>We were told in 2023 that there’d be no more jobs within months and the singularity was here.
I never recall hearing that other than from people strawmanning what the labs were saying.
It's the same as conservatives who tirelessly repeat "In 1995 they told us the world would be underwater by 2015, those climate scientists are full of shit" - no, no one ever said that, you just listen to grifters who only can strawman.
Actually it was mostly said by the bonkers AI-obsessed Redditors (for whom it seemed to be the absolute consensus), though the tech bro CEOs like to allude to it too. They just make it just vague enough to scare investors and governments but also be plausibly denied later when it turns out not to happen.
By the way, I don’t think climate denial has (or at least should, though I know Americans like to politicise everything under the sun) anything to do with ‘conservatism’.
> Humans are close to their ceiling. AIs are just getting started.
The whole point of mathematics is to vastly exceed that natural ceiling by gradually building a framework for understanding. In fact it’s wrong to speak of a ceiling altogether. If there were a ceiling, we’d have hit it long ago.
AIs have already swallowed the entire history of human thought, but apparently they’re ’just getting started’. I can only assume you don’t know what mathematicians actually do.
Abstractions can certainly enable this kind of "telescoping" effect of understanding, but not everything can be compressed with clever abstractions. Some things are inherently incompressible and there is no neat and insightful short explanation for why it is true, just a massive proof, but it may still have provably good properties for building a chip or power plant.
We have naturally only explored the mathematical universe in the parts where telescoping via clever abstractions can get us. But there is much more. Being able to juggle more things in your mind at the same time can have qualitatively massive benefits.
Information theory and proof theory, algorithmic information theory etc has of course explored this.
It’s not ‘of course false’, and, to be honest, I can only assume you have little idea what mathematicians actually do.
Most pure mathematicians are no more interested in ‘producing commodities’ than any other academic is. That’s not what the subject is about — at all. The confusion arises because mathematics turns out to be extremely useful (no surprise; it’s quite useful to have a detailed understanding of the basic principles of reality).
Again, this seems to be an alarmingly common fallacy here on HN. As a commenter above observed, pure mathematics (and that is what we’re talking about here) is in important ways closer to the humanities than it is to other sciences.
I was talking primarily about the majority of people who study mathematics, or anything else, who don't end up full-timers at it. I think we'd live in a better society if there was a serious possibility that everyone who studied math in undergrad could actually go on to be a mathematician if they wanted.
Friendly warning to those who might not be aware: the vast majority of comments below posts like the above will be left by (otherwise intelligent) programmers who think mathematics is a closed system where one attempts to solve endless Olympiad-type problems. I wouldn’t take any of it seriously at all. Better to listen to what those who actually know what the subject is about have to say.
Unfortunately, mathematics (especially pure mathematics) is by its very nature very, very poorly understood by those who haven’t worked as a mathematician. Even worse, those who don’t understand are seemingly not at all aware of their misunderstanding and are entirely confident in their (very wrong) characterisation of the subject.
I did systems administration for a university math department for several years. I came to the conclusion that mathematics (and perhaps philosophy) were both topics where it was likely that no staff members in that department could describe "what goes on here" and that possibly even within the department, one professor may not be able to describe what another professor's actually doing.
The closest I could come to describing math is "some abstract process where imagined structures are characterized and extended; the most critical part of the process is identifying where seemingly independent structures are found to actually be fungible in some previously undiscovered way".
A simple example is
"hey, did you know that x^i is the unit circle?"
"what's i?"
"i is defined as if you square it the result is -1"
"what does that have to do with circles?"
> Mathematicians can also consider wholly redirecting their skill sets to work on real world problems. I’ve actually been encouraging mathematicians to consider thinking about working on government or other large-scale societal issues.
The fact that this is a radical departure from the norm is part of why mathematics (and philosophy) is often seen as some intangible or ungrokable science to many outsiders, as they're generally approaching it from a perspective of "Okay, but why, what is this useful for?", and the answer "For the science of it" doesn't tend to land with people that aren't already passionate about said science/discipline and are just trying to figure out what it even is or involves.
Doesn't help that there is a pervasive sentiment in American Academia (not sure about elsewhere) about Math being *the* hard science, and I mean hard as in difficulty, so a lot of people get intimidated by it before they ever give it a chance very early on in their academic life and carry that through the rest of their education.
