> I think you’ve have a bad experience because writing a proof is explaining deep understanding.
I think your wording is the key—coming up with a proof is creating deep understanding, but writing a proof very much need not be explaining or creating deep understanding. Writing a proof can be done mechanically, by both instructor and student, and, if done so, neither demonstrates nor creates understanding.
(Also, in statistics more than in almost any other mathematically based subject, while the rigorous mathematical foundations are important, a complete theoretical understanding of those foundations need not shed any light on the actual practice of statistics.)
You're right. Coming up with a proof is a creative process. Each major proof in mathematics is so unique, that it usually gets named after its inventor. So we have Euclid's proof that there are infinitely many primes, Euler's proof that e is irrational, and Wiles' proof of Fermat's last theorem.
I think your wording is the key—coming up with a proof is creating deep understanding, but writing a proof very much need not be explaining or creating deep understanding. Writing a proof can be done mechanically, by both instructor and student, and, if done so, neither demonstrates nor creates understanding.
(Also, in statistics more than in almost any other mathematically based subject, while the rigorous mathematical foundations are important, a complete theoretical understanding of those foundations need not shed any light on the actual practice of statistics.)