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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

12 votes

Examples of conjectures that were widely believed to be true but later proved false

In introductory functional analysis one learns that every normed linear space with a Schauder basis is separable. The converse of this was a famous question raised by Banach- does every separable Bana …
7 votes

Examples of conjectures that were widely believed to be true but later proved false

Polya conjecture was proved to be false in 1958.