[DroneBetter]

counterpoint to > easily four or five years of study just to play around a bit it depends significantly on the branch of maths you choose! I've been told by a professor of fluid mechanics that he has difficulty posing and approving subjects of undergrad dissertations because the knowledge threshold for contributing meaningful ideas reliably is so high, but in my primary interest (combinatorics) this is very much not the case.

the OEIS is replete with old sequences that no-one has considered in much detail in a decade or two, and have a lot of 'low-hanging fruit' for one willing to toy with them.

https://oeis.org/A185105 is a good example of such a sequence; "sample the elements of a random permutation of [n] in a random order and record each one's cycle (under repeated iteration), then T(n,k)/n! is the expected of the kth distinct cycle recorded," which seems like it would have been of some interest to someone in the last ≈13 years (since ie. it's well-known that the first cycle's length is uniform in [1..n]), but didn't receive any formulas until I happened upon it recently with my own toolbelt (which is quite modest and certainly could be learned in less than 4 years).

the OEIS is an excellent resource for both readinh and sharpening one's amateur teeth on novel (ie. unexplored, or at least undocumented) problems and very rewarding, if that's your goal with learninh maths