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Can AI do maths yet? Thoughts from a mathematician

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Re: Can AI do maths yet? Thoughts from a mathematician

#131

Post by lupire »

red75prime wrote: post #85
voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

> there is no reason to believe a connection between the mechanical model and what happens in organisms has been established The universal approximation theorem. And that's basically it. The rest is empirical. No matter which physical processes happen inside the human brain, a sufficiently large neural network can approximate them. Barring unknowns like super-Turing computational processes in the brain.

That's not useful by itself, because "anything cam model anything else" doesn't put any upper bound on emulation cost, which for one small task could be larger than the total energy available in the entire Universem

Re: Can AI do maths yet? Thoughts from a mathematician

#132

Post by upghost »

optimalsolver wrote: post #123
upghost wrote: post #119

Earlier quoted context omitted.

Insightful comment. The thing that's extremely frustrating is look at all the energy poured into this conversation around benchmarks. There is a fundamental assumption of honesty and integrity in the benchmarking process by at least some people. But when the dataset is compromised and generation N+1 has miraculous performance gains, how can we see this as anything other than a ploy to pump up valuations? Some people…

It's sadly inevitable that when billions in funding and industry hype are tied to performance on a handful of benchmarks, scores will somehow, magically, continue to go up. Needless to say, it doesn't bring us any closer to AGI. The only solution I see here is people crafting their own, private benchmarks that the big players don't care about enough to train on. That, at least, gives you a clearer view of the field.

Not sure why your comment was downvoted, but it certainly shows the pressure going against people who point out fundamental flaws. This is pushing us towards "AVI" rather than AGI-- "Artificially Valued Intelligence". The optimization function here is around the market.

I'm being completely serious. You are correct, despite the downvotes, that this could not be pushing us towards AGI because if the dataset is leaked you can't claim the G-- generalizability.

The point of the benchmark is to lead is to believe that this is a substantial breakthrough. But a reasonable person would be forced to conclude that the results are misleading to due to optimizing around the training data.

Re: Can AI do maths yet? Thoughts from a mathematician

#133

Post by voidhorse »

gmadsen wrote: post #98
voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

I hear these arguments a lot from law and philosophy students, never from those trained in mathematics. It seems to me, "literary" people will still be discussing these theoretical hypotheticals as technology passes them by building it.

I straddle both worlds. Consider that using the lens of mathematical reasoning to understand everything is a bit like trying to use a single mathematical theory (eg that of groups) to comprehend mathematics as a whole. You will almost always benefit and enrich your own understanding by daring to incorporate outside perspectives.

Consider also that even as digital technology and the ratiomathimatical understanding of the world has advanced it is still rife with dynamics and problems that require a humanistic approach. In particular, a mathematical conception cannot resolve teleological problems which require the establishment of consensus and the actual determination of what we, as a species, want the world to look like. Climate change and general economic imbalance are already evidence of the kind of disasters that mount when you limit yourself to a reductionistic, overly mathematical and technological understanding of life and existence. Being is not a solely technical problem.

Re: Can AI do maths yet? Thoughts from a mathematician

#134

Post by mensetmanusman »

hash872 wrote: post #108
mensetmanusman wrote: post #103

Earlier quoted context omitted.

The reason why this is so disruptive is because it will effect hundreds of fields simultaneously. Previously workers in a field disrupted by automation would retrain to a different part of the economy. If AI pans out to the point that there are mass layoffs in hundreds of sectors of the economy at once, then i’m not sure the process we have haphazardly set up now will work. People will have no idea where to go beyond…

If there are 'mass layoffs in hundreds of sectors of the economy at once', then the economy immediately goes into Great Depression 2.0 or worse. Consumer spending is two-thirds of the US economy, when everyone loses their jobs and stops having disposable income that's literally what a depression is

This will create a prisoner’s dilemma for corporations then, the government will have to step in to provide incentives for insanely profitable corporations to keep the proper number of people employed or limit the rate of layoffs.

Re: Can AI do maths yet? Thoughts from a mathematician

#135

Post by aiono »

amelius wrote: post #125
jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

Don't most mathematical papers contain at least one such error?

Where is this data from?

