[kenjackson]

I think most people would agree if pressed. Math is so ridiculously useful prior to trig. Almost any white collar job relies on these maths. Trig is an interesting inflection point in that so much math gets built on top of it, although its not that useful in of itself. And then after trig, things become much more fragmented and you really need to go into specific subfields to determine which branch of math is of value.

For example, if you go into medicine and medical research having a good understanding of statistics is useful, but very little in calculus or analysis is useful (and even if you do need Calculus, most of the useful stuff for those fields is taught in the 1st semester of Calculus).

[mlyle]

I think a lot of things use calculus concepts, even if calculus isn't explicitly invoked.

A whole lot of finance and pharmacology are about exponential functions and their derivatives and integrals, for instance. A whole lot of fields use optimization, even if "just asking the computer to do it", etc.

I admit I am weaker now in calculus and linear algebra because I lean on CAS and simulation a lot... but at least I know how it works so that I have an idea of what I'm doing.

[kenjackson]

To be clear, I'm not referring to the concepts as they exist in the universe. But rather the actual material taught in the courses. For example, there's a lot topology that we use in the real world, but the material in the class is only of use to a small percentage of people in the world.

I spent a chunk of my career optimizing FDMs and FEMs, but above and beyond that I haven't had a great need for Calculus until I started doing some deep learning. Again, very particular subfields.

And I suspect the work that you're talking about is exactly what I was thinking about when I wrote that even if Calculus is needed, it's the stuff taught in the first semester.

[mlyle]

> but above and beyond that I haven't had a great need for Calculus until I started doing some deep learning.

I think a whole lot of what we talk about in compsci... calculus is table stakes. Sure, it's not differential equations, but how do we talk about behavior at the limit or nonlinear scaling without it.

Even just making up functions that are smooth in their derivative and cross though a few points is something I've had to do a lot for decent heuristics.

> And I suspect the work that you're talking about is exactly what I was thinking about when I wrote that even if Calculus is needed, it's the stuff taught in the first semester.

What's taught in the first semester varies a lot. I'm familiar with AP Calc BC, and sure-- a little bit of the stuff in the last half of the course (differential equations, vector-valued functions) is a little more esoteric for many careers. But a lot of stuff isn't so much (polar coordinates, the "practical integration" stuff that uses basic mechanics, calculator skills, etc)