Genuine question, from someone with a non-math background - at what point does the constraint become the number of unsolved conjectures remaining, instead of the ability for LLMs to actually solve for one?
Ten advances in mathematics and theoretical computer science
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Re: Ten advances in mathematics and theoretical computer science
#892Re: Ten advances in mathematics and theoretical computer science
#893Genuine question, from someone with a non-math background - at what point does the constraint become the number of unsolved conjectures remaining, instead of the ability for LLMs to actually solve for one?
Not entirely following the question, but there are an infinite number of conjectures, the blinding majority of which serve nearly no purpose to humanity. Consider that for every executable program one could create a conjecture, and therefore a mapping exists from executable programs to conjectures. Now, consider the infinite possibility space of executable programs…
Anyway, unless you mean conjectures that humans have already posited, or ones that are particularly famous, that list is much shorter, but also contains conjectures that I’m not convinced can be solved before the heat death of the universe using all available compute power. P != NP is a conjecture, for example. Also a lot of prime number conjectures that are extremely computationally expensive.
Re: Ten advances in mathematics and theoretical computer science
#894Earlier quoted context omitted.
> 8. Do they reduce the workweek Sure. Often to zero.
I'm talking statistically, not what happens for a lucky few. Keynes was hoping that our workweek would be 20h/week by now, through technological advancement. Instead places like the US are thinking about adopting 9/9/6 and some US states are legalizing child labor again.
> what happens for a lucky few.
I'm talking about the unlucky.
Re: Ten advances in mathematics and theoretical computer science
#895Earlier quoted context omitted.
you are working on coding. they are working on things like "creative writing" remember that gpt 4o was popular among those who had ai as a romantic partnet?
Well that's on purpose lol. OpenAI does not want you falling in love with their chatbot and have been deliberately training it to be less romantic.
sure they do if it makes them money, probably just not worth the controversy right now
Re: Ten advances in mathematics and theoretical computer science
#896Earlier quoted context omitted.
How do I directly benefit from this supposed "growth"? Seems like its just making things worse for most people.
Plenty of people are making money from AI? And I am not sure I've seen it "making things worse for most people" yet, do you have a source behind this? If your source is AI layoffs, there were plenty of layoffs with the invention of the horseless carriage, but that doesn't mean it made humans worse off overall. There are reasons to be skeptical about progress and AI and all that but the 'making things worse for most p…
most devs i talk to say that they would love to go back to coding without ai, if everyone had to do it, so there's that. Oh also scammers have gotten so much better with llms, so a significant amount of peoples lives are worse due to that
Re: Ten advances in mathematics and theoretical computer science
#897People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…
Yes, the rate and nature of the results being produced is impressive, and Anthropic have recently invested in building out more in-house capability to do life sciences research (see e.g. [1]).
Overall I'm excited for this acceleration in discovery, even if it's causing disruption to existing research workflows. I wrote a bit about it recently [2], after seeing Levent Alpöge's counterexample to the Jacobean conjecture.
[1] https://www.cnbc.com/2026/06/30/anthropic-launches-ai-drug-d...
[2] https://scholarlyfutures.substack.com/p/frontier-models-tran...
Re: Ten advances in mathematics and theoretical computer science
#898People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…
Yes, the rate and nature of the results being produced is impressive, and Anthropic have recently invested in building out more in-house capability to do life sciences research (see e.g. [1]). Overall I'm excited for this acceleration in discovery, even if it's causing disruption to existing research workflows. I wrote a bit about it recently [2], after seeing Levent Alpöge's counterexample to the Jacobean conjecture…
Life sciences will get way more interesting once Demis Hassabis completes his simulated cell and we have more genomic foundation models
Re: Ten advances in mathematics and theoretical computer science
#899Earlier quoted context omitted.
Another interesting question is why the frontier labs are piling on pure maths, which has little direct economic value compared to something like law or improving the efficiency of their own models? How much OpenAI and Anthropic are paying to serve these models for ordinary users is the elephant in the room. A cynical take is that the frontier labs are trying their best to pump up their pre-IPO valuation through flas…
> Another interesting question is why the frontier labs are piling on pure maths The reason is that the original scaling axes (parameters, training tokens, test-time compute) have saturated already, but RLVR (reinforcement learning from verifiable rewards) is still scaling well. And math has this nice property where you can synthetically generate arbitrary volumes of rewards to train the model, because math is self-c…
do we have any concrete idea of how well the models are scaling now? I agree with these 10 results being impressive, and it is easy to think "wow, and last year the models were barely able to solve IMOs problems". But for me it is perfectly possible that a non sofic group could be found by 100 good IMO students working on all the different strategies that have been proposed (OpenAIs solution was based on "expander graphs", which were introduced to solve the problem some years ago), so it could be that current AI is simply many (say 1000) old models working in parallel. This is linear scaling, not exponential. It could be I'm completely wrong also, the problem is that we have little information.
Re: Ten advances in mathematics and theoretical computer science
#900Earlier quoted context omitted.
Cambridge Analytica gathered data to build targeted profiles and used these profiles for political advertising without informed consent: https://en.wikipedia.org/wiki/Facebook%E2%80%93Cambridge_Ana...
Yes, but there is little evidence this had a meaningful effect on votes.
Don't think that it matters if it was effective.
There's a reason attempted murder is a crime even if it was unsuccessful