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Comment by kenjackson | Hacker News Reader

While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig. Not to say there aren’t useful aspects, but the curriculum is so inefficient. And maybe it’s because everyone needs some part of it, but that part is different for each person.

Math is interesting in that the early foundation is so useful, but the use drops off quickly. While I feel like other areas often become more useful as I learn more. Possibly because I haven’t spent 15 years on that topic like I had math.

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“math does lose its usefulness around after trig”

This is the most jarring thing I’ve read today. I can’t say I agree, but I haven’t spent 15 years studying math myself, so who am I to disagree.

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).

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.

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.

> 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)

Wouldn't say math loses usefulness after trig. But rather, due to how it is (usually, my experience being in Chile) teached it rapidly becomes too abstract, decouples from its "real world" use cases and then it is easy to forget the forest for the trees.

The Mathematics for Machine Learning book[1] exposes this as a top-down vs bottom-up problem. While both approaches have pros and cons, a sweet spot may lay somewhere in the middle and that needs you to embrace some inevitable backtracking (i.e. college curricula should not forget to add some courses where world modelling using the math and throughfully explaining why that underlying theory and math is actually useful in describing and/or predicting reality).

PS: I also think there is still a lot of focus in resolving problems manually.

[1] https://mml-book.github.io/book/mml-book.pdf, page 13.

>While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig.

Statements like this are a big part of the reason statisticians never trust anyone who works in "data science". The whole field is basically applied statistics/calculus and you're saying none of that is useful.

Sorry, the statement I made wasn't intended to be connected that way. Data science uses a bunch of math beyond trig. I meant that in general math beyond trig becomes much less useful. I was talking about the general usefulness of different levels/types of taught math for white collar jobs/living. Not what is of use for data science.

"math does lose its usefulness around after trig"

Not if you want to leave open the possibility of majoring in engineering, physical and biological science, or economics.

ChatGPT might argue linear algebra and calculus are useful.

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