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This post might somewhat answer your question: https://www.quora.com/What-is-it-like-to-understand-advanced-mathematics-Does-it-feel-analogous-to-having-master

This post might somewhat answer your question: https://www.quora.com/What-is-it-like-to-understand-advanced-mathematics-Does-it-feel-analogous-to-having-mastery-of-another-language-like-in-programming-or-linguistics/answers/873950?share=1 https://www.quora.com/What-is-it-like-to-understand-advanced...

graycat 8y ago
At least from my academic degrees through Ph.D. and peer-reviewed published papers, I qualify as a mathematician. So, I'm interested in the OP and your link to quora. I've read a lot of high level descriptions of math including some from some famous mathematicians that I regard as total BS. In strong contrast, the quora link was pretty good. Some of the best parts in that quora link I had to discover for myself, and the quora link is the first explanation I've seen by others. For the OP, naw, I can't go along with much of that. In strong contrast, I loved learning, using, creating, publishing, teaching math and still do. Most of what I learned was from what I studied from outside a formal academic course; I studied the material because I wanted to understand it and did like learning it. The work was great fun, not frustrating or unpleasant in any sense. Even in courses, mostly I just wanted to learn the material and often ignored the class and teacher, concentrated on one or a few books, studied alone, and learned the material, generally for the course standards, quite well. Sorry the OP had a tough time multiplying matrices and understanding eigen values -- I had no such problems. To me, matrix multiplication is glorious because it is an associative operation and from what we can see from that -- amazing when think about it a little. For eigen values and eigen vectors, those are astounding, the keys to the polar decomposition which IMHO is the crown jewel of linear algebra and one of the more amazing results in all of math. The most difficult material studied was just from writing that didn't explain very well. One example was most of the explanations I read for the simplex algorithm of linear programming. Really, a super nice way to approach the subject is that it's just a nice, nearly obvious, tweak of Gauss elimination.
- MadSudaca 8y ago
  I don't have much training in mathematics, but from what little I have, I can say that coming up with conjectures is not easy and having your conjectures be false can sometimes be disappointing. Thus most time spent in a problem is usually in a state of disappointment. Due to this I can relate a bit to OP.

graycat 8y ago

At least from my academic degrees through Ph.D. and peer-reviewed published papers, I qualify as a mathematician. So, I'm interested in the OP and your link to quora. I've read a lot of high level descriptions of math including some from some famous mathematicians that I regard as total BS. In strong contrast, the quora link was pretty good. Some of the best parts in that quora link I had to discover for myself, and the quora link is the first explanation I've seen by others. For the OP, naw, I can't go along with much of that. In strong contrast, I loved learning, using, creating, publishing, teaching math and still do. Most of what I learned was from what I studied from outside a formal academic course; I studied the material because I wanted to understand it and did like learning it. The work was great fun, not frustrating or unpleasant in any sense. Even in courses, mostly I just wanted to learn the material and often ignored the class and teacher, concentrated on one or a few books, studied alone, and learned the material, generally for the course standards, quite well. Sorry the OP had a tough time multiplying matrices and understanding eigen values -- I had no such problems. To me, matrix multiplication is glorious because it is an associative operation and from what we can see from that -- amazing when think about it a little. For eigen values and eigen vectors, those are astounding, the keys to the polar decomposition which IMHO is the crown jewel of linear algebra and one of the more amazing results in all of math. The most difficult material studied was just from writing that didn't explain very well. One example was most of the explanations I read for the simplex algorithm of linear programming. Really, a super nice way to approach the subject is that it's just a nice, nearly obvious, tweak of Gauss elimination.

MadSudaca 8y ago
I don't have much training in mathematics, but from what little I have, I can say that coming up with conjectures is not easy and having your conjectures be false can sometimes be disappointing. Thus most time spent in a problem is usually in a state of disappointment. Due to this I can relate a bit to OP.