![]() But no one could prove it.įermat's Last Theorem first intrigued Wiles as a teenager and inspired him to pursue a career in mathematics, but it wasn't until 1986 that a key piece to the puzzle fell into place. No one ever found three integers that worked with n greater than 2, and most mathematicians suspected there weren't any. There are many sets of three integers for which Pythagoras's equation holds true - for example, 3 2 + 4 2 = 5 2. Better known as the Pythagorean theorem, this equation immortalizes the ancient Greek mathematician Pythagoras, who proved that "the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse." (The case for n = 4 was actually proved by Fermat independently of his cryptic remark.) However, a proof of the more general case - that is, for all integer values of n greater than 2 - eluded professionals and amateurs alike until Princeton University's Andrew Wiles brought 300 years of mathematical advances to bear on the problem.Įveryone who's ever taken high school geometry has run into the case when n = 2 - in mathematical symbols, x 2 + y 2 = z 2. Over the years, mathematicians did prove that there were no positive integer solutions for x 3 + y 3 = z 3, x 4 + y 4 = z 4 and other special cases. ![]() Fermat never got around to writing down his "marvelous" proof, and the margin note wasn't discovered until after his death.įor 350 years, Fermat's statement was known in mathematical circles as Fermat's Last Theorem, despite remaining stubbornly unproved. He was referring to the claim that there are no positive integers for which x n + y n = z n when n is greater than 2. In the 1630s, French mathematician Pierre de Fermat jotted that unassuming statement and set a thorny challenge for three centuries' of mathematicians. The most famous note ever scribbled in a book may very well be, "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain."
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