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:

1. The acceptability of the use of the axiom of choice
2. The acceptability of proofs that rely on assuming that a computer has performed a certain computation correctly
3. The debate over intuitionistic logic versus classical logic
4. Hilbert's re-examination of Euclid's axioms and his discovery of unstated assumptions therein
5. Debates over the use of infinitesimals in calculus, culminating in Weierstrass's epsilons and deltas. There are of course many others.

Edit:

The above re-formulation of the question was provided by Timothy Chow and copied directly from the meta.mathoverflow thread about this question.

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:

1. The acceptability of the use of the axiom of choice
2. The acceptability of proofs that rely on assuming that a computer has performed a certain computation correctly
3. The debate over intuitionistic logic versus classical logic
4. Hilbert's re-examination of Euclid's axioms and his discovery of unstated assumptions therein
5. Debates over the use of infinitesimals in calculus, culminating in Weierstrass's epsilons and deltas. There are of course many others.

Edit:

The above formulation of the question was provided by Timothy Chow and copied directly from the meta.mathoverflow threadas provided by Timothy Chow about this question.

Mathematics

It is often associated with verifiability and rigorous widely believed that mathematicians have a uniform standard of what constitutes a correct proof. However, I know 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:

1. The acceptability of the use of the axiom of choice
2. The acceptability of proofs that Cantor's theory rely on assuming that a computer has performed a certain computation correctly
3. The debate over intuitionistic logic versus classical logic
4. Hilbert's re-examination of infinite sets was controversial in its time Euclid's axioms and wasn't immediately accepted by his discovery of unstated assumptions therein
5. Debates over the mathematical communityuse of infinitesimals in calculus, culminating in Weierstrass's epsilons and deltas. Are there other examples There are of course many others.

Edit:

The above formulation of the question was copied directly from the history of mathematics or any particular theorems that were met with resistance before being accepted?meta.mathoverflow thread as provided by Timothy Chow.

Mathematics is always often associated with verifiability and rigorous proof. However, I know that Cantor's theory of the infinite sets was controversial in its time and wasn't immediately accepted by the mathematical community. Are there other examples from the history of mathematics or any particular theorems that were met with resistance before being accepted?

Mathematics is always associated with verifiability and rigorous proof. However, I know that Cantor's theory of the infinite sets was controversial in its time and wasn't immediately accepted by the mathematical community. Are there other examples from the history of mathematics or any particular theorems that were met with resistance before being accepted?