So there ends up being a rather small pool of people that are in(to) the field, and rather high friction for stimualting interest in it from outsiders from the way that it's taught, and a massive difference in the perspective of it's use between it's diaspora and the unmathed masses.
Mathematicians who do work on "real world" problems are mostly doing so with theoretical physicists, genomicists, and cryptographers. None of these count as what people consider valuable other than because they are hard.
That said, few 50 (or even 40) years ago would have predicted that completely abstract number theoretical computations about primes, discrete logarithms, and elliptic curves would be the foundation of our monetary system.
> I did systems administration for a university math department for several years. I came to the conclusion that mathematics (and perhaps philosophy) were both topics where it was likely that no staff members in that department could describe "what goes on here" and that possibly even within the department, one professor may not be able to describe what another professor's actually doing.
And this is indeed why it is not going to be taken seriously as an academic or (more importantly) an economic endeavour done by humans anymore.
That won't stop the career mathematicians from protesting and having a cry here trying to justify themselves.
Good question, and maybe I should have provided an alternative description rather than just criticising.
Unfortunately, it is actually surprisingly hard to pin down, and I think mathematicians (and, as a student, I count myself as one to some degree at least) now have the task of making this a lot clearer. If we want to justify our existence in the face of new machines that can seemingly ‘do our work for us’ (so far in a restricted context), we should give a robust defence of our practice. If we can’t do this, we simply don’t deserve the funding (which, by the way, again contrary to some misguided statements here, isn’t very much anyway!). I think all of this will become clearer to outsiders as time passes, but for now it’s not easy to give a quick answer — though I can try.
Mathematics is about understanding things. Isn’t that what every subject is about? Well, I suppose so, but mathematics more specifically does something like the following:
(1) observe some phenomenon in ‘reality’.
(2) attempt to formalise that phenomenon in such a way that it can be manipulated purely symbolically.
(3) use this (perhaps fairly arbitrary; remember that we can invent as many formal systems as we like) system to deduce from our initial assumptions new facts that would otherwise have been very non-obvious.
It seems like outsiders have a decent grasp of (3) and the application of AI to it, but have very little idea about the other two steps. It seems to be widely assumed among non-mathematicians that problems are essentially god given and that the job of a mathematician is therefore to chug away on these problems, manipulating symbols and trying out tools, in the hope of learning a yes/no answer to each one.
The first two steps are by far the hardest and most important, and they’re also the parts that AI seems currently unable to help with.
NOTE: this is not a deeply insightful description of what the subject is about, and there are many better characterisations out there. I think Tao and various others have written recently about why complicated and inscrutable AI-generated proofs aren’t nearly as valuable as one might imagine. (That’s not to say there’s no value to such proofs; perhaps in time, as technology improves, mathematicians will come to accept AI as part of the process.)
If you want to understand all of this issues better, reading the recent slew of guest posts on Tao’s blog would be a very good start.
Despite loving Mathematics and having considered being a Mathematician myself, that wasn't a very robust defense. Also, even though I'm a big Terence Tao fan, I'm not sure he has sorted that out this defense in full himself.
This post which he forwarded was quite poor in my opinion. Confusing, all over the place with AI criticisms and promotion of the AI hazing being done by mathematicians.
X thousand mathematicians who want to protect their livelihoods signed a bunch of letters against AI. Duh. We've seen similar movements from every profession that has been displaced ever.
Terence Tao uses AI and has made a few good points on how to use it. But defensiveness leaks into almost every defense of the role of humans in Mathematics that I've read, even his own at times.
To be clear, I actually believe that Mathematicians aren't going away, but I dont have enough knowledge about the life of a professional mathematician to articulate a path forward.
This "path forward" is what I'd like to see. We need a top mathematician with enough intellectual honesty (Terence Tao qualifies, I think) to start this questioning with "there's actually no role for human Mathematicians" as one of the options on the table and go from there.
For me, mathematicians seem to be still having an inner discussion rather a making these essays for the more general public. In any case, I think that statements of the type "there's actually no role for human Mathematicians" are completely non-serious, so it'd sad that the discussion concentrates on that.
