# Day #5: From Pythagoras to the Mathematics of the 3rd Millennium

Q: Could you give at least 10 more proofs of the Pythagorean Theorem, and state how it is related to todays most actual mathematics and the most famous mathematical problem of all times??…

A:

### Pythagorean Theorem

Quite possible the most famous theorem in mathematics, Pythagoras’ Theorem states that square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.  Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can’t be claimed with any degree of credibility. Euclid’s (c 300 B.C.) Elements is considered the first proof of the theorem, but far from being the only one. There are at least 114 approaches to proving the theorem. Mathematician Bhaskara (about 1114-1185) proved the Pythagorean Theorem simply by drawing this picture and saying “Behold!”(Bhaskara’s (1114 – ca. 1185) Dissection Proof of the Pythagorean TheoremProof GIF).

Source: Pythagorean Theorem

The Pythagorean Theorem opened the most simply question: If squares of integer numbers may be the sum of two other squares of integers, is it possible that a cube may be the sum of two cubes, or more generally, with higher power than 2??… This became the most famous single problem in the history of mathematics. That one, that any one could understand, but no one could solve, until…

Source:

The Whole Story

Diophantus of Alexandria

Fermat´s Last Theorem

Sophie Germain = Monsieur Le Blanc and Fermat´s Last Theorem

Andrew Wiles and Fermat´s Last Theorem

https://arxiv.org/pdf/math/9503219.pdf

Documentary Film

“Certainly one thing that I’ve learned is that it is important to pick a problem based on how much you care about it. However impenetrable it seems, if you don’t try it, then you can never do it. Always try the problem that matters most to you. I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream. I know it’s a rare privilege, but if one can really tackle something in adult life that means that much to you, then it’s more rewarding than anything I can imagine” Andrew Wiles