Springer published the 6 volumes of the preceding series Mathematics and Culture and volumes 1-3 of the current Imagine Math series. After an interrupt for the two volumes Imagine Math 4 and 5, the current book is again a Springer publication. Several of these volumes were reviewed here (just search for Emmer). The books contain diverse contributions that reflect the presentations at a recurrent conference that wants to bring together scientists, mathematicians, and artists from different disciplines to discuss the influence of mathematics in our culture in the broadest possible sense. That means that the selection of contributions for this book is again showing a very broad plethora of papers ranging in style from proper mathematical to philosophical and from historical to a collection of pictures or everything else that is considered appropriate. Imagine Math 6 records the proceedings of the conference organized in Venice, Italy, in 2017. It has 24 papers grouped into 8 parts, although the boundaries between the parts are not very strict. What follows is a brief glossary illustrating the diversity of topics.
The first part is about the Iraqi architect Zaha Hadid (1950-2016) who created many remarkably fluid and jaunty buildings and constructions. Her ideas are continued by the company that still bears her name. The book contains many pictures illustrating her designs. Some topological and fluid dynamical aspects of these shapes are discussed by M. Emmer.
The second part is about Mathematics and the Media. Mathematical awareness is raised by expositions in the MUSE, the science museum in Trento, and the efforts of Frank Morgan, editor of the Notices of the AMS convincing the authors-mathematicians of the Notices to bring mathematics at a level acceptable for readers that are not mathematicians.
Osmo Pekonen is a Finish mathematician, who is also historian of science. He studied the life of Maupertuis, an 18th century French mathematician who was involved in an expedition measuring by triangulation part of an Earth's meridian in Lapland. The goal was to decide on the shape of the Earth (flattened at the poles or at the equator). Pekonen became so involved that he himself impersonated, on stage and in a film, the character of Maupertuis.
Music and mathematics have been connected since antiquity. So no wonder there is a part about this involvement. It is illustrated how algebra, topology, category theory, chaos theory, prime numbers, palindromes, etc. can be detected in music styles and scores.
In the part about applications, we learn that analysis of big data can lead to prediction of earthquakes or crimes.
The proof that by summing the divergent series of all the positive integers can lead to the surprising Ramanujan result -1/12 has been an internet hype for a while. It is used as a pretext to mention similar such cases of paradoxical results.
There is a paper that shows how computer analysis helped to reconstruct a parametrized virtual version of the Arch of Titus (1st-century CE) using some stones found at the archaeological site of the Circus Maximus in Rome.
The mathematical analysis of soap bubbles clusters is another example of semi-applied mathematics.
On a more linguistic level we find an interesting contribution discussing the fact that the formal language of mathematics is only used among mathematicians, and hence is not used by the common people. Even the relatively elementary mathematics of antiquity was essentially for an elite. Common people did not have or were not able to read books. And yet, occasionally, some of the mathematics or mathematical terminology has entered common social language not only today but also in previous centuries.
Part 5 about visual mathematics, could also be part of the set of applied mathematics papers. The three contributions here deal with design problems: how design students express the concept of "balance" in their projects, how a numerical model is derived from visual information that can be used to simulate the heart function, and a third paper is on the design of gears, with not only the traditional circular ones but also the elliptic and polygonal ones, some nautilus shapes, and even amusingly weird ones.
Mathematics and art is of course an obligatory part in this kind of books.
One paper is about non-convex star-like (2D and 3D) mathematical objects throughout history.
Another describes the role of the pentagram in the art of the Dutch sculptor Gerard Caris.
And a last one is from the photographer Vincent Moncorgé presenting his project in which he wants to capture with his photos some real-life mathematicians at work in their natural habitat, avoiding the characteristic formulas. This is quite interesting since it may remove the biased public opinion about a mathematician as a weird and unworldly individual.
Mathematics and physics is the title of the penultimate part. Topology and physics in fluid dynamics has some historical roots (the dichotomy between continuous and discrete), but that is of course also of major importance for quantum mechanics. So these two (fluid dynamics and quantum theory) are the two somewhat related topics of this part.
The last part is about mathematics and physics. Emmer discusses the book from 2015 Éloge des mathématiques reflecting a dialogue between the French philosopher Alain Badiou, and a journalist Gilles Haéri (also available in English In Praise of Mathematics 2016).
There is a paper showing how Luca Pacioli (447–1517) was influenced by the work of Euclid and another one is computing the dimensions of the heaven, the hell and the purgatory as described in the Divina Comedia of Dante.
The first chapter of Simon Singh's book The Simpsons and their Mathematical Secrets is reprinted.
And finally the work of the Scottish science writer Mary Sommerville (1789-1872) is discussed.
This brief survey should convincingly illustrate that mathematics has deep roots into our culture. Some more technical contributions may be hard to follow for some readers if not trained well in mathematics, and other readers may be a bit intimidated by the philosophical jargon used in the more contemplating contributions, but the book is broadly readable in general. There are in this volume remarkably many colour pictures included. If you liked the previous books in the series, you will love this too. If you don't know any of the previous books, this volume might be a fine occasion for jacking up your cultural backpack.