In around 1637, Fermat hinted that he had “discovered a truly marvelous proof” that an + bn = cn cannot be true for n>2. Proving this deceptively simple theory required the contributions of dozens of mathematicians over a span of some 350 years. Unfortunately, while biographical aspects of the story are competently told, the author is unable or unwilling to explain important mathematical concepts in layman’s terms. If the following paragraph makes sense to you, then you probably fit the target audience of this little book:
Here, a periodic function could be conceived as having a periodicity both along the real axis and along the imaginary axis. Poincaré went even further and posited the existence of functions with a wider array of symmetries. These were functions that remained unchanged when the complex variable z was changed according to f(z)——>f(az+b/cz+d). Here the elements a, b, c, d, arranged as a matrix, formed an algebraic group. This means that there are infinitely many possible variations. They all commute with each other and the function f is invariant under this group of transformations. Poincaré called such weird functions automorphic forms (82).
If, like me, you were completely nonplussed by that description, then the only thing of value you will likely get from this book is a deeper understanding of the fact that concise ≠ comprehensible.
[Why I read it: I came across it while sorting through some of my Dad’s books.]