4) The skill to produce great math and skill to produce great philosophy are secretly the same thing. Many people in either field do not have this skill and are not interested in the other field, but the people who shape the fields do.
FWIW I have reasonably strong but not-easily-transferable evidence for this, based on observation of how people manipulate abstract concepts in various disciplines. Using this lens, math, philosophy, theoretical computer science, theoretical physics, all meta disciplines, epistemic rationality, etc. form a cluster in which math is a central node, and philosophy is unusually close to math even considered in the context of the cluster.