[eh_why_not]

What was most remarkable to me from this transcript, was how strong of an equal the AI agent comes across compared to the user (Tao). And Tao is one of the top mathematicians of modern times.

Yes, Tao is guiding it to where he wants to go. But also, Tao is actively learning from it and relying on its explaining, analysis, and inference abilities. You can easily imagine this conversation having taken place between Tao and a PhD thesis student, or even another professor, explaining their results.

What can we imagine and predict about the future anymore? Maybe a year - or two model releases - from now, the AI assistant will be undeniably stronger than Tao, and not an equal anymore.

[john_strinlai]

>Maybe a year - or two model releases - from now, the AI assistant will be undeniably stronger than Tao, and not an equal anymore.

we're kind of well past that (in my opinion), if you consider that this is the same ai assistant that can help you with a recipe, diagnose a weird sound in your car, help with biology homework, translate languages, and so on.

even in math alone, i think its indisputably already stronger than Tao, considering it has approximately this much depth in ~all of the math subfields.

[eh_why_not]

Agreed, it's stronger "horizontally". But I also think that we're not far away from it being stronger vertically; i.e. superior to Tao, in that such turn-by-turn guidance by him in solving sophisticated and difficult problems will not be necessary for long.

[stkdump]

I strongly suspect that the horizontal and the vertical strength are not perpendicular. I suspect having a very wide knowledge gives you access to patterns that reproduce across fields that an expert would lack.

[noosphr]

It only has that depth because you prompt it towards the experts that understand that depth.

An example that happened 10 minutes ago: contracts in racket, it kept arguing that you can't use -> in a contract of a function with a rest argument. I had to mention ... explicitly that it wrote the code correctly.

[larsfaye]

Yeah...I know I should be massively impressed, and I am to a degree, but isn't this what we should expect? LLMs can pick up on patterns that no human can see. In that sense, they really are a type of "search engine", but I use that term loosely. Tao is using them as a way to sift and sort theories and information that the model has a plethora of training data on. It's like being able to converse with the codex of humanity, and extract data via an algorithm that is highly adept at sorting through it.

[cootsnuck]

Also I feel like people are not noticing in Tao's chat that chatGPT fairly often is doing web searches. So it literally is acting as search engine sometimes, and that too is incredibly effective when done right. So in addition to Tao using his prompts to "search/sift through vector space" the LLM is also literally just searching the web to augment its "knowledge" at inference time too.

Which, to me, again demystifies these tools. They are incredible tools, but still "just" such.

[mettamage]

> It's like being able to converse with the codex of humanity, and extract data via an algorithm that is highly adept at sorting through it.

Bingo

Thanks for laying it out so clearly.

This is what I feel LLMs are really good at yea. Almost to the point that I'd say this is what they are. But I'm not quite convinced that it is that, but it seems to point that way

[lpd59]

To be fair, Tao's specialty is not algebraic geometry.

[buzzin_]

Interestingly enough, ChatGPT started his answer like this only once:

"This is exactly the question I would ask next. My impression is: Most standard invariants are...."

And this was a response to this prompt:

"Is there a chance of an indirect argument of X ~ A^3 coming from computing some invariant of X that forces it to be A^3? (I am not all that expert in algebraic geometry but I'm thinking like degree or Betti numbers or something.)"

[ImaCake]

I find it helpful to think of LLMs as reflections. If you can talk like an expert mathematician at the model it will respond like one. While Terrance's first prompt looks trivial I expect a first year Uni student would be hard pressed to provide something that good.

I guess it is kind of the inverse of the "you are an expert mathematician" prompt engineering of gpt3.5. Since no one ever says that to an expert mathematician when they are doing expert math the model immediately reflects that it is not an expert mathematician.

[chegra]

Isn't LLM doing something like argmax{x} P(x|context) where x is the next word, and context is the words before including your instructions? Thus, the LLM output is heavily depending on your instructions, and if you input an expert context it would produce an expert result. Consequently, domain expertise has a significant bearing on what you can achieve from LLM.

[sanderjd]

I dunno. To me, this seems like kind of a counterexample (pun intended?) to that thesis. Would a conversation with another AI have been as fruitful as this conversation with Tao? Certainly not! Will that change in a year? I dunno, but it seems like those goal posts keep moving, and I'm a bit skeptical.

[ilaksh]

I think you're mostly right, and there is still a lot of "cope" in this thread about how much he needed to guide it.

But I would say that in some ways it's already obviously superhuman. The reason I think it's lacking in some jagged ways still at the expert level is because although it's highly optimized to be incredibly capable in many domains, it still doesn't have quite the same raw capacity for complexity in understanding one problem that humans do.

I believe that LLMs (really should be called VLMs for most of them) can still get much larger, and that will push the absolute complexity level and general IQ way over human level.

They are maxing out at like 5 or 10 trillion parameters right now. I believe we will see 50 and 100 trillion parameter models and models with large portions of that active. It will round out the jaggedness and probably more than double the raw intelligence that a human can achieve. It's not a linear scaling but who knows what the limit is and can go significantly higher with the same architecture I think given continued improvements in training and hardware scale.