Fermat's Enigma by Simon Singh
In 1637, Pierre de Fermat, a renown amateur-but-genius mathematician, was reading Diophantus's Arithmetica and wrote the following margin note:
I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it.
In other words, although there are many three integer solutions to Pythagoras's Theorem,
X^2+Y^2=Z^2
There are no three integer solutions for higher powers,
X^3+Y^3=Z^3 X^4+Y^4=Z^4 ....
Unfortunately, no written record of Fermat's proof has ever been found. Worse, Fermat had a reputation for pranking his fellow mathematicians by claiming to have secretly solved impossible problems. For 350 years, it was uncertain if a proof ever existed. But that didn't stop a lot of people from trying, including some of the best mathematicians in history.
In this book, Simon Singh provides a thorough account of the many efforts to prove Fermat's Last Theorem. Particular attention is given to Andrew Wiles's successful solution in 1994, the result of a seven year solitary effort that shocked the mathematics world.
The book is structured very well. Singh expertly interweaves the history and mathematics behind Fermat's conjecture in an easy to understand and engaging manner. Singh describes the complicated mathematics involved just enough to appreciate Wiles's solution without going into too much detail. The narrative flows evenly and holds the reader's attention well.
Wiles's story is incredible. He was first fascinated by Fermat's Last Theorem as an adolescent. After earning a PhD in mathematics, Wiles found himself uniquely positioned to pursue a proof. He made the bold decision to both work in secret and devote all of his time to developing a proof. For seven years, Wiles worked night and day in isolation until he finally succeeded. After a fatal flaw was found during peer review, he spent an additional year fixing the proof. Wiles's focus, dedication, and determination are truly inspiring.
Fermat's Last Theorem is great book if your into math, history, and solitary geniuses overcoming the odds.
