[paint_your_wagon]

” I have a wonderful proof...the margin is too small to write it down”

from Goedel, Escher, Bach on Fermat’s last theorem.

[MUDDOG]

Fermat’s Last Theorem is the most famous modern (since 1600) long-unsolved problem. He actually did write that in the margin of a book.

It was finally solved a few years ago.

Another modern problem was to find the roots of the general fifth-degree or higher polynomial by basic algebraic operations and taking roots. It was shown impossible in the 19th century.

Famous ancient problems would be trisecting the angle and duplicating the cube by compass and straight-edge, which were proved to be impossible in the 19th century.

Another ancient problem was to construct the regular septagon with compass and straight-edge, which Gauss did.

[FredZarguna]

Completely misnamed. Fermat did not prove anything, and it is not his theorem. It was simply a conjecture; but Fermat made many conjectures, some of which were wildly wrong.

For example, Fermat conjectured that 2^2k+1 was prime for every positive integer k. The great Leonhard Euler blew up this conjecture in a few hours.

The correct name is Fermat's Last Conjecture, which has been Andrew Wiles Theorem since 1995.

[scrabblehack]

It was from Fermat himself (but in Latin).