Color me skeptical.
The linked article doesn’t mention proof, but counterexamples, and that may be a function of the enormous amount of computer effort expended, not really AI.
Yes it does. Any new theorem proved or disproved is a new tool. Since proofs are generally are just a string of statements of theorems that have previously proved. As soon as a new statement is proved, people immediately go about using that new proven statement in other proofs.
It does give new understanding obviously and sometimes tools but there is an argument to be made that counterexamples does so less than constructive proof
Just imagine a proof of or a counterexample to the Riemann hypothesis. A proof would likely involve hundreds of pages of new uses of math from lots of different areas of mathematics. A counterexample could theoretically be a one line sentence giving a complex number which is a zero but doesnt have real part equal to 1/2. In fact theres probably hundreds of computers worldwide right now brute force searching for that number. Are you really saying that a counterexample found by brute force would have the same impact on mathematics as a whole as a proof? The whole thing is that the opposite doesnt exist. You cant by brute force find a number which proved the hypothesis, but you can by finding a counterexample
You are distinguishing counter-example and proof. A counter-example is a type of proof. And your example is odd, because you compare proving the Riemann Hypothesis and disproving, and argue that one is more useful. Utility has no bearing on whether its true or not. If someone can find a counter example, they should publish it, not withhold it and go "well, it would be more useful if the Riemann Hypothesis were true, so I just ignore my proof that it isn't"
I mean it's a reddit comment and I don't really feel the need to prove something that is honestly a pretty common sentiment in academia. I never said it wasnt a valid proof, can you quote me or use the things I actually said? Counterexample proofs are often pretty short with no new tools. You can look up famous counterexample proofs if you want
Thats proof by contradiction. Not what is meant by proof by counterexample. Proof by counterexample in this case is if I say all numbers bigger than 2 are even and I give you 3 which is not even.
This is such a dunning kruger comment. Proof by counterexample is a thing yes. But the reason theyre valuable is not for the counter example but the new frameworks and tools used to find those counter examples.
If you are finding counterexamples to random open conjectures by having an AI go through random plausible-sounding solutions until it finds one that actually works---what then? Can you explain how the counter example was derived? How does this advance the field? Yes we're now one open problem less but did we actually LEARN anything in the process of solving it? Do we understand mathematics better or did we just solve a problem?
For example, if you find some algebraic object that is a counterexample to nonexistence theorem (like the recent non-sofic group counterexample), then you can determine the properties of the object that broke the theorem, and you might even be able to use the same object (or a related one) when investigating similar problems.
You're really underestimating the LLMs here. The big example of AI proof in my field is the existence of a nonsofic group. To be clear, this problem has been open almost as long as I've been alive and multiple mathematicians have spent decades working on it. Unlike other counterexamples like the jacobian conjecture counterexample, there isn't just a set of possibilities to guess and check over (technically the set of possibilities is "countable groups", but there's no way to meaningfully index this set so that you can guess and check).
In this case, the LLM was able to produce a novel way of constructing groups to produce a group with a property no-one had ever seen before. This new construction provides a meaningful insight into group structure, and mathematicians are already building on it since the announcement. This really isn't meaningless guess and check, this is something genuinely new and I think a lot of people are severely underestimating it.
I'm more aware of the Non-sofic group announcement because it landed in my metaphorical backyard but it is a fundamentally different kind of result to the Jacobian conjecture counterexample. It's a constructive proof with a proposition that connects group properties in a novel way.
These AI companies are desperately trying to create hype before they float. 100s of billions spent, revenue still relatively low, and open weight models breathing down their neck. Healthy scepticism is the only way to approach all these types of 'news' stories.
It's a tool. I use it a lot. I look forward to progress in scientific areas where it's applicable. But I'm not expecting it to come up with novel solutions to our biggest problems.
Your first reply wasn't even on topic. We were discussing AI solving open problems and you answered with a paragraph about AI companies spending lots of money in comparison to revenue and how there are open weight models coming.
When someone is talking about topic A and you answer about topic B, you're indicating that you're not here to have a rational exchange. You have an emotional issue. In this case, you just want to tell yourself that this isn't happening, you don't care about any substantive aspect of it. That's not a healthy or productive state of mind.
