As a developer (it sounds like), you were probably never even a drop in the bucket dumped into the ocean of the proprietary software market. Most people don’t want to change their own oil.
I'll personally pay (and do pay) for good development tools. I prefer free software tools primarily due to ethical and philosophical reasons (and I also want my code doesn't depend on any tool which can't be obtained in the future), but I have a couple of non-blocker, high quality, yet closed source tools in my arsenal.
> Initial Members of the Advisory Group on Mathematics and Artificial Intelligence (opens in a new window), hosted at the Institute for Advanced Study (opens in a new window):
Martin Hairer signed the Fields Medallists' letter and is in the advisory board. Camillo De Lallis and Ravi Vakil both endorsed the letter and are also on the advisory board. I'm not sure what "incentives" you're talking about.
You had me until the last part. There are obvious incentives to avoid (and advertise avoidance of) signing a paper that some perceive as hostile to OpenAI in exchange for remaining in consideration for a prestigious post endowed by OpenAI. If you "not sure" about those, then you're being quite generous.
Also there is some instinctual understanding of the work moving a big heavy rock takes, and how to do it. No such corollary for algebra and hence some civilizations never discovered or understood it.
I also agree with the parent, and I would also suggest "hallucination" is better than "error" which might imply an available deterministic correction. Hallucination makes it clear we're dealing with something different than an "error" or "bug".
For humans hallucinations are a particular class of error, so I find hallucination more descriptive than either error or bug.
I also think it’s relevant because a hallucinator often doesn’t recognize that the hallucination isn’t real. That’s more accurate for the LLM than either lie or confabulation, IMO. They algorithm is trained to produce strings of text that have semantic meaning based on some statistical likelihood of tokens appearing next to each other. The LLM algorithm is working as intended.
Hallucinations are also often emergent from a particular state or situation, which reflects the generative aspect of LLMs.
Hallucinations are sometimes resolved in humans by grounding exercises. “Touching grass.” The same is true for LLM hallucinations. Inaccuracies are found by cross-checking the output against an internet search or another LLM.
I disagree, for me "error" is way, way more accurate than "hallucination", but i did take applied statistics in college and that might have influenced my vocabulary. Maybe that for the general public, "hallucination" is a better description, i might have biases in this case. But "error" is _definitely_ more accurate.
If people want to call "drisse", "aussière", "balancine" and "ecoute" all as "boat ropes", they are correct. In english, i would certainly call them all "boat ropes" in any case, as i never needed to translate their names. It isn't the most accurate in my opinion, but as long as you're not working on them (or manning a boat in my analogy), who cares.
> Of course I know that the original (real estate) developers did the cost analysis, but when you see those abandoned places - very much objectively you can conclude that they made an error. A miscalculation, or an error in judgement.
Or just a good bet that didn't pay off when textile manufacturing all went to Asia?
Max Junestrand has consistently said Legora treats the model layer as swappable, selecting across frontier providers rather than building the product around one.
OpenAI didn't need to name Legora and Harvey in the second paragraph of the launch post.
They are pre-empting the obvious interpretation of Astra for Law: that moving this far up the legal stack puts them in direct competition with their biggest legal AI customers.
“Don't worry, they can build on us” is a pretty conspicuous message to include on launch day.
They have clearly thought about some pessimistic outcomes.
>Max Junestrand has consistently said Legora treats the model layer as swappable, selecting across frontier providers rather than building the product around one.
Vendor-neutrality for LLMs is such a weak thesis all around, whether for providers or consumers. It weakens the product by being promiscuous and gains no material benefit at all.
LLMs are magic byte(byte) functions, it doesn't make sense to say "we have different providers for magic".
Different flavors of magic require different ritual components and in the name of all that is stable and production worthy, please don't get a necromancer to do your civil construction magic.
Vendor-neutrality helps reduce lock-in, and OpenAI and Anthropic are big enough that the reduction is valuable.
Switching from ChatGPT Enterprise to Legora at my firm was a godsend, it's so much better for legal work, even with the frequent changes to the underlying models.
They are cutting into their market. They can dress it up however they want, they might not be competing for enterprise contracts yet (hence the fluff statement), but they will.
Yeah, it should be freely available, you have to be able to know the rules you're supposed to obey in order to obey them well. I've been making a free API for US law search, you can point whatever model you want at it: https://law.agentlookups.ai/
Very much a work in progress, only federal and state so far, no municipal codes yet, and no case law yet. Big hole, I know. Also working on making the search ranking work better.
