For the DU Mathematicians - Elegant New Approach To 350-Year-Old Math Riddle [View all]

[malaise]

http://www.redorbit.com/news/science/1112796238/fermats-last-theorem-gets-simplified-030413/
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In 1637, the French lawyer and part-time mathematician Pierre de Fermat put forward a simple and elegant numerical riddle that would puzzle and confound math geeks for 358 years. Known as Fermat’s Last Theorem, or simply Fermat’s conjecture, the theorem states no whole, positive numbers can make the equation xn + yn = zn true when ‘n’ is greater than 2.

Using a roundabout, backdoor approach that involved dizzyingly complex number theory, the Oxford mathematician Andrew Wiles demonstrated conclusively in 1995 that Monsieur de Fermat was, in fact, correct: The equation is unsolvable.

Now, however, Colin McLarty, a professor of philosophy and mathematics at Case Western Reserve University claims there’s a far simpler way to prove Fermat’s theorem – one that doesn’t involve complex mathematical wizardry with names like “modularity theory” and “epsilon conjectures.”

McLarty demonstrated even the most complex and abstract of Grothendieck’s ideas can be justified using very little set theory. What is known as ‘standard set theory’ is simply the collection of the most commonly used principals, or axioms, used by practicing mathematicians. Grothendieck’s work included the notion of the existence of a universe of number sets so large standard set theory could not even prove they exist.

In McLarty’s vastly simplified approach to Fermat’s problem, he says all mathematicians need is basic ‘finite order arithmetic,’ which uses even fewer sets of numbers than standard set theory.