- Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

Math is not just a part of physics. Heck, even *applied* math is not just a part of physics. And even in physics, I learned that there are two types of mathematical thinkers: geometers and algebraists. It would be a mistake to assume that all math that is part of physics is geometry, like this author does. General relativity is most intuitively geometry, and quantum mechanics is intuitively algebra, though you can formulate both the other way. For both math and physics, I think you need both even though most of us tend toward one or the other.

For example: the determinant of a matrix only fully makes sense if you understand it as both the change in volume of a paralellipiped, and as the product of the eigenvalues. These are the same mathematical statement, but one of them leads to a more geometrical way of thinking and the other more algebraic. Even if you are more of a native "algebraist" like me, remembering the geometric definition of the determinant can still help.

It may be that French math schools have all taken crazy pills and kicked the geometers out. The author is obviously more geometrically inclined and therefore rather irked about the whole thing. Though he might be right: if he is considering Landau and Lifshitz to be "not abstract" maybe they are starving for more grounded math education in France.

I absolutely hated analysis for years after I got my degree for all the physics tangents in the calculus/advanced calculus sequence that I had to digest and memorize because they'd be on tests. I was interested in logic and combinatorics, and later topology via category theory. If I wanted to study physics, I would have signed up for physics classes. Mathematics is bigger than physics.

Yeah that's dumb. Engineers are taught that manufacturing is applied engineering, engineering is applied physics, and physics is applied math. Math isn't applied anything; it's the only discipline you can conjure out of pure thought. I would have figured the mathematicians would be insufferably reassured about that.

I get that, though I see myself leaning more and more toward physics as time passes. That said, both category and type theory help me a lot every day, even though it's rarely something I use directly.

Anyway, Arnold wrote it, so there's no surprise it's biased. I don't agree with the article, at least not in 100%. I did, however, find it has some good points and IMO it's thought-provoking enough to be shared.