Preparing for the GMAT
Part IV: The Lesson from Fermat's Last Theorem
For over 400 years, Fermat's Last Theorem was merely a conjecture. Formulated in the year +/- 1650 by a French mathematician, the "theorem" stood out for it's simplicity. It was a simple extension of the famous Theorem of Pythagoras, which we have all heard about. Fermat's Last Theroem was a statement, that you could never find a Theorem of Pythagoras for integer exponents greater than 2. In other words, though there were many triples of numbers that "solved" the famous equation (x)^2 + (y)^2 = (z)^2, there would be no such integer triples to solve the similar equation (x)^3 +(y)^3 = (z)^3, nor indeed ever for any exponent other than 2.
Simple-sounding though it may be, that "reversal" of the Theorem of Pythagoras was not actually proved for about 400 years. Imagine that: four hundred years, during which no one found any example of three numbers that fit that equation, for any exponent other than 2. Fermat is a famous mathematician even today - the inventor of differential calculus, the finest number theorist between Archimedes and Gauss, and, in addition, a full-time lawyer.
I never forget the time spent by those tireless and for the most part nameless mathematicians who spent untold and undocumented hours, trying to solve Fermat's Last Theorem - and failing. Eventually, after 400 years, their cumulative efforts were rewarded, when one of their number offered what is generally regarded as proof - 89 pages' worth.
Even now, Fermat's story is still shrouded in mystery. Students of the topic know, that Fermat famously suggested that an elegant proof of the theorem did exist, but was too long to fit in the margin of the book in which the theorem was stated.