Re: Can AI do maths yet? Thoughts from a mathematician

#136

Post by GuB-42 »

glimshe wrote: post #27
jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

Isn't Wolfram Alpha a better "ChatGPT of Math"?

Wolfram Alpha can solve equations well, but it is terrible at understanding natural language.

For example I asked Wolfram Alpha "How heavy a rocket has to be to launch 5 tons to LEO with a specific impulse of 400s", which is a straightforward application of the Tsiolkovsky rocket equation. Wolfram Alpha gave me some nonsense about particle physics (result: 95 MeV/c^2), GPT-4o did it right (result: 53.45 tons).

Wolfram alpha knows about the Tsiolkovsky rocket equation, it knows about LEO (low earth orbit), but I found no way to get a delta-v out of it, again, more nonsense. It tells me about Delta airlines, mentions satellites that it knows are not in LEO. The "natural language" part is a joke. It is more like an advanced calculator, and for that, it is great.

Re: Can AI do maths yet? Thoughts from a mathematician

#137

Post by dns_snek »

fn-mote wrote: post #72
4ad wrote: post #57

> FrontierMath is a secret dataset of “hundreds” of hard maths questions, curated by Epoch AI, and announced last month. The database stopped being secret when it was fed to proprietary LLMs running in the cloud. If anyone is not thinking that OpenAI has trained and tuned O3 on the "secret" problems people fed to GPT-4o, I have a bridge to sell you.

This level of conspiracy thinking requires evidence to be useful. Edit: I do see from your profile that you are a real person though, so I say this with more respect.

What evidence do we need that AI companies are exploiting every bit of information they can use to get ahead in the benchmarks to generate more hype? Ignoring terms/agreements, violating copyright, and otherwise exploiting information for personal gain is the foundation of that entire industry for crying out loud.

Re: Can AI do maths yet? Thoughts from a mathematician

#138

Post by busyant »

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete?

But I'm wondering what other people think of this analogy.

I used to be a bench scientist (molecular genetics).

There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's".

Nevertheless, I still moved the field forward in my own small ways. I still did respectable work.

So, will these LLMs make us completely obsolete? Or will there still be room for those of us who can dot the "i"?--if only for the fact that LLMs don't have infinite time/resources to solve "everything."

I don't know. Maybe I'm whistling past the graveyard.

Re: Can AI do maths yet? Thoughts from a mathematician

#139

Post by pixl97 »

lupire wrote: post #131
red75prime wrote: post #85

Earlier quoted context omitted.

> there is no reason to believe a connection between the mechanical model and what happens in organisms has been established The universal approximation theorem. And that's basically it. The rest is empirical. No matter which physical processes happen inside the human brain, a sufficiently large neural network can approximate them. Barring unknowns like super-Turing computational processes in the brain.

That's not useful by itself, because "anything cam model anything else" doesn't put any upper bound on emulation cost, which for one small task could be larger than the total energy available in the entire Universem

I mean, that is why they mention super-Turning processes like quantum based computing.

Re: Can AI do maths yet? Thoughts from a mathematician

#140

Post by exprofmaddy »

voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

I'm with you. Interpreting a problem as a problem requires a human (1) to recognize the problem and (2) to convince other humans that it's a problem worth solving. Both involve value, and value has no computational or mechanistic description (other than "given" or "illusion"). Once humans have identified a problem, they might employ a tool to find the solution. The tool has no sense that the problem is important or even hard; such values are imposed by the tool's users.

It's worth considering why "everyone seems all too ready to make ... leaps ..." "Neural", "intelligence", "learning", and others are metaphors that have performed very well as marketing slogans. Behind the marketing slogans are deep-pocketed, platformed corporate and government (i.e. socio-rational collective) interests. Educational institutions (another socio-rational collective) and their leaders have on the whole postured as trainers and preparers for the "real world" (i.e. a job), which means they accept, support, and promote the corporate narratives about techno-utopia. Which institutions are left to check the narratives? Who has time to ask questions given the need to learn all the technobabble (by paying hundreds of thousands for 120 university credits) to become a competitive job candidate?

I've found there are many voices speaking against the hype---indeed, even (rightly) questioning the epistemic underpinnings of AI. But they're ignored and out-shouted by tech marketing, fundraising politicians, and engagement-driven media.

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