I agree, but it's still something we shouldn't eliminate a priori. I think Mathematics as a profession will be greatly enhanced by AI, but I can't prove that.
My understanding when I was practicing is that the trend in modern mathematics is to focus on spaces with a certain kind of structure, and maps between those spaces that preserve it, and then what are invariants are preserved by those maps. Structure-preserving maps between categories of such spaces - "functors" in the language of category theory - are especially neat.
That's certainly different from Olympiad-style problems.
Actually, if you were to convert most software into mathematical notation it would look incomprehensible. We are not interested in gatekeeping as much by making things look more convoluted than they need to.
This is a great point. When I was learning machine learning in the early 00s, there were many papers where I would struggle to understand exactly what the mathematics was trying to communicate, but where I would look at the matlab source code and say to myself "that's all?"
In my observation, most programmers and engineers lose their math chops over time. The math they need is mostly baked into their tools, such as CAD. If a problem requires more advanced math, it's given to a "math person" in the department. Often, the "math person" is also not allowed to touch the production code.
i'd be on board with this concept but the author seems to believe his point is generalisable to all under industries, hence committing the same fallacy you're talking about at a large scale.
but you're still right. i disregarded his take, as you would with mine re. math.
Check out the story about the personalized cancer vaccines. I think AI stands to play a significant role in enabling things of that sort going forward.
I have a strong sense that almost none of the commenters and blog post authors ranting here about mathematics have any clue about mathematics or its culture. I do not recognise any of these descriptions of mathematicians at all, and can only imagine they’re based entirely on experiences of other, almost entirely unrelated, parts of academia. This is not the first time I’ve seen it online, but recent events seem to have exacerbated it.
Not sure quite what animates the absurd hatred of one of the least greedy groups of people on the planet, but it certainly isn’t experience. To anyone with any, it just looks like absurd derangement.
Has and will. Are you going to back that assertion up at all, or just repeat it like that other viral thought-terminating cliche: ‘this is the worst the models will ever be’?
No it isn't. Best and worst and ill-defined anyway but the chess ELO score of various LLMs has fluctuated up and down, it's not been montonically increasing. What is the best answer to "how do I make cocaine"? The models are getting larger, with more compute and RAM backing them, but that doesn't automatically make them better if you don't define how you're measuring better-ness.
None of the frontier labs care about Chess as it's already a solved problem. If they did, the models would be much better. It's really not that hard. Google has a paper on grandmaster level chess without search from transformers.
Better obviously means better, like how they became better than they were 6 months and a year ago.
"Better" is not one dimensional across all use cases even if model capabilities are improving in aggregate.
e.g. If someone said "this is the worst they'll ever be" in response to some writing with obvious LLM cliches in 2024, I'm not convinced that prediction was actually correct.
The focus of OpenAI/Anthropic pivoted aggressively to the agentic performance arms race instead of making a more human sounding chatbot so regressions in writing ability aren't really a concern anymore if agentic benchmarks improve.
The first time I heard a recommendation to use Claude was specifically because it sounded much more "human" and natural than ChatGPT. Fast forward to now and idiosyncratic Claude-isms repeated every other sentence and its convoluted verbosity has become a widely mocked meme.
Right but we're talking about a single subject here - mathematics that labs are incentivized to keep improving for some time.
>e.g. If someone said "this is the worst they'll ever be" in response to some writing with obvious LLM cliches in 2024, I'm not convinced that prediction was actually correct.
2024 creative writing prose was...the last few versions have stalled, but I think they're still better than 2024.
I would describe better as how much of my work I can delegate to the agent. Right now I'm delegating much more to Astra high than 6 months ago to Opus 4.6. Every dev has this feeling, it's weird to even argue what a better model/harness means.
Chess is not solved in any meaningful sense of the term. Computers have been better than humans since the 90s, but better chess programs are released all the time.
It's solved in that we have had grossly superhuman capabilities for some time. It's not interesting for frontier labs. I suspect you understand this and the greater point so why be needlessly pedantic ?
We were told in 2023 that there’d be no more jobs within months and the singularity was here. At some point you have to realise it’s not happening.
Let me know when the other (much harder) millennium problems get resolved, let alone explained in a satisfactory way.
reply