It is widely believed that mathematicians have a uniform standard of what constitutes a correct proof. However, this standard has, at minimum, changed over time. What are some striking examples where controversies have arisen over what constitutes a correct proof?
Examples of this include:
- The acceptability of the use of the axiom of choice
- The acceptability of proofs that rely on assuming that a computer has performed a certain computation correctly
- The debate over intuitionistic logic versus classical logic
- Hilbert's re-examination of Euclid's axioms and his discovery of unstated assumptions therein
- Debates over the use of infinitesimals in calculus, culminating in Weierstrass's epsilons and deltas. There are of course many others.
The above re-formulation of the question was provided by Timothy Chow and copied directly from the meta.mathoverflow thread about this question.