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by ecshafer 6 days ago
Terrance Tao's chatgpt conversation is really interesting for a variety of reasons:

1. The counter example wasn't just a brute force selection, the polynomial is structured in a very specific way that ends up getting the result.

2. Terry Tao's questions are very specific and prompts the AI in a useful way, that without high math training you are not going to get the same information out of it. Terry seems to see some aspects of the problem and counter example and uses AI to brute force some parts of it.

4 comments

It feels very humbling that here is one of the smartest humans on the planet asking questions, and the LLM keeps answering in this "Yes, it's really simple if you think about it" way, like a professor talking to a talented student.
I had a similar reaction with the language but also response times and language. It reminded me of a quote about Jon von Neumann from Edward Teller:

"Von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."

Von Neumann is an interesting historical character that nobody has ever heard of, e.g: for such an accomplished inventor, that so few minutes of video footage exist of him.

>I sometimes wondered if he used the same principle when he talked to the rest of us.

I can come pretty close to a humbler example of this, as the more-extroverted "bad twin," of an identical set: my own genetic equal is bored to tears interacting with 90% of daily interactions... we both started with good brains/IQ, then went to the same college; but while twin spent the next decades solving EE problems (and co-founding startups), I "kicked back" and smoked myself sillyretarded, electricianing, relying upon bullshit and sheer luck to get to where I [barely maintain] am.

Watching my twin deal with any normal-intelligence persons is such an unpredictable shitshow, but I pretty much always know he's "dealing with us toddlers" who mostly never grew up. His patience is limited but willing.

Glad he can get by among us mere mortals. I have other similarly-minded brothers, but only this one identical twin.

I definitely heard of him. The CS focused high school I went to in Hungary was named after him, his portrait on the walls, etc.

I think lots of people have heard of him. I agree, that he is probably not as famous as some of the other scientists of the era though.

>Von Neumann is an interesting historical character that nobody has ever heard of

huh? He's pretty famous to anyone who has studied either the history of computing or of the development of the atomic bomb.

What? Every CS grad learns of Von Neumman architecture and by extension of the man himself, at least I recall doing so, in much the same way as Turing and Church.
Fascinating.

I mean that.

I also think to do STEM well, one needs to find that inner child.
I hate it when it picks that register. I think it stops if you contradict it more, which he’s not doing.
"Yes—and I actually think this is the right way to think about the construction."

Always the smarmy tone.

A lot of “advanced” concepts are simple once you find the right way to frame them.
Terrance Tao is GOATed.

That’s what I got from reading about a third of that exchange.

I mean that’s clear from reading anything about the dude, but to _experience_ it so to speak is different.

A true mark of brilliance is someone who makes something difficult seem easy by framing it just right.

In this instance ChaGPT is just expanding upon his prompts. Not to diminish, it’s amazing what it’s capable of.

It is ~a meme on subreddits that developers struggling to get good results out of any given model is a "skills issue."

But I think your comment drives at some authentic take on this. Skill with AI is not only crafting iterative prompts the agent will understand, but also very high domain-specific knowledge of what the prompts explore.

One without the other can result in frustration or worse.

A naive hope is: you see that the LLM is so good at coding that all you need to do is supply a "yes/no" on what you want.

Turns out that understanding the technical domain is important to getting good results, even if the LLM is more capable at producing output. -- It's still a case of "garbage in, garbage out".

I think for many newbies, they see the LLM is so good at programming and so figure they don't need to learn anything. Apparently not so.

It is a skill issue. Such developers have to take a problem, isolate it and explain it to someone/something else with enough context to be able to work with it.

It is perplexing how many developers lack this basic skill, some of them borderline lack theory of mind and are incapable to understand that other people can't see the unspoken part in their heads.

It has been a good long while, but in my undergrad the engineering dept did not put a lot of emphasis on being a well rounded individual. It was more about passing physics and getting through all of the math.

One of my first jobs out of undergrad was technical writing on EDA tools for Mentor Graphics Calibre product. For many years, I did not appreciate that experience--it seemed orthogonal to what I'd gone to school.

