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- Hacker News
- > “A big problem is AI is being used a lot by people who aren’t mathematicians, who don’t have a huge mathematical background and are not capable of verifying the output,” Bloom said. “They like to move fast, ask their AI to check it, it grows and grows. We’re seeing a lot more of these 100- to 200-page papers that people are posting. ‘I solved this theorem; I got AI to generate the proof and check the proof and write the paper.’ But no human has read it, and no human is going to read it. It’s a huge challenge now.”
Mathematics has the same problem as open source projects that are overwhelmed with AI slop!
- is probably a mix of other math papers that combined can solve this, the ingredients were already out there and they got trained with it.by m3kw9
- could be, I guess we'll see.
but even that, if done correctly, is quite impressive. It sure sounds very useful given the number of papers out there.
by ewidar - Because pattern recognition and deduction is automatable and LLMs are superhuman at low depth high depth problems. Nextby vatsachak
- It seems that AIs are really good at finding counterexamples now.
Even if progress by AIs in proving conjectures lags, it seems likely that AIs collectively will, in the next few years, find counterexamples to nearly all the Erdős (and other) conjectures that are actually false and also provably false.
That means we will able to assume that nearly all the remaining conjectures are either true or undecidable.
Surely, that's good for folks who just want to know where the truth boundaries in mathematics lie.
It's obviously causing a lot of soul-searching amongst professional mathematicians.
Arguably, they should have given less weight for the last 100 years to Hardy's view in 'A Mathematician's Apology' [0]:
> It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
Rota takes a much more balanced view in 'Indiscrete Thoughts' [1].
"Problem Solvers" take Hardy's view:
> ... The mathematical concepts required to state mathematical problems are tacitly assumed to be eternal and immutable. Mathematical exposition is regarded as an inferior undertaking. ...
While for "theorizers":
> Mathematical exposition is considered a more difficult undertaking than mathematical research.
If professional mathematicians can reinvent themselves, there will be plenty of work left to do to explain the results of AIs to other humans.
There probably needs to be a new career path into professional pure mathematics other than doing novel research in a PhD.
[0] https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
by delhanty - > That means we will able to assume that nearly all the remaining conjectures are either true or undecidable
I mean, we could. But it doesn't really make sense to think that AIs are perfect at finding counterexamples, just because they are good (or even better than us). My general opinion is that they are orthagonally intelligent, that is, they are intelligent in an entirely different way to the way that people are. They are undoubtably clever, but the distance between when they are better than us at their best skill (or even most skills) and when they are better than us in all aspects is going to be MASSIVE.
by RugnirViking - Counterexamples can be decidable and arbitrarily ugly or difficult to find. If you know anything about mathematics it's trivially simple things can yield extremely complex structures. And that can absolutely include terse conjectures whose solutions are in fact decidable but only with proofs that would consume more than a bit of memory for every particle in the universe. Not logically undecidable, but physically impossible to prove in our physical universe.
Further down the scale are ones that are decidable only by machines that we would never have the wherewithal to construct, even though they could physically be constructed with the material we have to work with.
by anzuhoeren - I'm not sure we should take it as a given that AI will not also become better than humans at mathematical exposition.by aesthesia
- Disappointing lack of "Why" in an article that starts with it.
Are they actually doing something new and novel, or are they just absorbing that "a=b as was proven in transcendental hyper-circular group theory; and b=c was proven in universal quantum superposition"; and they're the first to find the connection that a=c? And several of the problems are counterexamples, not novel proofs of correctness?
Its fascinating either way, but it'd be nice to actually understand more of what is happening.
- One of the recent problems was actually proven with elementary results. It did use a technique not usually applied to the problem space, but it wasn’t a hyper specialized result.by LPisGood
- something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives.
Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ?
Then we're going to enter a totally different world.
by bsaul - Not really. These same techniques fall flat on their face when applied to most physics and chemistry problems. All of academia has already been doing ML4Science for the last 8 years. God knows how many billions have been spent.
The only two major highlights are weather modeling and folded protein backbone prediction.
Mostly everything else, either lacks enough data, or there are contraits on the size of the foundational models that render them impractical or they just fail to generalize.
by numbers_guy - Those long standing math problems solution may serve as building block for solving the experimental science ones.
- For example, protein folding has been figured out by AI. This was a very big moment for science and yielded a nobel prize. Alphafold 1 happened 4 years before the first version of ChatGPT and the LLM craze we see today.