Right now it's just a bunch of crawlers for the individual states. If there's interest, I could periodically stand up snapshot torrents or something. That something you'd be interested in?
Alternatively, if someone else knows an all-in-one option that exists, I wouldn't mind retiring those crawlers...
Not op, but that's a very interesting proposition. While the law and legal code are technically property of the people, I'm not aware of any single point of download for it all.
There’s no single point of download for it all because there’s thousands of autonomous entities that issue law and adjudicate cases, at least 51 of them distinct sovereign entities.
We could enforce (suggest?) a common format / api at the federal level. Especially if it’s incentivized with funding that more than justifies the cost of maintenance. Similar to how federal interstate funding is only available to states with a 21+ drinking age.
Yeah, going to the courts and municipal code seems like it's going to be a heavy lift. Many of them seem to hang off of municode, though, so maybe it's not a huge number of unique crawlers.
There is none, not for statutes and definitely not for case law; even at the appellate level where you have multiple federal circuits, then 50 states, then territories, military, tribal and a whole host of other niche courts. And the appellate court systems can be split into districts, and by lower and higher levels.
Then if you want to really get into it, The People should also be able to access trial court level, and at that point you have over 3000 distinct court systems with their own access systems, usually requiring logins and CAPTCHAs, and half of them not even having anything accessible online at all, and the other half only having recent stuff online and the rest rotting in a flooded basement.
That’s awesome! I especially like RECAP as a method for freeing things from PACER.
Seems like you all are already doing a lot of what I’ve been aiming for with mine. Are there useful ways to contribute, or have you all gotten it to a pretty good place technically, and it’s mostly a matter of spreading it at this point?
> By using the legal search index, Astra for Law can search U.S. case law, statutes, regulations, court rules, and administrative decisions across a corpus of more than 230 million URLs, with sources added daily. Our work with Free Law Project, the nonprofit behind CourtListener, brings its case-law collection covering more than 99.9% of published U.S. precedential case law (opens in a new window) into this research experience.
CourtListener already has an MCP interface and Grok is quite good at pulling from it. In my experience, Grok 4.6 is quite good at analyzing legal cases and human-written documents. Better than Opus 5. I'm not sure if it's better than Fable 5.1 on that task, b/c I'm not willing to spend my precious Fable tokens on case law searches lol.
the thing is a lot of the legal work which will go through this is drafting 100 and 1 variations of draft versions of standard contracts not containing any trade secrets where the contract can be drafted with "replacement/place holder names"
the kind of work mostly done by juniors not yet through their final exam and other "non" lawyers etc.
so it's a slippery slope of "lets just use it for <this> things where it doesn't matter" and then out of laziness and convenience it creeps into all the other places (at least for drafts).
> With that interpretation, the issue becomes slightly different: is it more important that the collective understanding of the mathematical community should be as advanced as possible or that there should be answers to as many problems as possible? Or are those two aims valuable in different ways, so that there is no point in declaring one of them more important? Or are they so inextricably linked that it makes no sense to argue that one is more important than the other? And when we say “important”, for whom are we saying it is important: for mathematicians, or for society as a whole?
This is easy to me. Truth should be the North Star. If there is a fundamental truth that can be found via mathematics, then the shortest route to that truth should be preferred. While LLMs are definitely capable of solving problems in search of truth, I agree with Tao that instant "true/false" results threaten to short-circuit the traditional avenues we have used to escape local minima in the search for truth. Their products may be the junk food that provides immediate satiation in exchange for long-term health. Perhaps it's wrong, though.
I think it is easy to just roll of a local maximum, however, you may get stuck in a local minimum.
I kid, of course, but I do wonder where the use of local "maximum" comes from, what is maximum there? Why do you not see this as a landscape of hills and valleys where marbles with certain energies may indeed get stuck in deep enough holes... Of course, I just assume and picture gravity pointing down in that landscape, but hey. I'm human, I feel it is expected of me.
There's some interesting stuff in a book on Katathymic Imaginative Psychotherapy where patients are asked to picture a mountain. As far as I remember it's about using the process as diagnostic tool. What does the mountain look like? Is it a steep rising, rugged massif or a shallow hill. Are you looking up, do you picture yourself climbing it, or are you on it's top etc. While it said that it's always a contextual matter and in the conversation there was a suggestion of imagining to climb the steep massif, being potentially related to narcisim. Whenever I think of it i associatr that with casper david friedrichs painting.
