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Comment by daynthelife | Hacker News Reader

As mathematician, I actually agree. We could do a lot more to communicate ideas in a way non-experts can understand.

For instance, most people are familiar with polynomials. Take a polynomial in x (with integer coefficients) and substitute x for 5t everywhere. So for instance, 2x^3 - 8x + 3 becomes 250t^3 - 40t + 3.

The Rees algebra Z[5t] (here Z is the integers) is then just the set of all polynomials you can get this way.

If Wikipedia introduced it like this, I don't think most people would have a problem understanding.

The concept is not (at least not always) actually that complicated, like others are implying. It's our communication that is lacking.

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As a hobby mathematician, I agree. I know quite a bit about rings and ideals, but I don't understand much from the article on Rees algebras. Wikipedia has a lot of articles on mathematics that are explained badly, I prefer to find information elsewhere, typically I ask an AI for a good introduction on a subject (and usually that links to PDFs with over 100 pages that keep me going for hours).

And Wikipedia is particularly bad for this. It is a good reference for things I already learned, but for learning, if I am not able to get to a professor, I find math/stack overflow to have many more examples and explanations, and sometimes for an overview YouTube lectures. And really for concrete things like polynomial rings over R, I often found starting up Mathematica and just playing around with some computation is sometimes useful. (Forget about p-adic things tho).

I sometimes think it would be good to rename some of the things that have historical names to mnemonics more descriptive than a proper name. But that would be difficult.

A mathematics book that was once on the front page here said the same. Mathematica by David Bessis.

I'm sure you're right that there's poor terminology, and Wikipedia math is certainly daunting. But in general the many mathematical exposition PDFs scattered across the Internet are beautifully written by careful, intelligent people. I'm a software engineer who's spent many hours reading them and also trying to do graduate classes as an adult. It's unfortunately common on Hacker News to encounter people who think that "I'd be good at math if only they used code to explain it" or "I'd be good at math if it used better terminology/notation".

The truth is that math is hard: few other subjects have anything close to its crazy conceptual breadth and depth, with hardish concepts being built upon hardish concepts in many layers.

I've had quite some success during my CS BSc math classes with inventing/using verbose but clearer notation and rewriting things more explicitly, programming things up, playing with Mathematica etc.

For example, Fourier is more clear to me as: F{t -> sin(t)} = omega -> (...) instead of F(sin(t)) = (...). Or D{x -> x^2}(x) = 2x instead of (x^2)' = 2x

Abuse of notation is very common, like using f(x) both as the function and as the return value at some input x etc. For example, the chain rule is often notated in a way that hides a lot. Math uses so many single letter variables, uses huge formulas instead of factoring out parts and using multiple lines, math people don't seem to appreciate namespaces and dislike nested variable scoping etc.

It's not magic that makes everything super easy, but it helps.

I agree with this - real analysis and functional analysis with have the cognitive complexity of three months worth of the cognitive of software puzzles in each weekly problem set.

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