But yeah, most problems in physics, chemistry or biology require labs on top of actual hard thinking. You need to be able to design experiments in a certain way. Once you have the funding, the right tools, the right people to use those tools, then you can use LLMs to increase the speed of the calculations and so on.
There have been other discoveries though by deepmind: https://deepmind.google/blog/millions-of-new-materials-disco...
by est31 - It's hard to see problems in those fields falling at anywhere the same rate as math, because they are all experimental fields.
There may be some problems of type type "why does X happen?" that appear answerable in terms of known science, but even these would need verification. If you want to make advances in fundamental physics, then a promising AI-generated theory might take a decade and billions of dollars to prove or disprove.
Math is a rather unique field in being entirely theoretical, axiomatic and self-referential. It is basically the best possible case not just for AI to advance without needing experimental verification, but also specifically for today's AI technology of auto-regressive LLMs and RL training, whereby valid reasoning steps learnt in one context will also be valid in another context (i.e. there is some generalizability of learnt reasoning) as long as you have learnt the pertinent aspects of that context that the validity depends on.
- The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly.
I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
I often see comments that some of the users here long to "make a computer do neat tricks all day", and I can't help but think meager sponsorship could go a long way in this area. Existing grant structures, being much more traditional, are constrained by their cost.
- Honestly, I think our extremely liberal disability benefits scheme achieves this to a large extent (albeit possibly with downsides for both the recipient and society).
Look at all of the crazy stuff made by unemployed trans people/autists over the past decade, disproportionately from countries with strong welfare states.
by AussieWog93 - When Gwern needed a fellowship to come to SF he got one. When he had his “great idea” it was funded. The truly unique people out there find a way. Any government bureaucrat will just find the Jason Ardays of the world.by arjie
- > Though I admit his heart attack probably wasn't a coincidence, sadly.
He died aged 83...
by e4325f - > I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.
Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.
by qsort - Non-Erdős problems are also falling.
The AIs seem to have some combination of very broad familiarity with math (enabling relevant things from other subfields to be brought in to the proof) as well as patience and "sitzfleisch" (stamina in working through details even if they aren't immediately obviously promising.)
An obvious area for improvement would be automated generation of new conjectures and attempts to prove (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.
by pfdietz - Generating new conjectures is easy. It's generating novel conjectures that's hard.by CBLT
- When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound?
How can we possibly make use of these breakthroughs if we don’t understand them? How could we ever make anything useful with them?
Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands? How do we tell truth from fiction?
- I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?by the_sleaze_
- Mathematics is an unusually dense (if not the most dense...by a few large steps) field. So lots of areas of mathematics are extremely deep and narrow without any real shortcuts, even for seasoned mathematicians.by WarmWash
- The field has been dealing with this for a long time.
Since at least 2014, which was my first brush with the phenomenon when someone published a 13GB proof [0].
The consensus is that such a proof is potentially illuminating, though further work is likely required. If for instance, conjecture A is true if and only if conjectures B & C are true, and B is proven false through one of these such proofs, then we can see that A is also false given that we accept the disproof of B.
Though, the sense is that further work is likely required because it is easy to see that further work along the same direction, or in directions depending on the proof will be hard or impossible if there are not enough humans or agents that are capable of understanding and utilizing the proof. Making it 'more elegant' will increase it's utility despite not proving anything new.
This is adjacent to all of the work done to create multiple proofs using different techniques. Having the same information (that X is so) in different languages (algebraic, geometric, via harmonic analysis, etc) allows for researchers not familiar with the original technique to participate in further research.
[0] https://www.newscientist.com/article/1997488-wikipedia-size-...
by goodmythical - Latest presentation of Terence Tao on what current advancements in AI mean for math discusses (among other things) those issues: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...by tumdum_
- I think it's the scientist version of "I vibecoded ten apps this weekend (at one point I'll have real users too)".
Because it's math, it's all mysterious and genuinely impressive, but in the end, if no human cares about it (apart from attention grabbing "it's so over" tweets and articles), does it really matter?
by serial_dev - This seems like an extreme exaggeration from a few people claiming to not understand a very recent result. This cycle of a new result being discovered, and reaearchers needing some time to truly digest and disassemble it, is normal.by hgoel
- > When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
by eru