# Pierre de Fermat’s Last Theorem Celebrated With A Google Doodle

Google’s gone geeky for today’s Doodle.

If you look closely at the Google Doodle for today, you can see the faint outline of the company’s name, appearing as recently erased markings on a chalkboard. What takes center stage is the mathematical equation x^{n} + y^{n} ≠ z^{n} (when n > 2)

If you mouse over the doodle, this message will pop up: “I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain.”

This equation is called Fermat’s Last Theorem and was first proposed in 1637 by Pierre de Fermat. Today is Fermat’s 410th birthday.

Fermat, a French lawyer and amateur mathematician, proposed the x^{n} + y^{n} ≠ z^{n} theory as an extension of the concept of Pythagorean triples.

We all learned in basic algebra about using the Pythagorean Theorem to find the side lengths in right triangles – a^{2} + b^{2} = c^{2}. where “c” is the hypotenuse.

Basically, the square of one shorter side plus the square of the other is equal to the square of the longest side.

Pythagorean triples are sets of positive integers a, b, and that fit the a^{2} + b^{2} = c^{2} equation. For instance – 3, 4, and 5 is a set:

3^{2} (9) + 4^{2} (16) = 5^{2} (25)

There are many other sets of Pythagorean triples, including (5,12,and 13) (11, 60, and 61) and (65, 72, and 97).

That’s where Fermat’s Last Theorem take off. His x^{n} + y^{n} ≠ z^{n} (when n > 2) states that there are no sets of integers for x, y, and z that satisfy the equation when n is greater than 2. Basically, the equation will never work for any set of integers when they are taken to any higher power than 2 (squared).

This theorem is said to be the basis of modern number theory.

Fermat simply stated this theorem and left it to other mathematicians to prove, and they tried – for 358 years. No mathematician could write a proof of Fermat’s equation until 1995 when British mathematician Andrew Wiles offered the first complete proof as part of the modularity theorem for semistable elliptic curves.

The proof was over 100 pages longs and took Wiles 7 years to complete. He was subsequently knighted for his accomplishment.

In other geeky Doodle news, Google recently honored the father of modern genetics Gregor Mendel with a Doodle referencing his famous pea experiments.

What do you think of today’s Google Doodle? Let us know in the comments.