There are many open problems in maths, most of which have the decency to sound appropriately daunting. For example, is it the case that “every Hodge class on a projective complex manifold X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X”? I have no idea what most of those words mean, so I’m certainly willing to believe that this is a Very Hard Problem. However, many open problems sound like they really should have been solved by now. In this post I’ll discuss a few “embarrassing” open problems in maths that are far harder than they might appear.

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