In Steve Yegge’s linked post:

> Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap.

This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who have no formal training in engineering or computer science but we’re able to self-teach the concepts. The same cannot be said of mathematics, which requires deep, dedicated study. Most programmers I know know very little mathematics, and it’s not like I’d claim I know a lot either. I’ve forgotten more than I know.

He even mentions how little math he took, so I’m not sure he’s an authority on the subject. Most of his post is just surface level platitudes. I’m generally confused why I see his posts referenced so frequently.

To be clear, this isn't some attempt at gatekeeping. It's just that mathematics is a very deep, difficult, and misunderstood subject. I think maybe only true philosophy is harder because there, it's usually not even clear what the questions are.

> mathematics is orders of magnitude more intensive and difficult than most programming

But what level of programming and mathematics are you comparing here though? because college-level algebra and calculus is really not that hard imho (once it "clicks" for you, but it's the same for programming), and if we are comparing math as in what you see in a BSc/Msc of Mathematics (or research-level) then I agree it's hard but you have to compare for an equivalent level of programming.

> simple fact that shows this is the amount of programmers who have no formal training in engineering or computer science but we’re able to self-teach the concepts. The same cannot be said of mathematics

I would blame it more on the fact that programming is a very useful tool for people outside Computer-Science, it has very direct applications and you can monetize it very easily, so it's very likely that they might want to learn it, however, rarely you see someone deciding to take Calculus just for the sake of it if they never bothered with it in College.

Overall I agree with you, but personally I find math more difficult, most people probably do but I don't think it's inherently more difficult, it's just that people are less used to study it.

I would hard disagree that undergrad level Analysis or even just the trickier corners of vector calculus are within the bounds of what programmers can easily pick up without dedicated and guided study. Everybody's gangster until they have to parameterize some bullshit helical structure in R3.

Comparable levels of programming, what we expect of CS juniors, are regularly picked up by "the guy who is good with Excel" in office settings as it's mostly a function of experience and exposure, not theory.

And now my worthless anecdotal evidence: I self taught myself into professional programming and it was a simple matter of banging my head against a wall until shit started working. The feedback loop, "did the thing crash or not", permitted me to learn on my own. I wouldn't even begin to understand how to self-teach myself Stokes Theorem or some shit, and have zero ability to author the proofs required to reach the conclusions higher level mathematics are built on.

I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up.

What if we had something similar for mathematics?

Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax".

I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of professional mathematicians.

When learning math / seeing other learning math I've noticed that simple errors such as typos often slow down or hinder understanding of the subject.

After you get the hang of the system, you can play with the interactive theorem prover behind it: Lean [2]. There's also plenty other interactive theorem provers (Coq, Isabelle, HOL, Mizar, Metamath, ...) but Lean has a lot of traction amongst mathematicians at the moment.

There are no limits to the math you an do with this. There is mathlib [3], the main mathematical library. It covers a lot of undergraduate material [4], and plenty of stuff beyond that [5]. The community has even covered some state of the art research math in Lean [6a, 6b].

You are very welcome to hang out on the leanprover zulip [7]] and ask questions about the Natural Number Game or anything else that is Lean-related.

[1]: https://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_gam... [2]: https://leanprover-community.github.io/ [3]: https://github.com/leanprover-community/mathlib [4]: https://leanprover-community.github.io/undergrad.html [5]: https://leanprover-community.github.io/mathlib-overview.html [6a]: https://github.com/leanprover-community/lean-liquid [6b]: https://www.nature.com/articles/d41586-021-01627-2 [7]: https://leanprover.zulipchat.com/