I taught a Perceptron how to light fireworks once. Forgot to teach it that fireworks would blow you up if you didn't back away. Stupid Perceptron.

Continuing from old thread...

Ah yes the statement made in the margin, I was unsure if that was what you meant. But Andre Wiles in his book on the history of number theory states that "Fortunately, just for once he had found room for this mystery in the margin of the very last proposition of Diophantus; this is how it goes." He [Fermat] then goes on to use his proof by descent by working from a right triangle whose sides are "assured mutually prime", with certain restrictions being made on the number for the lengths. Factoring and working and using his three square methods he proves the case for n = 4.

Which makes me wonder: brilliant minds like Kronecker, Gauss, Krummer, Cauchy, Germain and Euler could not solve this problem after pitting their might on it, yet alone Fermat could? Perhaps Fermat only meant hat he has shown how for n = 4 the number is triangular? Maybe he assumed his method of proof by descent would work indefinately, perhaps he had too much confidence in it and did not forsee the complications and complexities ahead? Although I feel that he had something in mind I cannot help but also note that he was a lawyer...

Yeah, since so many great mathematicians were stumped on this problem for so long (Lindemann as well, who proved Pi was trancendental, offered many proofs that were wrong), it makes everyone believe that Fermat possibly was mistaken. But you and I know that sometimes it takes just a little luck to find the right thinking. I just happen to believe him that's all. LOL, about the lawyer, well you have to do something to eat I suppose.

Mushi, perceptrons are only as smart as their master hehehe...

aite, nothing but good can come from it anyway, at worst you'll just end up inventing some new mathematics [smile]