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Review: Fermat's Enigma (4/5)

What an epic story. Andrew Wiles spent seven years creating a 200-page proof of Fermat's last theorem--plus an eighth, tense year fixing a hole in the proof--and within it all redefined math and number theory with several discoveries that would have been Earth-shattering if they were given just on their own. The math is beyond us all (trust me), yet author Simon Singh provides enough for our understanding, and enough drama to make modular forms and elliptic equations seem sexy.

Pierre de Fermat [Wikipedia] was a French lawyer in the 1600s who was also an amateur--albeit virtuoso amateur--mathematician. He would taunt others with theorems and withhold the proof as a challenge. Quite the bastard. One proof which was never revealed was for what is labeled his last theorem. "Last" because it was the last to be proven (proof changing a "conjecture" to a "theorem"). The theorem states:

The proof is considerably more complex. It took 350 years to prove, and in 1993 Andrew Wiles did it (I don't think I'm giving anything away, so no spoiler alert). Here's the paragraph from the book describing when he resolves the error of the initial proof:

Iwasawa theory [Wikipedia] on its own had been inadequate. The Kolyvagin-Flach method on its own was also inadequate. Together they complemented each other perfectly. It was a moment of inspiration that Wiles will never forget. As he recounted these moments, the memory was so powerful that he was moved to tears: It was so indescribably beautiful; it was so simple and so elegant. I couldn't understand how I'd missed it and I just stared at it in disbelief for twenty minutes. Then during the day I walked around the department, and I'd keep coming back to my desk looking to see if it was still there. It was still there. I couldn't contain myself, I was so excited. It was the most important moment of my working life. Nothing I ever do again will mean as much.

The book is filled with that sort of passion. And it's cool to actually find newsgroup notices as quoted in the book from when after the proof was announced:

• 1993-11-18 14:20:39 PST, Leonard Evens calls for calm
• 1993-11-26 08:38:52 PST, gossip continues
• 1993-12-04 09:32:24 PST, Andrew Wiles on sci.math admitting to a problem with his proof
• Wed, 26 Oct 1994 08:45:58 EDT, Karl Rubin announces the final fix

Last week, I had fortuitously TiVoed and watched the Nova special about Archimedes [Wikipedia] titled Infinite Secrets. Fermat's Enigma begins with a history of math dating back to Pythagoras [Wikipedia] (an engrossing story) and continues up to Wiles. I'm continually amazed at how little math I really understand. Programming is logic with some math--the reverse only occurs for specific problems. What Andrew Wiles and those who came before him do with math is astounding--sublime--yet I'm happy to just appreciate it from a distance.