"Beauty is in the eye of the beholder" is a well-known cliche'. And it can be very difficult, if not impossible, to explain to someone who has no knowledge or experience to fall back on why something as abstract and abstruse as mathematics can be said to be beautiful. It would be interesting to conduct an informal survey to test the hypothesis that those who succeed in mathematical studies are those most likely to recognize the beauty of mathematics.
Frenchman Cedric Villani won the Fields Medal (the mathematics equivalent of the Nobel Prize) in 2010 for his work, with former student and colleague Clement Mouhot, on "nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation."
But I didn't need to understand what this was about in order to follow Birth of a Theorem: A Mathematical Adventure, Villani's story of his work in this area. Yes, there are plenty of equations about as comprehensible as hieroglyphics. But the reader does not need to comprehend the math in order to grasp what life as a mathematician is like, as Villani describes it. Villani describes the joy of discovery, the fear of making a mistake that could negate all his work, the struggle in wrestling a problem to the ground. As many wunderkinds do, he spends long hours absorbed in his work, trying to make sense of a small part of the universe. When he succeeds, the reader breathes a huge sigh of relief with him.
I grasped just the tiniest bit of the mathematics he describes, but it reminded me of the pleasure of seeing something unfold in mathematics. I only understood part of the esoterica presented on these pages, but it left me wanting to dig into old math books to decode and more deeply appreciate the mathematics. As a graduate student taking courses in theoretical statistics. I had glimpsed one example of mathematical beauty when I learned about the close relationship between the concept of moment in mathematics and the concept of moment in physics.
You don't have to be a mathematician to appreciate this book, but I must concede the obvious: only someone with an interest in mathematics may appreciate it.