I have a friend that recently moved to St Petersburg, and has shared with me that the Russian vision on pedagogy of mathematics greatly challenges the current western consensus. We are physicists by training, and we were complaining how pure mathematics books didn't make any pedagogical sense because the results are never motivated, their power and applications never discussed and the proofs never give any profound insight into the meaning of the results, they mostly seem like parlor tricks to us.

He shared this small comment article with me today: "On Teaching Mathematics" by V.I. Arnold
(4chan is not letting me write the link, I'll try to put it in a second post)


I am curious to hear your opinions on this. I mostly tend to agree, thinking back on my time at University when I was studying differential manifolds and how the way the mathematicians were seeing it made no practical sense to me, it seemed superfluous. I must admit that not all professors were like that, I had a few that were a lot more visual and really seemed to understand the implications of what they were teaching, and not just trying to spit out auto-consistent and safe results.