I have discovered a truly remarkable proof but this margin is too small to contain it,"
Pierre de Fermat
Google doogles Fermat's Conjecture on the 410th Anniversary of his birth.
I'm sure you've heard that Fermat's Last Theorem was proven in 1995. Fermat's conjecture stood for 358 years until a young fella from Britain came along and pulled all the threads together.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two, as long as a, b, and c are not equal. This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult math problem".
Andrew Wiles first became aware of Fermat's Theorem at the age of 10. He was fascinated by the simple equation that even a 10 year old could understand and had remained unproven for so many years. He resolved to be the first to solve the seemingly intractable problem.
If you have the time the BBC video series Horizion presented "Fermat's Last Theorem" (about 50 minutes). The very interesting story of how Andrew Wiles proved the famous theorem. Even if you can only add and subtract I believe you will find this video informative and entertaining.