Fermat proved 350 years ago that no three integers exist that satisfy the equation X^4 + Y^4 =Z^4 and since that time few have bothered to look for such numbers because they knew it was a fool's errand; but suppose Professor Bozo, a eccentric computer scientist, decided to look anyway and suppose he used his physical computer and found 3 large integers that actually worked. What then? Obviously people (including me) would say Bozo was lying, but then suppose thousands of reports came in from all around the world of people trying Professor Bozo's integers on their own physical computers and finding it's true, the 3 Bozo integers really do solve the equation. What then? Would mathematicians say that all that shows is that the laws of physics can cause a physical system (like a computer) to be in a logically inconsistent state and Fermat was right and physics was wrong? No, they would say that either there was some subtle error in Fermat's proof that nobody in the last 350 years has been smart enough to catch or that Fermat had started his proof with some "self evidently true" axiom that he shouldn't have because it wasn't true regardless of how self evident it seemed to be.
In this case even mathematicians, even mathematicians who specialize in number theory, would give physics the last word in determining what is true and what is not, and if a system made of matter that obeys the laws of physics says that there are three integers that satisfy the equation X^4 + Y^4 =Z^4 then that's just the way things are and mathematicians are just going to have to learn to live with it. Maybe you think this is all a little far fetched, but compared with some other thought experiments I've seen on this list the idea of a mathematician being wrong really isn't all that far out into the stratosphere. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
