Lesser known unsolved mathematical problems I find unreasonably fascinating:
* Is the Leyland-mapping injective?
* We have Kadane's algorithm for the maximum subarray problem, which runs in O(n), is there an algorithm for the maximum submatrix problem which runs in O(n²)? What about higher-dimensional tenors?
* The polyhedral numbers conjecture: is every number the sum of m+1 n-hedral numbers, where m is the number of vertices of the polyhedron. Does it hold for any n-dimensional polytope?