This is the third in a sequence of the yearly collected anthologies of insightful papers on mathematics. The idea is to bridge the gap between professional mathematicians and a broader public. Papers give an accessible account of major mathematical achievements, discuss philosophy and history of mathematics as well as teaching aspects.
After the editions of 2010 and 2011, Pitici succeeds again in bringing together a wonderful collection of papers on mathematics. The foreword is delivered by the Fields Medal winner David Mumford.
The papers are not mathematical in the the technical sense of theorems, proofs and formulas. They are on mathematics and are accessible to a broad public. Like in the previous collections, the major themes are philosophy, teaching, history and the dichotomy and mutual influences of pure and applied mathematics. The papers were carefully selected from the existing literature. They were not written especially for this collection but only typeset in a uniform way. Except for the introduction in which Pitici surveys the contents and the foreword in which Mumford ponders on the synergy of pure and applied, of abstract and concrete mathematics, which is a recurrent theme in other contributions of this volume.
The 24 papers are relatively short (an average of 12 pages) but nevertheless succeed in addressing an intriguing idea, or an insightful mathematical topic and are just long enough to keep the attention of even a slightly interested reader from the beginning to the end. But who shouldn't be highly interested in questions such as Is mathematic discovered or invented? or Why is there a philosophy of mathematics at all? or Why Math works. The reader can also enjoy an exposition about more advanced mathematical topics such as string theory, the zeta function, the volume of a ball in higher dimensions or the mathematics of music and the music of mathematics. Or he might be interested in more playful applications like the mathematics of dancing, origami weaving, of transformations in photography, or the application of game theory applied to mating and dating. History is represented by contributions on Augustus De Morgan, Jean Bernoulli and Georg Cantor, the history of infinity from Hilbert to Woodin and of the history of the routing problem (see also the review of In pursuit of the travelling salesman in this database) and the concurrence of the history of mathematics and science. As important as the history is for the mathematics of today, for the mathematics of the future it is equally importandt how we teach mathematics to our students now. Hence the importance of the papers on math teaching. For example how do we transfer the different meaning that a variable may have in different environments and how the education of the teacher will be passed on unwittingly to the students, sometimes in a very subtle way. This applies to the teacher's background on applications but also, more generally, on his own philosophical opinion. Anyway, the ultimate guidelines on how to be an optimal teacher of mathematics are yet to be defined.
This is indeed a collection of the most wonderful writings on mathematics that have appeared recently. Not elementary at all and yet accessible to a general audience. Of course this is just the top a a gigantic iceberg, a top that has been selected on the basis of space and copyright limitations. This allows to make a selection of the best among the best that have already been selected as the best by demanding journals such as Science, The mathematical Monthly, and Scientific American. However, these are picked out of a longer short-list of possible candidates. Pitici gives a list of 43 papers that have been considered at some point but didn't make it to this volume. The titles in this list sound as appealing as the ones that were included in this volume, which makes you regret that the book is not thicker than it is.
Similar selections are published on a regular basis. For example the Mathematics and Culture series (edited by Michele Emmer, and published by Springer, reviews in this database Vol.I, Vol.III) which concentrates more on the connection between mathematics and all forms of art. The series What's happening in the mathematical Sciences (edited by Barry Cipra and now by Dana MacKenzie, and published by the AMS) which collects papers that explain important mathematical evolutions or breakthroughs for a broader public. By their focus, these series do not overlap with but are complementing the Best writing on mathematics. It is no waste of time to read all three.