the two kinds of unsolved math problem are "we think it might be infinite but we've solved it definitively up to 12,478,329,709,179,875,728,943,982,427,349,234,293,487" and "we've spent the past thirty years trying to find out if 2 is a valid answer"
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in reply to @hthrflwrs's post:
How many kinds of maths problems are there? We think it might be infinite but we're also trying to prove it's just 2.
a lot of problems in topology are only really hard in 3-5 dimensions; fewer makes it easy and more gives you more "structure"
See my favorite pop-math fact that there are infinite regular polygons (2d), five regular polyhedra (3d), three polytopes in 5d and higher, but 4d has, for some reason, six of them: 4d analogs of all the 3d ones, then a bonus one that doesn't exist in any other dimension (the 120-cell).
The 24-cell is the outlier actually, the 120-cell corresponds to the dodecahedron