Once I did become a professional SWE, something that took me too long to realize was that writing documentation and tutorials for people and looking after the quality of onboarding materials was almost never rewarded.

I came to see it more of a liability with ~all emphasis being on human code gen.

I listened to an interview with Steve Yegge earlier this year, one of his concerns was that many people just don't type very fast or read very quickly. IIRC, he expressed concern this would continue to be a big barrier to successful use of AI.

I previously commented on annotation for coding agents that an important skill was knowing the beat of a conversation.

I think that extends into critical reading. For example, it is not that unusual for a Washington Post article to put some ~explosive detail deep in the article--this is called "burying the lede."

I see this regularly reading AI output. That is: the AI will lead with the strongest claim it can state cleanly, but not the most explosive implication.

With Claude Code and Codex, you're looking essentially neverending walls of text dense with technical information.

So now you have to have high domain expertise, a good understanding of written communication, a sense for the beat of a conversation (which assists in identifying understatements or overstatements), and the ability to dense text outputs quickly and then highlight critical statements for further exploration.

I'd almost describe part of this work as that of a skilled interviewer.

I wonder how much this overlaps with the seeming inability of so many developers to ask good questions. They want to jump right into screen sharing and talking about the issue. They cannot sit down and summarize the problem accurately and describe the things they have tried already. It's always "let's hop on a call real quick and walk through it". Just tell me what the damn problem is!
>It is ~a meme on subreddits that developers struggling to get good results out of any given model is a "skills issue."

*GIT GUD* (at prompting)

I think we have a couple of years of "being good at talking to the LLM about your field of expertise" being a useful human skill, until that too gets washed away
Maybe?

At the end of the day, even if they are some insane oracle (pun intended), they're still bounded by training data and how it relates to the real world. Even if they're a near perfect tool, we are still the interface between them and our lived experience. If that stops being the case then why do we care about the output?

This assumes it doesn't graduate to just killing all of us and doing it's own thing, but within this paradigm it doesn't really have goals.

>Even if they're a near perfect tool, we are still the interface between them and our lived experience.

Until they are embedded into automatons that can interact with the world.

(To be clear, I'm both on board with this, and I think it's the natural progression. Currently they are bounded by their training set, but interaction with the world is the imperative for theory -> test -> analysis -> update that is essential for growth and creativity.)

they're still bounded by training data and how it relates to the real world.

Yes and no. They can extrapolate and build upon the training data, as was the case with the last dozens of math proofs

Yes, but the point being for the LLM to be useful to us it has to do something relevant for us and we have to define what is relevant. Even if you view them as fully human level or beyond (in terms of agency) there's still some purpose that we have to help provide them with.

To put it differently, if you have some idealized model in front of you that can do anything a team of humans can do, what do you say to it? It's still just a model that takes an input and provides an output.

I don't understand. You will ask it for something you want, and instead of needing to pay a the team of people with expertise, it will just do it for you.

Someone will still need to ask for something (or maybe it will just run autonomously making things it thinks we'll like) but it won't require any expertise in the field.

I can’t help but believe that reality will keep the interactions more useful when coming from a person with expertise in the field, e At least for technical questions.

For things like sickness, old age and death, generally the lacks are not knowledge but the consistent will of the group. Like global warming, there is no real profound knowledge gap except how to get everyone to agree to mitigating the carbon burn. Perhaps it is likely LLMs would be able to persuade the group to stop burning the carbon before it’s [more] uncomfortable, but the small group of people committed to accelerating the carbon burn can also pay for LLM persuasiveness.

Of course they can't just talk to themselves and improve the knowledge of the world. They are just stochastics parrots that give you an average answer.

LLMs giving you something novel would be like if you let a model play chess against itself and become the best player in the world this way. Totally impossible.

/sacrasm

I’m curious whether we could get the same results by gathering a large number of PhD students and having Terence Tao treat them as an AI.
He is well known for the large numbers of collaborators he has worked with to develop new math in all sorts of fields. Grad students in general wouldn’t be sharp enough to benefit maximally from his skills, but other math professors.