This pattern of argument keeps repeating in every place.
Pro tech people: technology removes bottlenecks. Sometimes we use those bottlenecks as a side effect to build muscle and so on. But removing bottlenecks gives us much higher degrees of freedom. It is up to us to coordinate and make use of the technology.
Anti tech people: bottlenecks are fundamentally useful. They should remain and technology shouldn't remove those so easily. Humans cannot coordinate as well when the bottlenecks are removed, so lets not remove them so quickly.
>It is up to us to coordinate and make use of the technology.
1) Coordination is hard, and 2) "us" is a hopelessly nebulous term that appears inclusive but is almost always exclusive.
I think people would have said the creation of social media platforms like Facebook was neither good or bad, but rather it was "up to us to coordinate and make use of".
But did our society really have a say over how Facebook and other social media sites were able to embed themselves in our everyday lives? I would argue the answer is no.
Its not a conspiracy. Its 25 fields medalists who think exactly like how I put it. Ideally, they can just take whatever the technology gives as soon as possible and use it. They don't want it because they don't think the community can rearrange and coordinate such that they can make use of the new found degrees of freedom.
That's literally all there is to it - they don't believe in the rearrangement.
I don’t think the letter is even anti-tech progress. I also don’t think the tech companies are primarily pro-math progress (not that I think you think that). It’s primarily “anti-unnecessarily-destroy-the-human-systems-of-mathematics-just-for-benchmarks-and-marketing”
> … the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned.
Counterpoint: I'm not anti tech at all. In fact, I sell an AI harness for legal.
I think you've set up a false dichotomy. I'd propose to you the middle ground that a lot of us are concerned that VC-backed AI slop is "solving" problems in indigestible ways that hollow out the core. This applies in OSS as well as mathematics.
Please help me understand this and I'm asking this in good faith.
Why can't OpenAI publish whatever it wants. And the math community can use it or not use it. Fundamentally OpenAI's solutions are high signal - they are incentivised to not deliberately mislead people. Let the individuals in math community choose to read it or understand it? If OpenAI wants to publish something, let them do it in the current channels using peer review using whatever time is required.
What's wrong with this? The math community thinks this will destroy previously unwritten ways of prestige allocation and remove incentives that used to exist. I say that the community can rearrange and allocate prestige and time in different ways to maximally use the technology.
>Why can't OpenAI publish whatever it wants. And the math community can use it or not use it.
The "math community" is not an isolated entity that is free from the confines of society. It's made up of lots of people who coexist in a system that requires you to assert your right to live.
Furthermore, the "math community" is overwhelmingly supported by outside donations to keep it running. That's not to say people don't practice math for the fun of it, but that if you're researching problems like Navier-Stokes, you almost certainly are being paid by another party to do so. But those parties may hold new forms of technology over the professional mathematicians head in the name of "productivity", or they may even believe in light of this tech that paying a human to practice math is no longer worth it.
Therefore, mathematicians find themselves coerced by the market to adopt new tools in order to get by, even if the mathematical community largely finds it distasteful.
It feels like the scene from Blazing Saddles where Mel Brooks' character says "We've got to protect our phony-baloney jobs, gentlemen."
If the math community was previously not entirely aligned with what society was expecting, and these changes threaten that previous arrangement, that sounds like a "you" problem for math, not a problem for OpenAI.
If they can't align with society's needs and demands then some creative destruction is coming their way.
Well said. It’s on them to adapt. They make it look like it’s society’s problem (which it is) but also put the ball on OpenAI’s court which it shouldn’t.
Next time you devote 20 years to developing the skills to further humanity only for an unethical group of people to replace you with a stolen version of your work let’s talk.
They can use the new proofs as foundations for future proofs.
But many folks just won't be motivated to attack or help digest solved problems because there's less extrinsic value in doing so. Tao and others argue that it's this human effort that finds human-relatable abstractions which spurn further investigation. Take the humans out of the loop, and they'll stay there, is the argument as I understand it.
I read this multiple times and also recollected the original letter. You can’t really blame me for thinking this is a straaaange request.
“Don’t help me solve my problems because it removes the incentive to be in this field” is how I hear it. Honestly.
I would say the incentives HAVE to change because of new found capabilities.
Imagine accountants asking companies to reconsider producing calculators because we used to value accountants for how well they did arithmetic!!
Edit: my main point is that the math community has full agency to do what it wants with new found tech. Instead, asking to change external entities like OpenAI to be careful with releases is a strange thing to do. Why not change yourself and adapt?
