Most mathematical results would be unreachable by amateurs due to the sheer amount of background knowledge, especially of existing literature, required to make

Most mathematical results would be unreachable by amateurs due to the sheer amount of background knowledge, especially of existing literature, required to make progress on a problem (and in some cases to even understand the statement of the problem, e.g. https://en.m.wikipedia.org/wiki/Hodge_conjecture https://en.m.wikipedia.org/wiki/Hodge_conjecture). Elementary graph theory and combinatorics are somewhat outliers in this regard, as there is not so much "theory" per se that one has to build on or work with. Tim Gowers's "Two Cultures" essay is an interesting read on this topic: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf