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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.
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Examples of conjectures that were widely believed to be true but later proved false
The Markus-Yamabe Conjecture in differential equations was posed in 1960. It states that if $f:\mathbb{R}^n\rightarrow\mathbb{R}^n$ is a $C^1$ map such that $f(0)=0$ and the eigenvalues of the Jacobia …
14
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The work of mathematicians outside their professional environment
Steve Smale won a Fields medal in 1966, at least in part for proving the Poincaré Conjecture for dimensions five and higher. He induced some controversy when, as written on Wikipedia, he said that his …
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Examples of simultaneous independent breakthroughs
A completely new algorithm for calculating $\pi$ was independently discovered by Salamin and Brent in 1976. This iterative algorithm, which doubles the number of correct digits with each iteration, is …
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Examples of simultaneous independent breakthroughs
I'm looking for examples where, after a long time with little progress, a simultaneous mathematical discovery, solution, or breakthrough was made independently by at least two different people/groups. …