... to do number theory as if it were physics, where one looks for conjectures by playing with prime numbers with a computer. For example, a physicist would say that the Riemann hypothesis is amply justified by experiment, because many calculations have been done, and none contradicts it ...G. J. Chaitin
Now in physics, to go from Newtonian physics to relativity theory, to go from relativity theory to quantum mechanics, one adds new axioms. One needs new axioms to understand new fields of human experience. In mathematics one doesn't normally think of doing this. But a physicist would say that the Riemann hypothesis should be taken as a new axiom, because it's so rich and fertile in consequences. Of course, a physicist has to be prepared to throw away a theory and say that even though it looked good, in fact it's contradicted by further experience. Mathematicians don't like to be put in that position.
6 years ago