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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.

21 votes

Most striking applications of category theory?

The recent developments in homotopical algebra (after 1990) would not be possible without the use of category theory, and more precisely the theory of locally presentable and accessible categories. I …
9 votes
1 answer
746 views

Algebraic structure on homotopy groups of spheres

It is about a "conjecture" I heard (when I was student). There would exist an algebraic structure on the homotopy groups of spheres such that this algebraic structure would be the free algebraic struc …
Philippe Gaucher's user avatar
28 votes

Small ideas that became big

I don't know if this post will answer your question but it's about the higher homotopy groups of topological spaces. The story is told here: https://ncatlab.org/nlab/show/homotopy+group. In 1932, E. …