Wednesday, April 10, 1996
Why I think Fermat never gave his simple proof.
Pierre Fermat was an amateur mathematician who made many assertions without bothering to prove them. All of them have now been proven or disproven although the statement about x^n + y^n = z^n was the last, which is why it's called Fermat's Last Theorem (although, it's really a conjecture).
I don't doubt that Fermat found the simple method that I've given quite rapidly and that's what he mentioned. If you notice, that method doesn't give a proof for n<5, so he went ahead and constructed the proofs for n=4 and attempted n=3 which Euler fixed later (or did I get it reversed?).
As he rarely gave proofs anyway, Fermat wouldn't have seen the necessity of giving the simple proof again after he had realized it was correct. Once he couldn't get it in the margins of his notebook that was it for the rest of us getting to see it from his hand. Possibly he continued to work on n's higher than four just to find another route, which it seems doesn't exist unless you use complex and very modern techniques.
I guess if someone could go back in a time machine and tell him how much time and effort was spent, possibly he might have given the simple method. But then again, maybe not, considering the progress in mathematics that has been generated because of the search.
In any event, Fermat alone is proof of the need for outsiders in any field (although he proved himself to be a mathematician of the first rank). One of the scary things about mathematics today is how it forces out dabblers. They are called cranks or characterized as schizophrenic. No one understand most of the math anyway except the specialists in that particular field.
Would Pierre Fermat be taken seriously today? Or would he be dismissed as just another schizophrenic with delusions? What great truths are hidden as potential in the mind of someone out there who would be dismissed as an "amateur".
Food for thought, eh?
I don't doubt that Fermat found the simple method that I've given quite rapidly and that's what he mentioned. If you notice, that method doesn't give a proof for n<5, so he went ahead and constructed the proofs for n=4 and attempted n=3 which Euler fixed later (or did I get it reversed?).
As he rarely gave proofs anyway, Fermat wouldn't have seen the necessity of giving the simple proof again after he had realized it was correct. Once he couldn't get it in the margins of his notebook that was it for the rest of us getting to see it from his hand. Possibly he continued to work on n's higher than four just to find another route, which it seems doesn't exist unless you use complex and very modern techniques.
I guess if someone could go back in a time machine and tell him how much time and effort was spent, possibly he might have given the simple method. But then again, maybe not, considering the progress in mathematics that has been generated because of the search.
In any event, Fermat alone is proof of the need for outsiders in any field (although he proved himself to be a mathematician of the first rank). One of the scary things about mathematics today is how it forces out dabblers. They are called cranks or characterized as schizophrenic. No one understand most of the math anyway except the specialists in that particular field.
Would Pierre Fermat be taken seriously today? Or would he be dismissed as just another schizophrenic with delusions? What great truths are hidden as potential in the mind of someone out there who would be dismissed as an "amateur".
Food for thought, eh?
# posted by James Harris @ 12:55 