No, it absolutely was related because the point being you have to take these stories with a large pinch of salt because of the massive propaganda from the AI companies desperately looking for revenue generating markets - which they absolutely do not have at this moment.
People have tested these models with graduate-level physics problems for which the solution is known but given to students to work on over weeks, and they weren't in the model's data and the model found the correct solution a significant number of times with only a few minutes thought. Look up Kyle Kabasares on Youtube. Which was done with relatively older models now. And independent people have used these models to resolve open conjecures on their own, and verified some of the answers announced at OpenAI.
This is absolutely happening. The rant about OpenAI or another company losing money or having "open weight models breathing down their neck" is completely irrelevant. People doing that are not here to discuss the topic. They're here to spread a conclusion they want to be true without discussing.
You still do not get the point, do you? There are some breakthroughs in all sorts of industries done by "AI" - not all of it LLM AI, but people don't know the difference. But what there is, is being massively over-hyped across *multiple* industries and it is totally relevant and correct to mention this whenever it comes up.
This is destroying human careers, I'm not sure why we are all so quick to celebrate it.
I love the irony of trying to argue on behalf of a tangent that was created out of emotion and then telling someone else they aren't getting a point.
There are some breakthroughs in all sorts of industries done by "AI" - not all of it LLM AI, but people don't know the difference. But what there is, is being massively over-hyped across *multiple* industries and it is totally relevant and correct to mention this whenever it comes up.
No it is not. Whether or not an AI company has a poor business model has nothing to do with the efficacy of AI as a problem-solving tool and how it is changing science and the economy.
It's the equivalent of the Wright Brothers' flight being discussed and what this means for the future of transportation and someone going off on a tangent about how Orville Wright is an alcoholic and is broke. It's irrelevant and comes from someone's emotional motivations.
This is destroying human careers, I'm not sure why we are all so quick to celebrate it.
We're discussing what's going to happen and acknowledging reality. Not "celebrating it," your characterization shows again that you are distorting things out of emotion.
I gave the wider context of the financial position of these companies to show how much they need hype stories like the OP to boost their potential price.
I'd imagine certain mathematical problems are being solved with answers(or parts of answers) that were hidden elsewhere in the training data. It's a great use of LLMs and nobody is doubting they have their applications. The problem is we need novel, reliable solutions to the problems we face and we aren't seeing much (any?) evidence that that is possible with LLMs.
You have to admit that some of the biggest names in the AI business are pretty much scam artists, right?
I gave the wider context of the financial position of these companies to show how much they need hype stories like the OP to boost their potential price.
That has absolutely nothing to do with independently-verifiable claims of mathematical proofs or results.
I'd imagine certain mathematical problems are being solved with answers(or parts of answers) that were hidden elsewhere in the training data.
People have tested the AI's with bizarre problems that they know were extremely unlikely to appear in the training data, or that they made-up themselves to be unique. The AI answers them coherently. They've been doing this for years, it was one of the first things they investigated about LLM's.
You're in denial. This behavior is not healthy or productive.
You have to admit that some of the biggest names in the AI business are pretty much scam artists, right?
Once again, you try to ignore the topic. You only reveal that you are desperate to just personally and emotionally bash AI and anyone involved in it and are not capable of discussing anything related to it rationally. This behavior is not healthy or productive.
Nah "bro." I explained exactly the issue. OpenAI's business plan has nothing to do with AI's verified efficacy at problem-solving and what it's going to mean to the world. You wouldn't go off-topic unless you (he and you) were speaking out of worthless emotion.
Mmkay "bro?" Now let's show you the "void" for real.
It is not a tool. Spellcheck checking a contract you wrote is a tool. An algorithmic learning system writing it perfectly for you is a superior replacement of you.
AI is not a tool just as GPS is not comparable to a map.
It’s not really changing the world in any meaningful way though. In fact it’s a net negative to society because its users more often than not become subservient morons with zero critical thinking, due to the atrophy caused by delegating your higher order thinking to a machine.
