Love Fantasia Mathematica? Readers share 100 books like Fantasia Mathematica...

Frenkel came from the Soviet Union, where discrimination against Jews made it impossible for him to get into Moscow State University. During the oral exam they sent two graduate students to question him, pick holes in his responses, and ensure he failed. He turned to an informal network of Soviet mathematicians for help.

Like him, they were denied serious employment in the field, but after the 'cold war' against the Soviet Union, Harvard invited him to take a fellowship that later turned into a permanent job. Years later, when his old tormentor from Moscow State arrives to give a talk, he confronts the man in a lecture room with first-hand evidence of allegations against the system. Faced with a victim, the Russian mathematician's denials rang hollow. 

This book reaches beyond mathematics to anyone of independent thought in an environment where it is not permitted to step out of line or,… show more.

It provides an engaging description of the work that went into proving a famous result, first mentioned by the French mathematician Pierre de Fermat in the margin of a book.

The question was whether a sum of two nth powers of whole numbers could be the nth power of a whole number. It is certainly true for n = 2 but was not known for any n greater than 2. Fermat thought he had a proof that this was the case but later wrote proofs when n was 3 or 4, so his earlier claim was not taken seriously.

The general result turned out to be much harder than anyone imagined, and 350 years later, its truth was implied by another conjecture that was finally proved by Andrew Wiles, as this book explains. I admire the fact that the author distills some essential points from what turned out to be… show more.

This book presents excerpts from original contributions to mathematics by scholars of the past. It includes principal developments from Neolithic times, from Mesopotamia, and from the ancient Greeks, right up to the modern world.

The extensive and well-chosen quotations make this a unique book. I found the excerpts from original sources rendered it a mine of valuable information for me or anyone else interested in the long history of mathematics.

Hermann Weyl was one of the most influential mathematicians in the twentieth century. Born in North Germany, he worked for many years in Zürich and later moved to the Institute of Advanced Study in Princeton.

He was a colleague of Einstein in both places, and his book on Symmetry is a classic. This slim volume was a stimulus to me when I wrote my book.

What if children are not little adults but a different species? Perhaps children are butterflies who develop into caterpillars? Child psychologist Allision Gopnik asks wonderful questions about human development. She notes that most of us produce our best art and ask our deepest questions (“Why is the sky blue?”) as small children.

Childhood, she says, is our time of basic research; adulthood is the time for practical applications. Like Jean-Jacques Rousseau, she celebrates the unique gifts of childhood, but she does not offer suggestions about how we might recapture those gifts. 

The Univalent Foundations program in foundations of mathematics launched by Voevodsky and others in the past decade and a half has contributed to a promising new paradigm unifying computation, mathematics, logic, and proof theory.

Understanding the core elements of this research program, Homotopy Type Theory, is essential for contemporary philosophers who want to engage directly with current developments in mathematics and computer science.

Corfield is a well-established name in philosophy of mathematics, and this book is the best introduction to Homotopy Type Theory for philosophers.

Working within themes and problematics that will be familiar to philosophers with a basic background in logic, Corfield covers the elementary constructions of homotopy types from a logical point of view and provides plenty of provocative suggestions for how these formal tools might reinvigorate philosophical research today.

For decades, the most famous opening chord in rock and roll was an unsolved problem, since no one could reproduce it. But in 2004, Jason Brown, a professor at Dalhousie University, used mathematics to recreate the opening chord of the Beatles hit song, “A Hard Day’s Night”. I remember when newspapers around the world reported on Jason’s findings, as I was at Dalhousie at the time, as one of Jason’s Ph.D. students.

Jason’s Beatles story serves as the final chapter in this wonderful book, a collection of short vignettes about how mathematics relates to every aspect of our lives, including garbage pickup routes, grocery shopping, political polling, and social networks. The book’s thesis is that as we understand mathematics better, our lives become more meaningful. I couldn’t agree more.    

This remarkable book is authored by Francis Su, the past president of the Mathematical Association of America. The author describes human flourishing as follows: “a wholeness of being and doing, of realizing one’s potential and helping others do the same, of acting with honour and treating others with dignity.” He explains how human beings, of all ages and ability levels, can experience flourishing through the doing of mathematics.

In each of the final twelve chapters, the author explores a trait of mathematics, how it relates to our journey as humans, and how the development of each trait enables us to flourish: Exploration, Meaning, Play, Beauty, Permanence, Truth, Struggle, Power, Justice, Freedom, Community, Love. As a mathematical researcher and educator, I have experienced these traits first-hand, and recommend this book to anyone and everyone.

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.

This is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.