> Please do not ask the LLM to break the universe :)
Eh, every school db should be able to service a student called "Robert'); DROP TABLE Students;--", and every public facing LLM should still work even if asked to calculate the last digit of pi - that fulfills two noble purposes: 1) is fun and teaches whoever is responsible for the service some valuable lessons in craftsmanship or 2) if the service is built robustly (i.e. simple token limit and time limit per user), that's an easy way to gain street cred
> If this turns out to be true I think my take above is not correct, in the short term people will have to stop sharing updates because otherwise openai will dishonestly race to finish their work.
Which I don't see a reason for Anthropic and "Open"AI not to, given their not so stellar track record with IP of individuals/entities-that-are-not-rich-enough ;)
"But I realized after a while that talking to people casually about Fermat was impossible, because it just generates too much interest, and you can't really focus yourself for years unless you have this kind of undivided concentration, which too many spectators would have destroyed."
But yes; him reaping the benefits of himself having the idea first was part of it too; as far as I am aware.
-----
Which is still something completely different than some anonymous organisation keeping mathematical research secret because it is better for hype reasons. One is competition between individuals or groups within a field; the other is boring and sometimes borderline nihilistic generating of mathematical knowledge as an marketing asset.
It is a strong argument in this case though, because Terence Taos expertise is directly linked to his ability to not misstate the history of mathematics.
Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote.
On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions).
All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.
I mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously.
Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
> in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
That is well-known I assumed and continue to assume.
> I'm not seeing the direct link you're talking about
You are stating that link yourself; indirectly: "though I consider it unlikely that he is [being unaware of any mathematical history]". Why is it unlikely, precisely?
- Maybe because it is unlikely that he recieved the mathematical teaching that frequently does not contain history of mathematics (wild! I wonder which university you have in mind in particular) that you seem to be refering to?
- Or maybe because he is quite the opposite of a person that never ventures outside of their own area; being blind for other fields, or ones own history; as evidence by being famously collaborative across different fields, having a popular blog where he writes about non-mathematical topics too and last; him being one of the main proponents of foundational topics such as formalization of mathematics; or the use of LLMs for mathematical research.
Does all that really make it more likely to you that Tao is not aware of the existence of counterexamples like those the commenter above mentioned - more likely than the commenter simply having missed a nuance or taking something out of context?
If so; I would be genuinely curious why - people work differently, and I am always happy to learn, or close gaps in my own understanding.
Any one of the arguments you make here is already stronger than the original one. The problems with appeals to authority isn't that they are always false, it's that they are not a good argument.
And you say his "expertise is directly linked to his ability to not misstate the history of mathematics". And frankly, I disagree. If he happened to be misguided or even outright wrong about some parts of mathematical history I wouldn't think any less of him, nor do I think it matters much for the work he's actually paid to do. At worst it would result in an online discussion, which is arguably a good outcome not a bad outcome.
It should obviously not come as a surprise that having areas of the brains working differently can explain an awfull lot of things... but to answer your question directly, yes of course of course there are!
Simply look up all the many, well
-supported and -researched known correlations with ADHD first. In the second step, you can construct the set of all possible correlations, and subtract the well-researched ones if it. What is left is the set of correlations that are either not explained by ADHD (the big majority I would assume) or explained by ADHD, but as-of-yet unknowingly so.
This might be a bit anticlimatic, but clinical psychology is pretty straightforward study design and statistics, and set theory is not that new either, so... no big surprises I am afraid.
100% agree on the ad angle. Ads normalised using digital products/services by paying with data and attention.
That is one of the reasons why I would love to see - reasonably priced - paid services, or even have governments offer them (as in: Source is open, hosting is being paid by the government). Given the role social media, the internet and so on plays today, it might make sense to treat this as a common good.
But that side track aside; I think that privacy respecting, ad free products can be offered for cheap, if their goal is only to finance themselves, development and gain a small margin. And true, network effects / buyin is real, but I also think that the market for ad-free digital spaces/services will continue to grow, as hopefully people become more and more aware of how precious and limited their attention really is.
Given your position and the responsibility that comes with it; I sure hope you updated your mental model in another way than simply "they are acting irrational"... It's not clear from your comment that you did, but it sounded a bit like it.
> I suspect that the next big AI breakthrough will result at least in part from constraining LLM decisions with old AI approaches. Frank Coyle presented the idea of ontologies constraining LLM output about a month ago: https://www.youtube.com/watch?v=Sir59K8ZDPU
Interesting, thanks for sharing!
I plan to give it my own shot with vibing my own harness; I plan to use https://glean.software/ as the central database for everything code, then for documentation. After that, it could be used for bookkeeping for reasoning in a style similar to what you describe; after all, Angle, the query language of Glean, is a https://en.wikipedia.org/wiki/Datalog with some extras (I don't know which yet), so stuff like onthologies could be queried quite well, I would guess.
If you mean letting an LLM generate code for a Prolog planner from an English problem description, that has been done successfully already with last year's models eg [1].
Appreciate the link! That is not what I had in mind though; for them, the Prolog Code is the goal, for me, Prolog is an interface language within a system I build. That code could be generated on the fly, but I lean more towards fixed templates that can be instantiated by input some variables by the LLM that is doing agentic code, rather than having that LLM reproducing that query code completely on the flow.
The reasoning behind it is that I want to put as much logic as possible into the harness where it is deterministic, controled and fast - My goal is to make agentic coding usable for my purposes even with small local LLM models. Those might botcher generating Prolog queries sometimes, but they might might be able to used my API/interface/whatever reliably (and then the harness does everything else under the hood, including instantiating the Prolog templates and running the queries)
Hmm, I would say even older than that (which, of course, is in no way intended to be a value statement of any kind, I like the website and the project, cool idea! :D).
If you squint a little, the linked project is basically a https://en.wikipedia.org/wiki/A*_search_algorithm with optimized implementation, heuristics and so on. I also think that A* was associated with AI due to its use in path finding in early robotics - But I am not sure!
Eh, every school db should be able to service a student called "Robert'); DROP TABLE Students;--", and every public facing LLM should still work even if asked to calculate the last digit of pi - that fulfills two noble purposes: 1) is fun and teaches whoever is responsible for the service some valuable lessons in craftsmanship or 2) if the service is built robustly (i.e. simple token limit and time limit per user), that's an easy way to gain street cred
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