shows up in a text by <em>J. Pavlus</em>. This is one of the Clay Mathematics Institute millennium prize problems. Solving it would gain you a prize of US$1,000,000.</p>
<p>
Large numbers usually entail also randomness and probability and these topics are the subject of several of the papers in this collection. The very basics of randomness are bravely reviewed in a short paper by <em>C. Seife</em>. <em>D. Knuth</em> illustrates that small random perturbations of harmonics in music are more pleasing. This is a general phenomenon. Perfect symmetry is boring. Slight deviations make symmetry interesting. How come that gamblers become addicted? <em>S. Johnson</em> shows that this is because the gambler has the wrong intuitive interpretation of the probabilistic laws like "I've been loosing so long, hence the next time I should win". Notorious errors in the early days of probability theory are placed in an historical context by <em>P. Gorroochurn</em>. In financial mathematics <em>E. Ayache</em> uses metaphysical arguments to conclude that probability should not be applied to states of the market, but that the market itself should be a category of thought to substitute probability. Probability can analyse the past, but it cannot predict the future.</p>
<p>
Geometry is another topic brought to the foreground in several of the texts. <em>R. Gross</em> uses the Jerusalem Chord Bridge to discuss Bézier curves, <em>D. Silver</em> shows that Dürer's "Painter's Manual" introduces the cuts of a cone. Although Dürer gives a construction method, he mistakingly thought that an ellipse was egg-shaped, i.e. thicker at the bottom than at the top. A somewhat understandable error because the cone is thicker there than at the top of the cut. More of a topological nature are the papers by <em>K. Delp</em> about how topological concepts like hyperbolic geometry that were used in design and fashion culture, while <em>F. and W. Ross</em> show graphical art that is produced by drawing just one very complicated Jordan curve. Mathematical history is reflected in the paper by <em>D. Lloyd</em> about the hoax that was caused by a picture of five neolithic carved stone balls from Scotland that presumably were models for the five Platonic solids. He gives good arguments against this conjecture. More history is represented by <em>J. Bennett</em> in his paper about the mathematical (mostly astronomical) instruments that were developed during the 16th to the 18th century.</p>
<p>
The paper by <em>F. Quinn</em> is about the revolutionary ideas in the period 1890-1930 that have drastically influenced sciences. This revolution caused some bifurcation between core mathematics and the applied vision. The paper bridges the gap between history and education. The latter is another recurrent topic in these collections of "Best Writings on Mathematics". Quinn argues that the cultural attitude towards mathematics in general and to core mathematics in particular that we experience today is largely a matter of neglected public relations. Hence high time to revise our ideas about mathematics education, since that has not fundamentally changed since the Greeks. <em>A. Sfard</em>'s contribution is another outspoken plea to drastically change our arguments of why we should teach mathematics and certainly how and what we should teach. Also <em>E. Maloney and S. Beilock</em>'s text about `math anxiety', that is shown to exist at a much earlier age than generally accepted is relevant in this context.</p>
<p>
Once more this is a marvelous selection of papers about mathematics written by the best. They do not drawn the reader into the mathematical jargon that is only of interest to the mathematical literate. In fact practically no mathematics is needed and formulas are almost completely absent. It is the best possible way of communicating mathematics to the non-mathematician and even the ones suffering from mathematical anxiety will enjoy reading the booklet. Of course this is only a relatively small selection but for the reader longing for more, Pitici gives in his introduction an even longer list of books, papers, websites and blogs that are equally worth reading. Pitici did once more an excellent job, and the result is highly recommended to all with a broad interest in science, history, art, education, philosophy,... which is almost anybody.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is the fourth collection of previously published papers that are brought together in one volume by M. Pitici. The idea is to provide generally accessible papers for the non-mathematician to give insight into the world of professional mathematicians by essays reflecting upon mathematics, its history, and the way it should be taught to future generations.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-069-1160-41-2 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£14.95</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">272</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10071.html" title="Link to web page">http://press.princeton.edu/titles/10071.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Tue, 04 Feb 2014 08:32:20 +0000Adhemar Bultheel45548 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2013#commentsThe best writing in Mathematics 2011
https://euro-math-soc.eu/review/best-writing-mathematics-2011
<div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">J.M. Gamboa</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Dept. Algebra, Faculty of Math. UCM, Madrid, Spain</div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/book-review/Review_0.pdf" type="application/pdf; length=47694">Review.pdf</a></span></div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is an anthology of very well selected articles about very different aspects of mathematics. Using the words of Barry Mazur about ''The Best Writing on Mathematics 2010'',A delight to read. This is a fine volume with lots of terrific articles that are as enticing as they are varied. The sum total is simply great''.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/mircea-pitici" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mircea Pitici</a></li><li class="vocabulary-links field-item odd"><a href="/author/editor" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">editor</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-691-15315-5</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00b15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00b15</a></li></ul></span>Mon, 16 Jan 2012 14:53:51 +0000Anonymous45435 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/best-writing-mathematics-2011#comments