Fermat's Last Theorem

Fermat's Last Theorem states that no three positive whole numbers a, b and c can satisfy the equation a to the power of n plus b to the power of n equals c to the power of n for any whole number value of n greater than two, even though the equivalent equation has infinitely many whole-number solutions when n equals two, the case corresponding to the Pythagorean theorem. French mathematician Pierre de Fermat wrote the statement in the margin of a book around 1637, famously claiming to have found a proof too large to fit in the margin, but he never published or otherwise recorded that proof, and no such proof by Fermat has ever been found among his surviving papers. The theorem resisted every attempt at proof for more than 350 years, becoming one of the most famous unsolved problems in the history of mathematics, until British mathematician Andrew Wiles, working largely in secret over roughly seven years, published a complete and accepted proof in 1995, correcting a significant gap discovered in his first announced 1993 proof with help from mathematician Richard Taylor. Wiles's proof did not use methods available in Fermat's own time, instead drawing on deep twentieth-century developments connecting elliptic curves and modular forms, which is why most mathematicians today believe Fermat could not actually have possessed a valid proof of his own claim.