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Comment by andyjohnson0 | Hacker News Reader

As the parent of a young adult currently half way through their maths undergrad, this kind of fills me with foreboding.

I know that proof assistants etc have existed for quite a while now, but what with this and the murmours about OAI's Q* model, I do wonder what will happen to maths as a human endeavour - and as a enabling skill for jobs that can financially support people like my child.

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I wouldn't worry about it. We're going to need humans with specialized mathematical training in the loop.

Besides, these things have a way of surprising us. Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

It's highly unclear to me what will happen. Probably learning math will be more accessible. But it's unclear how many humans will be involved at the forefront of math research. For example you can imagine a situation where in some parts of math large communities work in a direction guided by a few "visionaries". This sort of thing will not really happen after the commodization of theorem provers. Like instead of an advisor telling a PhD student a problem, they can just plug it in. On the other hand, in some sense the advisor and the student will be equal in the fact that the only thing you will need to do is ask questions?(last part is also speculative)

>Probably learning math will be more accessible.

I'm not quite sure what you mean. Isn't math already pretty much the most accessible thing that could be imagined? I can't think of any story of someone in the past century who wanted to study math but was unable to, except for reasons prohibiting any sort of academic study whatsoever (e.g. girls in Taliban controlled areas).

I don't think research math is that accessible! Granted theoretically it's possible to just read papers and do research--and possibly it's theoretically as accessible as possible. In practice people learn better with teachers and access to experts at the research level. If this pans out, we can commoditize access to experts (or even experts).

But even in 1913 a brilliant mathematician from the middle of nowhere could access a world class mentor. I would assume that this is so much easier these days. What would stand in the way of a modern day math prodigy from getting accepted into a good program?

Or is it about making this more accessible to students who are "merely good" rather than brilliant?

yes I mean more accessible to the general public yes.

Some people imagine AI will soon be a bit like being able to go to a university professor's office hours to ask questions and get detailed expert advice on any part of the undergraduate curriculum you're struggling with.

Except it'll be available 24/7 and you won't have to pass exams, spend $$$$, attend full time, and live in dorms and be in your late teens or early 20s to get access.

And you'll have to fact check every answer to make sure it's not a "hallucination".

> Besides, these things have a way of surprising us. Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

I see this reasoning a lot but for me it kinda screams "correlation is not causation". As time passed and technology advanced it was simply more widely used, both on a consumer and business level. Very well may be that if we had to write machine code by hand we would need 10x more developers and a salary of $1kk/year would be average at best.

Do you really think if we get some AI agent that can write a wholly working application based on natural language specification that wouldn't significantly reduce the need for human devs?

>There isn’t a rule of economics that says better technology makes more, better jobs for horses. It sounds shockingly dumb to even say that out loud, but swap horses for humans and suddenly people think it sounds about right.

Yes there is actually: https://en.m.wikipedia.org/wiki/Okishio%27s_theorem

Eh, kind of, but maybe not.

It talks about rate of profit over the economy as a whole. It says nothing about the distribution of said profits. Its assumed that human labors are the ones also reaping some of those profits because they are doing labor, hence wages from those labors remain stable. If for some reason there was 0 labor available to you the same premise could hold true, the rate the AI is earning could remain stable, you're just shit out of luck.

> Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

That analogy occurred to me too. But I'm not sure what the corresponding higher-level domain is that mathematicians might have to migrate to - in the way that assembly programmers started using high level languages. Writing prompts for maths LLMs, or wrangling teams of them, is hardly going to be well paid enough to facilitate a decent life in this era of late capitalism, or even pay uni fees.

And even if there are such higher-level domains, its not certain that they are compatable with available human cognitive ability or limits.

Lots of maths grads currently go into tech/finance/lifescience/whatever. I'm a dev and I can see those fields being eaten alive by this stuff. I don't want my kid to end up as a 2030-equivalent of a fully qualified assembly language programmer.

I hate to break it to you but most people with math degrees aren't doing math jobs today. The demand for such skills is low. While such an AI may displace some of the few jobs that do involve heavy math, it's likely your child will not be in that category.

I wouldn't worry too much.

