Fermat's Last Theorem

Well, I didn't realise that he hadn't got the prize back then! Thanks for bringing this to everyone's attention, hitchglitch. You're right about Simon Singh's book; it was one I always recommended to students starting out on an A level course. Fascinating (particularly the bit where he was lecturing about his proof and that Japanese guy said "I think there's a flaw in your proof - back to the drawing board for a few more years then!) An inspiring read. 

I always use Fermat's last theorem when teaching Pythagras' theroem. The story behind it is so interesting (well to me anyway). For those that don't know read on, others stop here.

Fermat's major inspiration came from Diophantus' Arithmetica, a mathematical treatise handed down from the ancient Greeks. Through this constant companion, Fermat was offered one thousand years worth of mathematical understanding, and the entire knowledge of numbers as constructed by the likes of Pythagoras and Euclid. It was when studying the Arithmetica that Fermat formed the habit of scribbling down his own notes in the margin of the book. One one page that had (wriiten in simple form):

 you can find numbers a,b, and c so that a squared + b squared = c squared  for example 3 squared + 4 squared = 5 squared but you can't find three numbers where a cubed + b cubed = c cubed, or any higher power)

In the margin Fermat had written:

I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain

This was his last theorem, did he really have a proof or not? was he just boasting? He never wrote one down and it took 400 years for someone to find one 

For those that don't know read on, others stop here.

 

I wish I took heed to 'others stop here', I now have a headache

no, I read it twice ,and haven't got a clue what's it's about , have I missed something????

A fascinating book.  I was given a copy in a 'Secret Santa'  many years ago.  An excellent Christmas pressy.  It doesn't matter if you're not a maths expert - it's the story that counts.

no, I read it twice ,and haven't got a clue what's it's about , have I missed something????

ok pay attention

the square numbers are 1x1, 2x2, 3x3, 4x4, 5x5 ....

or  1  4  9   16   25   36   49   64 ...

there are some square numbers that if you take two of them add up to give another square number,  9 + 16 = 25  is one but there are more.

The cube numbers are  1x1x1,  2x2x2,  3x3x3,   4x4x4,...

or  1   8    27    64    125

No two cube numbers add up to another cube number. That in essence is Fermat's last theorem. The intriguing thing is that he claimed to have a proof but never wrote it down and no one else could prove it till Andrew Wiles.

Corners ,I've got it now , why didn't you explain it like that in the first place ??

P.S , is that you in the photo??

Corners ,I've got it now , why didn't you explain it like that in the first place ??

P.S , is that you in the photo??

I do have the same type of sweater and open toe sandals (with black socks of course) but alas no. That is Andrew

I forgot to mention that I solved  it when I was at school many years before Wiles. The proof went something like this ...."by inspection .."

Well, I was always told off for not showing the intermediate steps especially the bit about aligning modular forms with elliptical equations.

by the way not knowing the square numbers could cost you £10000 see link https://www.youtube.com/watch?v=BbX44YSsQ2I