Sunday, July 19, 2015
"[Andrew] Wiles's landmark proof of Fermat's last theorem amounted to about one hundred pages of highly technical mathematics, prompting the science journalist John Horgan to write a provocative article titled "The Death of Proof." Horgan assembled a variety of reasons why proofs were becoming obsolete, including the rise of the computer, the disappearance of proofs from school math, and the existence of blockbusters like Wiles's. It was an interesting attempt to wrench defeat from the jaws of victory, to treat a historic achievement as bad news. Yes, we put a man on the moon, but look at all the valuable rocket fuel we had to use up.
"Wiles's proof may be a blockbuster, but it tells a ripping yarn. He had to use massive mathematical machinery for so simple a question, much as a physicist needs a particle accelerator many miles in circumference to study a quark. But far from being sloppy and unwieldy, his proof is rich and beautiful. Those hundred pages have a plot, a story line. An expert can skim through the details and follow the narrative, with its twists and turns of logic, and its strong element of suspense: will the hero overcome the last theorem in the final pages, or will the ghost of Fermat continue to taunt the mathematical profession? No one declared literature dead because War and Peace was rather long or because Finnegans Wake was not being read in schools. Professional mathematicians can handle a hundred pages of proof. Even ten thousand pages -- the total length of the classification theorem for finite simple groups, combining the work of dozens of people over a decade or more -- does not daunt them."
-- Ian Stewart, from "Letters to a Young Mathematician"
(p.s... sometime tomorrow I'll likely have a review of the new John Conway biography posted at MathTango) ...Now HERE.