I wouldn't worry. What this means is that mathematics as a skill is going to be back big time, because now you can actually use it everywhere.

Mathematics departments have been closing down for a while now, I think. I think this trend will reverse now. Mathematics itself will change in the process, but for the better.

This. Math proofs are useless in 99.99% of situations because they are far too expensive to actually use in production. Only something like AWS would use formal proofs to verify some system property for reliability.

With some super-math Q* bot, a mathematician could presumably create actual proofs/simplifications for complex real world problems/systems at very affordable time and costs (in weeks not years).

The mathematician in this case is far less skilled than the bot, but that doesn't detract from their market value. Most programmers are way less skilled/smart than the library authors that they rely on, that doesn't stop them from earning $$$, because they are useful.

There's a massive corpus of useful math proofs, just most of them have been implemented and are second nature now

I don't think it's true that "math departments have been closing for a while now"

It's an impression I had, I don't know any hard data. For example:

https://www.reddit.com/r/math/comments/l7yyir/not_joking_uni...

https://www.reddit.com/r/math/comments/15of64l/rumor_west_vi...

I think it's a very unfair assessment to make from these two examples. I think it's like saying Silicon Valley has been shutting down for a while and providing two examples of startups. I will say from my personal impression as someone in pure math, I disagree with this statement.

I don't know what "fair" has to do with that. These are two examples that caught my attention, and I might be wrong that this constitutes a trend. If you have data that says otherwise, please share.

I think the funding in pure math is not going down in recent years. Nor are math departments much smaller than they were say ten years ago. Otherwise I'm sure how best to give evidence of math departments not shutting down! Do I list healthy math departments?

I guess this would be a case of applied math ;-)

Joking aside, of course it is not on you to provide evidence. I would probably start with seeing how many universities have pure math departments over a time axis from now back to 2000 or so.

It might even be that the total funding increases, but is more centralised in the big universities. So a total funding timeline would also be good.

Correct - math departments are doing fine. Not quite as fine as CS departments, which get showered with piles of money and their grad students poached to make money in industry. But so long as other university departments want their students to know some combination of calculus, linear algebra, and statistics, math departments will continue humming along.

Perhaps this might cheer you up - https://statmodeling.stat.columbia.edu/2015/03/17/1980-math-...

Or perhaps not. In that blog, Gelman speaks of Gregg, who ended up as a GS VP, and says -

math olympiad = high school basketball star

pro mathematician = NBA player

Goldman Sachs VP = sports hustler

I actually worked with Gregg in fixed income at that time :) Gelman's blogpost received sufficient notoriety, atleast within GS & the IB community.

Yet GS VPs salary is closer to NBA player's salary, while math pro's salary is closer to sports hustlers' ...

I think its pretty clear that in the coming decade intelligence and cognitive labor is going to become very cheap. So your kid should develop some skills outside of that to stay competitive in the job market.

Any suggestions?

AI Software Engineering? Baker?

Stockpile metals and rare earth elements. Natural resources will be the beginning and the end of trade.

(not actually serious, at least not yet)

Plumber

general intelligence will become cheap? and so your suggestion is to develop skills outside of skills?

Personally i think markets will be so different from now that this question of where you'll have skills for jobs is less important than asking what will a job mean in 2040. But ok, maybe this is still a minority opinion.

I think it's pretty clear that cognitive labor will become even higher value in the future, as our tools get better and allow us to become more productive.

You speak the truth but people here will hate you for it.

In a way, all math proofs already exist. Humans just have to determine what is worth looking for and uncover them. AI will help us do the latter. But we still have to do the former ourselves.

It will still require sound mathematical knowledge and understanding, to know what are the interesting questions to ask. Even if AI knows all the answers, it doesn't change anything because the answers already exist anyway.

That kind of Platonism also implies that all possible computer programs already exist: because any program is merely a very large natural number, the set of which has infinite cardinality. I'm not sure how helpful this is for the practice of humans doing mathematics or software development though.

You do realize that we still learn (and not unnecessarily) addition despite having had calculators for 50+ years?

Math shapes your mind, that’s why we learn it.

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