1637 – France; 1993 – USA

Fermat’s theorem proves that there are no whole-number solutions of the equation ** x ^{n} + y ^{n} = z ^{n}** for

**n**greater than

**2**

The problem is based on Pythagoras’ Theorem; in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides; that is *x* ^{2} + *y* ^{2} = *z* ^{2}

If ** x** and

**are whole numbers then**

*y***can also be a whole number: for example**

*z***5**

^{2}+ 12^{2}= 13^{2}If the same equation is taken to a higher power than

**2**, such as

**then**

*x*^{3}+*y*^{3}=*z*^{3}**cannot ever be a whole number.**

*z*In about 1637, Fermat wrote an equation in the margin of a book and added ‘I have discovered a truly marvelous proof, which this margin is too small to contain’. The problem now called Fermat’s Last Theorem baffled mathematicians for 356 years.

In 1993, Wiles, a professor of mathematics at Princeton University, finally proved the theorem.

Wiles, born in England, dreamed of proving the theorem ever since he read it at the age of ten in his local library. It took him years of dedicated work to prove it and the 130-page proof was published in the journal ‘Annals of Mathematics‘ in May 1995.

###### Related sites

- Another proof of Fermat’s Last Theorem (plus.maths.org)