Ask HN: Programmers Who Want to Get Better at Math

[rossant]

I have some questions for programmers and software engineers who feel they're not good enough at math and want to improve, particularly with the goal of applying math to their current or future jobs, or who consider a career change. This might include fields like ML/AI, data science, graphics programming, video games, physics simulations, scientific and numerical computing, crypto, finance, signal processing, etc.

As the creator of the Awesome Math resource [1], I'm looking to gather and organize math resources specifically for those who fit this description. If that's you, what are your main challenges? Why does math feel difficult? Do you struggle with math notation, similar to how adult musicians without formal training can find modern music notation difficult? What stops you from picking up a math textbook and working through it? Have you ever tried that? What alternatives to traditional textbooks would work better for you?

If you had to go back to the basics, what level would you start from? High school? Middle school? Elementary school? For example, are you comfortable with elementary algebra [2]—solving linear and quadratic equations, simplifying algebraic expressions with fractions and powers, etc.? If not, is this something you feel you need to master before moving on to more advanced math topics?

If you could have a kind of survival guide before progressing to more advanced resources, what would you want included? What would be unnecessary? What topics would you want clearly explained? Which areas of math would you like covered—linear algebra, calculus, geometry, arithmetic, probability theory, combinatorics, something else? Do you know of any such guides? If you've tried them, what did you like about them, and what could be improved?

Feel free to respond here, but if you'd like to stay in touch as I continue developing this long-term project, please also send me an email (see profile) and let me know what you're interested in. I may reach out again later as I make progress.

[1] https://github.com/rossant/awesome-math

[2] https://en.wikipedia.org/wiki/Elementary_algebra

[geekodour]

i have my own syllabus kind of thing curated: https://geekodour.org/docs/updates/syllabi/#hb03-get-back-at...

i don't think my math problem is new. i remember after one summer vacation(we used to get one full month break in school during summers) after summer vacation i totally forgot how to do subtraction, i had difficulty subtracting 2 digit numbers. this was around 8th standard.

later this problem came up in other areas, i catch things pretty quickly but forget them faster! so the way i am currently approaching math and other problem solving is i keep in touch with everything very casually by doing minimal practice and this is good enough for me for now whenever i need to jump into more advanced stuff.

plus chatgpt/claude has been a lifesaver in this regard related to concepts but I don't think anything can beat the intuition that comes from practice. I've heard good things about math academy but idk if it'll be good for me as I don't like to do "math" on the computer and don't like quizzes much.

[shortrounddev2]

I recently went back to community college for Calculus; partly because I'm sick of being a CRUD developer, and partly because it's cheaper than therapy. One main issue I have with math education is that it seems like professors go out of their way to come up with contrived examples in order to demonstrate a concept, but they don't apply similar effort into coming up with pragmatic examples of how to USE the concept. (I was the "when will I ever use this?" kid). I think math exists to solve real problems, so we should give examples of solving real problems

Math classes are often constrained for time because their curricula are mandated by an accreditation institution rather than designed by education experts. I feel that math could be taught less mechanically and with more historical context for the concepts. I've heard that people retain information better when it's paired with a story, so I feel strongly that history should be taught side-by-side with math

[sloaken → shortrounddev2]

I struggled a LOT with calculus, the concepts were very hard for me to understand as they seemed theoretical.

I changed universities and the new school required Physics for CS majors. OMG finally something to explain the abstract calculus. I smoked the 2 physics classes.

[in9 → shortrounddev2]

> I think math exists to solve real problems, so we should give examples of solving real problems.

This is a view that, depending on the lecturer, can be the total opposite of their view. See, many mathematicians don't have this instrumentalist view on math and some even despise it with their heart. They don't care about applications and don't get particularly excited when a problem was solved in another domain with their technique.

Also, solving a particular problem is that, a particularity. They look for generalizations and for rules and methods that can be applied regardless of the domain. That is why weird and contrived examples are the bulk of their logic, since when you look for generalizations, those are the cases where it breaks. Does continuity implies differentiability? For almost all practical cases yes, but when you want to be general, thats when you get the Weierstrass function [1], a weird function that needs to be studied if you want to develop a theory of real valued continuous functions. Yet, such knowledge is extremely impractical for you average engineer or deep learning researcher.

And ok, you might argue that "I'm not at such level, I don't need those particular theoretically interesting cases since I'm not going to study advanced mathematics at that level". Ok fine, I respect that. But that is not part of the "culture" of mathematics (a culture which your lecturer likely comes from). Since the subject is learned and investigated with this "quest for generality which makes us study weird examples" this is how it is passed along, and this is how it is studied and structured.

All that to conclude: I think its best to respect how math is structured. First, it is precisely the type of thought that I think very other applied fields lack, but that actually helps solving problems. It is by seeking generality, and looking at corner cases that stuff gets built. And mathematicians are the best at formalizing those because this is how they advance their craft. Second, and last, its by creating your own investigation and development of examples that you can stride for a more applied and practical version of the course. That way you'll get the most out of the course.

[1]: https://en.wikipedia.org/wiki/Weierstrass_function

[eigenket → in9]

> Does continuity implies differentiability? For almost all practical cases yes, but when you want to be general, thats when you get the Weierstrass function [1], a weird function

Ok I have to jump in and disagree with you. Non-differential continuous functions are far more ubiquitous (and useful) than you're suggesting here. The most obvious examples are the absolute value function and ReLU (rectified linear unit) activation function which turns up in a machine learning/neural network context.

I think you're thinking about being non-differentiable everywhere, but it's very easy to cook up examples of practically relevant functions which turn up to be non-differentiable somewhere.

[mayanraisins]

I think I’m in your target audience. I’m a developer that studied Computer Information Systems instead of Computer Science to avoid the math classes.

I’ve often wondered if it was the material or how it was delivered that I struggled with. I seem to do better at math when there is a piece grounded in reality, like in physics or geometry. I can use that math to build a deck or calculate how fast an object is moving. Computer programming also falls into this category. I start to struggle when the math isn’t representing anything notable, and instead, just letters and relationships between them floating in space.

As a developer that values good naming and readability, I’m surprised that math uses single character variable names like x, y, h, or k, when it could be named what it is representing. I’m going to assume this is something that carried over from pen and paper, but maybe worth the extra writing when learning.

I have a long list of things I’d like to learn, such as speaking other languages and studying crafts outside of software development, but I do often consider going back to take another shot at math beyond intro Calculus.

Thanks for the resources and the goal of helping people like me. I’ll check them out.