Comment by blessedwhiskers

There's something quite interesting about the problems in number theory especially. The questions/relationships sometimes don't seem useful at all and are later proven to be incredibly useful. Number Theory is the prime example of this. I believe there's a G H Hardy quote somewhere, about Number Theory being obviously useless, but could only find it from one secondary source, although it does track with his views expressed in A Mathematician's Apology[1] - "The theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics."

You can find relationships between ideas or topics that are seemingly unrelated, for instance, even perfect numbers and Mersenne primes have a 1:1 mapping and therefore they're logically equivalent and a proof that either set is either infinite or finite is sufficient to prove the other's relationship with infinity. There's little to no intuitive relationship between these ideas, but the fact that they're linked is somewhat humbling - a fun quirk in the fabric of the universe, if you will.

[1] https://en.wikipedia.org/wiki/A_Mathematician's_Apology