Culture-dependent? I recall the story from France of the second-grader who, asked what 2x3 equals, replied "3x2", knowing only that multiplication was commutative.
This is a classic joke making fun of the issues with French education based on the Bourbaki [1] school of mathematics, see [2] for more discussion. Different issues than the USA, but also bad in my opinion.
[1] https://en.m.wikipedia.org/wiki/Nicolas_Bourbaki
[2] https://web.archive.org/web/20230315185224/https://www.uni-m...
FWIW, I understand where he's coming from but I fundamentally disagree (not in the least because for me, computer science applications of mathematics are much more interesting than physics ones, and these can be incredibly abstract).
And This observation:
> "genuine mathematicians do not gang up, but the weak need gangs in order to survive."
applies to programmers as well, and may be just about any profession/activity..
The problem I have with that argument is how historically unsupported it is. Some of the most abstract branches of mathematics, completely devoid of any real world connection, have become insanely useful later on.
Nobody thought that number theory had any value before cryptography showed that it did.
And it was Hilbert's push to put mathematics on an abstract and axiomatic foundation that led the way to discovering what "computation" is (and what its limits are) and therefore to the birth of computer science.
Vladimir Arnold was a well-known pure mathematician with a deep interest in physics. If you read his math books (many of them are good), he constantly uses examples from physics to explain math concepts.
That said, I'm not sure that he actually held contempt for math. It's fairly essential for theoretical physics.