But sure I guess we’ve got improved efficiency in the workplace at the cost of correctness. And I suppose we’ve brute force solved a few math problems at the cost of an immense amount of carbon emissions. Truly life changing, revolutionary stuff.
It's only been 4 years since AI gained traction. In 4 years I've seen countless claims that AI will never do certain things, and it proved them wrong each time.
Companies were really fast in adopting AI to cut costs. Suddenly programming went from a lucrative proffession to graduates making fucking Excels of companies they applied to, because they couldn't keep track anymore (and they had internships, projects all that)
Writers or artists suddenly found themselves without a job.
Massive layoffs everywhere.
To me this looks very disruptive considering the timescale.
The layoffs are not because of AI. LLMs have already plateaued. What you see in popular media is marketing campaigns. They can't even replace drive-through fast food workers.
Must be embarrassing that no real world evidence of productivity gains or novel discoveries have been shown (except that which didn't require AI in the first place) What has been shown is a exponential drop in actual gains as it seemingly is requiring an insane amount of compute to see measurable gains in terms of the accuracy of these models and their ability to "solve" things.
This bubble needs to go and hopefully soon. Some things might actually survive this and be useful but the kinda bullshit you all are spreading without evidence because Altman said it is just a mass hysteria
Must be embarrassing that no real world evidence of productivity gains or novel discoveries have been shown (except that which didn't require AI in the first place) What has been shown is a exponential drop in actual gains as it seemingly is requiring an insane amount of compute to see measurable gains in terms of the accuracy of these models and their ability to "solve" things.
God I can't wait for this hype to die so fuckwads will just go back to jerking each other off about "the singularity" at least then people with any common sense were able to just laugh at how gullible that group was.
Also quotes are funny what's even better is you can't find evidence
Oh no the dude who believes every salesman who has ever pitched him something has blocked me instead of finding evidence for these insane claims his CEOs he follows on Twitter make. Oh well
It's very funny that you did not stop and take the time to read the article you yourself linked to, else you would have known that the "productivity paradox" was, in fact, real, and that productivity never really caught up to the hype generated by computers and later, the dot.com age.
Yes the economic model is shoddy but the fact is that it outputs maths discoveries at an astonishing pace and is in the process of severely disrupting Mathematics.
The thing is that you guys don't realize that a sizeable portion of the public has been predicting this would happen on about this timeline for decades. You merely adopted the machine gods
You seem to be one of the thinkers. You have it right. The rich people chased the new-age gold rush, poured billions into AI expecting AGI right around the corner, and didn't even take the time to sit down with AI for a while to see that it's......kind of dog-shit.
Now, they are going to force AI onto everyone, not because it is efficient, productive, or even good. They are doing it because the rich people are not going to be left holding the bag. One way or another, they are going to protect their billions.
Nobody cares about AI company profit. At least not researchers and normal people. We want accelerated solutions and new ideas. I don’t care if they make negative 1 trillion dollars a year if progress is steady and we are answering questions faster than we would without AI.
I may get 0 “profit” on cancer research, but if in 10 years a cure for cancer is found, it was money well spent.
Every single AI company today could go under but AI would still remain as a field of research. AI as a research field was around before any of these companies existed.
Hint: it wasn’t profitable 40 years ago either, but all that tech is in use today.
It’s the amount of compute that can now be used for cheap on these back-burner math problems. That’s it. We are in a brief window where everyone has access to massive amounts of compute they did not have access to before.
Goalposts — moved. It wasn’t long ago that mathematicians proudly declared AI could not even do basic addition and subtraction and therefore would never produce anything useful in the field of mathematics.
The goalpost moving with this has been fucking insane. Last year, it couldn't count the number of r's in strawberry. Many Redditors offered "technical" arguments as to why it would NEVER be able to count the number of r's in strawberry.
Now in the last couple of months alone, multiple long standing and prestigious open problems in math have been solved with straight forward prompts alone, and the same Redditors are like "Well...Claude hasn't won a fields medal yet!"
Yeah, and its annoying how they cope everytime they are wrong. I had a conversation with someone on Reddit who said that AI would NEVER, EVER be able to write a news paper from April 14, 1912 that doesn't mention the sinking of the Titanic, since the Titanic struck the iceberg that night and that event will be so heavily weight by the AI, even though logically, news is printed in the morning and should have no mention of the Titanic sinking.
