[mark-t]

No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. Topology does, too, depending on which area you study and what you consider calculus. Sure, there are obviously fields that do rely heavily on calculus, as well as certain branches in the above fields, but my point was that it's nowhere near universally needed. I'm a graduate student at UCSD, and I can't remember the last time I used calculus in my research.

[mnemonicsloth]

This is terrible, wrongheaded advice. It's like Pablo Picasso, in the middle of his Blue Period, trying to convince younger painters that red isn't a useful color for serious artists.

If you want to study graph theory or combinatorics [1], then calculus will be pretty much useless to you, and you'll naturally go years without using it.

Calculus is also useless in some situations in abstract algebra (which are said to have combinatorial character). There are other parts of abstract algebra, e.g. Differential Galois Theory [2], in which calculus is pretty important.

Topology is similar. Elementary topology is part of the foundation supporting calculus, while algebraic topology is one of the tools that's useful when we try to do calculus (or solve differential equations) in non-Euclidean spaces.

Fields making heavy use of calculus include differential geometry, differential equations (ordinary or partial), dynamical systems or control theory. That subsumes most of physics. Fields underpinning (and largely inspired by) calculus include real and complex analysis, measure and integration theory (aka axiomatic probability theory). Also functional analysis, which is a generalization of linear algebra, which is the bookkeeping methodology of calculus in higher dimensions.

[1] The first sentence here says it all: http://en.wikipedia.org/wiki/Combinatorics

[2] http://en.wikipedia.org/wiki/Differential_Galois_theory

[mark-t]

That post does not contain any advice. It contains facts, none of which were contradicted by your post (a typical property of facts). I never told him not to study calculus. Given our current education system, that would be impossible anyway. I guided him more toward real analysis and suggested some other areas of math that might interest him. Since his only background is high school math, I felt it would be best to introduce him to something where proofs play a central role. If he can't stand that, then he probably shouldn't go into math.

[jibiki]

> calculus isn't that important for mathematicians

> Many pure math classes require no (or very little) calculus.

These are not the same thing (hence my confusion.) Your initial comment seemed to indicate that nobody does analysis anymore, which is just not true at all (look at the most recent fields medal.)

[mark-t]

Nope. I'm well aware that people still study analysis. I just meant that one doesn't necessarily need to learn calculus before taking the plunge into serious mathematics. Even in analysis, there's quite a bit you can do without knowing the stuff from a standard calculus class (though it certainly helps).