How maths is different from science

“It doesn’t matter how beau­tiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with exper­i­ment, it’s wrong.”

— Richard Feynman

In science we first observe a phe­nomena (e.g. the Moon orbiting Earth) — and then come up with a hypo­thesis (e.g. objects with mass attract each other) to explain it. That hypo­thesis is then tested by exper­i­ment; if the evidence from the exper­i­ment con­tra­dicts the hypo­thesis then it is dis­proved and must be rewritten. If the evidence does not con­tra­dict the hypo­thesis then it is sup­ported, not proved.

All the evidence in the world cannot prove a hypo­thesis, whereas only one piece of evidence is needed to disprove it. It would only take one instance of some­thing “falling” upwards to disprove the theory of gravity.

In maths the situ­ation is very dif­ferent: once some­thing has been proved, it is proved forever. No further research is neces­sary, no tests need to be per­formed. Pythagorus’s theorum about the lengths of the sides of right-angled tri­angles has been proved in many dif­ferent ways (Cut the Knot has 84 dif­ferent proofs), but will never be disproved.