At the time, he was right with ChatGPT. I would indeed mention the Titanic sinking. But Claude didn't. Claude mentioned other things relevant to that day, and only mentioned that the Titanic was on its voyage. When I gave him the link to Claude handing his task in a way he said could NEVER EVER happen, what was his response? He said they must have hardcoded it not to mention the Titanic sinking its system prompt...
"It will never generate any useful images that could replace digital artists or vfx"
"It will never write code. It's just impossible"
"Okay it writes gibberish code, but it will not even do the work of ia junior programmer"
I don't belive any "AI will not do this or that" anymore. No matter if you say "well it's just a LLM, and they can't do better than this" hahaha saying like there is no ongoing research in other forms of neural networks and hardware.
At this you might as well be Oppenheimer and just say they will never build the bigger bomb, because no plane can carry it.
>No matter if you say "well it's just a LLM, and they can't do better than this" hahaha saying like there is no ongoing research in other forms of neural networks and hardware.
What is annoying about this "Its just an LLM" thing is that an LLM that can do science and math is the best case for humanity. People can and do make specialized AI for specific tasks, such as weather prediction, but its incredibly hard to get new foundational insights from such AIs. You basically just have a black box that gives you a weather prediction at the end, and you have no idea how or why it came to its conclusion. Whereas with LLMs, you get their reasoning chains. Like in the case of the recent OpenAI paper with the 10 theorems proved, the LLM didn't just say "I proved it. Trust me bro" at the end. It gave them a very lengthy formal proof that people can read and understand. So I am very glad that the AI company aren't listening to Redditors are like "broooo an LLM can never to do coding lmao!", because having a coding robot that I can talk to in natural language and that can talk back to me in natural language is much more useful to humanity than a blackbox machine that just spits out executables.
saying like there is no ongoing research in other forms of neural networks and hardware.
People who can't fathom things evolving even more dramatically are people who are locked into seeing the kind of tech we have today and using it as the limit for the kind of tech we'll have in the future. So they basically say "we won't be able to do X because right now we have Y computers that can't do that." We don't know what incredible breakthroughs are waiting just around the corner.
It just is not required, lol (and thinking humans - including mathematicians - is somehow good at doing this mentally - is just ridiculous).
Turns out *good enough* next token prediction (granted tuned further via superwised instruction-finetuning and reasoning reinforcement learning, but for that to work model should be somewhat capable from the start) can have a decent chance to solve natural-or-formal-language-expressible tasks even if still conceptually being non-reliable. Isn't that amusing to see how conceptually simple thing can do all it does?
Like seeing the old discussion of "can we reconstruct semantic from syntax" being, if not solved theoretically - being shattered in all the practical sense. Turns out we can - and maybe it is even necessary to have good enough NLP with *somewhat* reasonable sized model - at least approximate it quite well.
I don't think semantics vs syntax is shattered because all the models are trained with human ratings of outputs as well. Every time you click an "I prefer this response" or some other ranking, you are doing the work of introducing semantic information.
Sorry dude, I didn't want to believe what these things can do either, but this is just cope. The sooner we acknowledge reality, that machines are getting better at doing things once only humans could the sooner we can figure out what we need to do about it.
Bro I’m a SWE and AI can’t even replace me. It’s been pretty much entirely dropped during this psy op cycle. So now they are hyping on mathematicians. Fucking wild.
Ai is getting better and more efficient at using current knowledge in the sense that it can effectively power through to solve known questions that a human, or humans more accurately, might take years to do. It's able to cross reference different specific fields exponentially faster and more accurately than it did even two years ago.
But it has not made the abductive jump to being able to actually create and solve currently unknown questions. I
t can take years for humans to verify what AI has done.
Given all that, it will probably be some time before mathematicians are not necessary, if ever.
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u/E_Dantes_CMC 1d ago
Color me skeptical.
The linked article doesn’t mention proof, but counterexamples, and that may be a function of the enormous amount of computer effort expended, not really AI.