The new Google Doodle is one of my favorites. It represents Fermat’s famous equation, his so-called Last Theorem. Pierre de Fermat was a 17th century French lawyer and an amateur mathematician (apparently math was hobby in those days), along with René Descartes (I think, Therefore I am) they formed two of the leading French mathematicians of the time. Fermat took up reading and proving many theories (and developing his own) from multiple sources, one of which was Diophantus’ Arithmetica; consider this to be one of the first textbooks in mathematics.
In this book was a chapter concerning Euclidean Geometry, specifically Pythagorus’ theorem (come on guys, remember triangles, x2 + y2 = z2), now this theorem had been proven many times, and studied by many civilizations including the babylonians. Fermat had solved and proven this equation easily, he then wrote in the margin of his copy:
“it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”
In other words he had proven that no 3 integers can satisfy xn + yn = zn unless n=2.
Fermat claimed he had proven this, but left us nothing. it took mathematicians 358 years to develop mathematics sufficiently (whole branches of pure mathematics were created to be used as tools for the solution) and finally prove it in 1995.
I recommend reading Simon Singh’s Fermat’s Last Theorem (Fermat’s Enigma in the States) an excellent pop science account of this theory’s story.
Remember kids, Let your Prometheus Unbound