Currently enjoying exploring Turing's Zeta function machine
https://history-of-mathematics.org/artifacts/turings-zeta-fu...
Mathematicians, especially young students often find interesting patterns, correspondences, sequences and proofs.
Sadly the pinnacle of math can make these joyful inventive discoveries pale in comparison modern formulations to quadratic formulas, pythagoras, quaternions, boolean algebra, etc.
History shows us that our own daily math discoveries may really be amazing achievements that we should be very proud of as there was a long period of time when very clever mathematicians knew nothing of the abstraction we just found.
So math history shows us our intuitions are equal to some of the giants whose shoulders we stand on and we are good mathematicians who can find things out for ourselves and not 'bad' mathematicians just because we can't regurgitate lengthy formulas on demand.