In ‘philomath’ the prefix ‘phil-’ plays the same role as in ‘philosopher’, a person who loves wisdom, and the suffix ‘-math’ plays the same role as in ‘polymath’, a person with a lot of learning. A philomath is a lover of learning.
I am a philomath in that I love being involved in the process of learning—not just the fascinating challenge of understanding new information, but also helping others who are doing so:
It does not suffice to hone your own intellect (that will join you in your grave), you must teach others how to hone theirs. The more you concentrate on these two challenges, the clearer you will see that they are only two sides of the same coin: teaching yourself is discovering what is teachable.
Edsger Dijkstra, My hopes of computing science
Another interesting etymological game can be played with ‘doctor of philosophy’. The word ‘doctor’ is derived from the causative of Latin ‘decere’, which means to be seemly or fitting: A doctor is a person who makes things seem right. A doctor of philosophy is a person who makes it seem right to love wisdom.
That seems like a good role for a philomath.