You're describing an improvised surgery on a living organism. Developing a complex system involving humans that is productive and doesn't collapse is extremely hard, so if it ain't broke don't fix it.
Might have to do with the circumstances of Open AIs conduct that was quite sketchy to say the least?
There is 25 people who see it as their responsibility to use their status in the field of maths to weigh in on public discourse regarding that field.
Fields medalists aren't made on some Fields factory. These are 25 people from different backgrounds, generations, educational institutions and countries. It's kind of incredible you guys think they decided to collude against OpenAI rather than simply addressing a concern about their field they believe is important.
Never said they were colluding. I said I have no patience for incumbents asking for restrictions on a technology that threatens the value of their expertise.
The Math community can "not use" a proof? How would that work? It's a little like coloured functions (async etc) - you have 'human proved' vs 'machine proved'?
I'm pointing out that the way Mathematics works as a discipline is that a new proof builds on existing proofs. If we have a bunch of machine-generated proofs, then a human Mathematician has to decide whether to reference any relevant machine proof that has been put out there.
If, as you suggest, human Mathematicians 'choose to ignore' a machine proof, then another human decides not to, what then? Mathematics bifurcates into 'pure human' proofs and 'mixed machine-human' or maybe 'pure machine'?
Consider that 'calculator' used to be a title for a role a human used to do. That went away, which is probably fine as there were other jobs and likely it was tedious.
Then consider that "just adapt" could be "adapt or die", and that maybe, just maybe there is no way to adapt to well-funded corporations churning out millions of proofs a minute.
I don't know, maybe AI companies have "agency" to not break everyone else's stuff, just to get more funding and a higher share price?
The way you get out of a local maximum is to force yourself to try something radically new every so often, even if what you were doing before was working just fine.
This is the 'stochastic' part of 'stochastic gradient descent,' and it's as important for human minds as it is for ANNs. These math wizards seem to be stuck in a rut of their own digging.
This isn’t true, as there are plenty of things proven beyond reach.
And plenty of things, eventually solvable, can create major problems that could both be avoided and the problem solved by taking a much better path.
Having technology and the ability to safely and sanely use the technology needs to progress together at a similar rate. The failure to do this is even a reasonable and common solution to the Great Filter. Jared Diamonds book “Collapse” has ample examples of cultures that wiped themselves completely out via not having this balance, so it’s not simply a theory.
as a society of researchers we've tended to cultivate pretty effective strategies for escaping local maxima. I think of it like ants, where you can see if you place an obstacle in between their nest and a foot source, they develop a path that loops around it. if you remove the obstacle, for some time they continue to follow the old looped path. However, some ants deviate and go around at random, exploring. eventually by chance one happens to find a quicker route. he gets a couple of his friends to follow him, by pheremone, and over time more and more take the quicker route, and they end up abandoning the old route
It works this way with research, with most following the current trends, and some curious souls searching around for other ideas, be they contrarians, dreamers, or just convinced of some strange truth. But if we're right, signs tend to slowly begin to point their way, and we can shift the whole hulking edifice of science towards their point of view.
The problem of llms is that while they may be able to find a shorter route, we can't follow them unless we understand the route. So the forces that slowly begin to change everyone's behavior are lost
The letter is not incompatible with “pro AI in math” unless one thinks arguing against extreme behavior such as corporations using millions of dollars to scoop results makes one “anti AI”, which is not a reasonable stance in my opinion.
> AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.
You can say it about becoming collectively overdependent on any technology. And I think there's a good case to be made that a similar phenomenon is true for other technologies e.g. over-reliance on (normal) computers has done similar things in my opinion, at least in my field of physics, where you get a more precise result but much less insight.
It is getting a lot harder for those people to justify using OpenAI to assist such endeavours. Afterall, OpenAI might just front-run you if they hear a rumor you solved some marquee problem that they can brag about in PR campaigns.
What do you mean by "fundamental truth"? If LLMs produce a collection of proved facts this doesn't sound like what I would call fundamental. It may be the case that there is no such thing as "fundamental truth", that the world is just a blizzard of facts, but in that case we would need to give up on using it as a guiding star.
Another trick is to arrive early and try to talk to as many people before hand as possible. They’re your allies during the talk—they’ll stick around and root for the person they met.
Same weights, same seed, same input tokens, same algorithm, same output tokens, probabilistic or not. Quantum effects have been de-noised, but I guess there are still random gamma rays.
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