# What is the difference between mathematicians and physicists?

One of the main differences between mathematicians and physicists (in general) is that:

• For a mathematician evidence, no matter how much of it, is no proof.
• For a physicist evidence, especially if there's no counter-evidence, is proof enough.

One could think that, both being scientists and having a scientific mind, they would both think alike. This doesn't seem to be so, though. There exist countless jokes about the difference in thinking between mathematicians and physicists, and they aren't really all that far-fetched.

Concrete examples:

During 350 years enormous amounts of evidence in favor of the veracity of the famous Fermat's last theorem (ie. xn+yn=zn has no solutions for any integer values of n larger than 2 and values of x, y and z different from 0) was developed by hundreds of mathematicians. The amount of evidence in favor of the theorem was simply enormous: By 1995 it had been proven that the theory is true for all values of n up to 4 millions. Moreover, it was proven that even if solutions to the formula exist, they are less and less likely to be found as n grows larger.

Moreover, absolutely no evidence existed that suggested the contrary, ie that the theorem is false.

Surely all this evidence should be enough to say that Fermat's last theorem is true and fact? I mean, come on, for the first 4 millions of values of n it was proven, and it was also proven that as n grows larger it is less and less likely that any solution to the formula could exist.

No. In mathematics no amount of evidence is proof. It doesn't matter if it is proven for 4 millions, 4 trillions or 4*101000000 first values of n. No amount of evidence, regardless of how large, is proof. Mathematicians do not go around claiming that a theorem is true if they do not have a mathematical proof, based solely on evidence.

It wasn't until Andrew Wiles developed a definitive, mathematically completely consistent proof in 1995 that mathematicians started claiming that Fermat's theorem is true.

This is rather different from physics: In physics evidence is proof. If there's enough evidence in favor of a theory and enough lack of evidence of the contrary, that is proof enough for physicists to go around claiming that the theory is true, fact and proven. When asked for the proof, the evidence is given as proof. This would never work in mathematics. As an example, just think about the theory of evolution.

Somehow I like the mathematician way of thinking more.