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Comment by lisper | Hacker News Reader

> Most mathematics isn't written for computers

I beg to differ. A lot of mathematics is written in LaTeX which is written for computers to render into traditional notation. No one uses LaTeX directly because it has a horrific syntax, but it doesn't have to be that way. There is no reason why one could not invent a notation that didn't require complex rendering. Programming languages are an existence proof.

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> No one uses LaTeX directly because it has a horrific syntax

I’ve interacted with quite a few mathematicians who readily mix raw LaTex into their emails! I have to squint but it seems to be a somewhat normal practice.

OK, TIL. Still, I think it's fair to say that for this purpose, LaTeX leaves room for improvement.

That is not what I mean by "for humans". Also, LaTeX != mathematical notation.

What did you mean then? (And it's true that LaTeX is not equal to mathematical notation, but it does contain a mathematical notation as a subset.)

Mathematical papers, textbooks, lecture notes, in-person and video lectures, etc. are produced and consumed by humans and not computers.

Well, duh, nothing is consumed by a computer for its own sake. The only reason to feed anything into a computer is so that what you feed in can be processed to produce something that is useful for humans. That doesn't change the fact that a notation developed when paper and ink were state-of-the-art technology may no longer be optimal in an age of keyboards and screens.

I read mathematics on screens but when it comes to working out exercises etc I still prefer to do it with pen and paper, so I prefer succinct notation.

I'm not saying that traditional notation should be abandoned altogether. Pen and paper are still useful for some things even in the age of computers. Nonetheless, computers exist, and you might get more leverage out of them if you don't restrict yourself to using a notation designed for pen and paper.

> Well, duh, nothing is consumed by a computer for its own sake.

Except, you know, proofs that are automatically checked by a proof system.

It's really hard to take a suggestion like "mathematical notation should be replaced by s-expressions" seriously. There's approximately 0% of working mathematicians who would think that this is a good idea (hell, not even most programmers think it's a good idea to write everything in s-expressions).

Prior to any major advance in any field of intellectual endeavor there are approximately zero percent of workers in that field who thought that the thing that led to the advance was a good idea. This is exactly why major advances are rare.

BTW, you might want to look up the work of Steven Wolfram and Gregory Chaitin. They both thought using s-expressions was a good idea, and they got quite a bit of mileage out of it.

> Prior to any major advance in any field of intellectual endeavor there are approximately zero percent of workers in that field who thought that the thing that led to the advance was a good idea. This is exactly why major advances are rare.

This argument would make sense if nobody had ever come up with an alternative system of maths notation, but MathML, Mathematica, Coq, Isabelle, Lean, and many others exist, and yes, probably even some notation based on s-expressions (you could do mathematics in Pie[0], although it's probably not super pleasant since it's a toy language). They get their use for specific situations, as I mentioned before, but they haven't replaced mathematical notation wholesale.

[0] https://docs.racket-lang.org/pie/

I think you're missing the point. The s-expression thing was just intended to be an illustrative example. I'm not actually advocating for it (at least not here). All I'm saying is that asking specifically why things are the way they are is more likely to lead to good ideas than just "asking dumb questions".

(And note too that even with a heuristic that improves your odds, coming up with good novel ideas is really hard and happens only rarely.)

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