How do you know anything is correct? LLMs can be wrong, humans can be wrong, you can be wrong. The motto of the royal society, is "Nullius in verba" which is a latin phrase : "take nobody's word for it," that's LITERALLY the motto of the royal society. Its your job as a scientist and critical thinker to test assumptions, oberve reality and use empirical inquiry to seek truth, and in the process, question ALL sources and test all assertions, from multiple angles if required.

You don't - the way I use LLMs for explanations is that I keep going back and forth between the LLM explanation and Google search /Wikipedia. And of course asking the LLM to cite sources helps.

This might sound cumbersome but without the LLM I wouldn't have (1) known what to search for, in a way (2) that lets me incrementally build a mental model. So it's a net win for me. The only gap I see is coverage/recall: when asked for different techniques to accomplish something, the LLM might miss some techniques - and what is missed depends upon the specific LLM. My solution here is asking multiple LLMs and going back to Google search.

Ask for sources. Easy.

The original summary is the paper’s abstract, which I read. The questions I ask are what I don’t understand or am curious about. Chances are 100% that I know what these are!

I’m not trying to master these subjects for any practical purpose. It’s curiosity and learning.

It’s not the same as taking a class; not worse either. It’s a different type of learning for specific situations.

Asking the right questions (in the right language) was important before and it's even more important with LLMs, if you want to get any real leverage out of them.

Yes. I usually test AI assistants by giving them my own work to summarize, and have nearly always found errors in their interpretation of the work.

The texts have to be short and high-level for the assistants to have any chance of accurately explaining them.

There is, but there is an equal risk if you were to engage about any topic with any teacher you know. Everyone has a bias, and as long as you dont base your worldview and decisions fully on one output you will be fine.

I've been doing this a fair amount recently, and way I manage it is: first, give the LLM the PDF and ask it to summarize + provide high-level reading points. Then read the paper with that context to verify details, and while doing so, ask the LLM follow-up questions (very helpful for topics I'm less familiar with). Typically, everything is either directly in the original paper or verifiable on the internet, so if something feels off then I'll dig into it. Through the course of ~20 papers, I've run into one or two erroneous statements made by the LLM.

To your point, it would be easy to accidentally accept things as true (especially the more subjective "why" things), but the hit rate is good enough that I'm still getting tons of value through this approach. With respect to mistakes, it's honestly not that different from learning something wrong from a friend or a teacher, which, frankly, happens all the time. So it pretty much comes down to the individual person's skepticism and desire for deep understanding, which usually will reveal such falsehoods.

There is, but just ask it to cite the foundational material. A huge issue with reading papers in topics you don't know about is that you lack the prerequisite knowledge and without a professor in that field, it may be difficult to really build that. Chat GPT is a huge productivity boost. Just ask it to cite references and read those.

For that sort of task: no, Tao isn't all that much better than a "regular researcher" at relatively easy work. But the tougher the problems you set them at, the more advantage Tao will have.

... But mathematics gets very specialized, and if it's a problem in a field the other guy is familiar with and Tao isn't, they'll outperform Tao unless it's a tough enough problem that Tao takes the time to learn a new field for it, in which case maybe he'll win after all through sheer brainpower.

Yes, Tao is very very smart, but it's not like he's 100x better at everything than every other mathematician.

Erdős rhymes with Kurdish.

EDIT: Oh and Erdős was the great collaborator. There is an Erdős number (Bacon and Ozzie too) which defines how close you are to him. eg if you co-authored a paper with Erdős you have a Erdős number of one. If you co-auth a paper with someone with an Erdős number of one, then you have an Erdős number of two etc.

I think that the Bacon (Kevin Bacon) number was the original and there is also a Black Sabbath number which is related to Ozzie (MHRiP).

I also gather that a very few people have managed a minimum measure of all three numbers. Feynman might be one of them (its too late to check).

They said:

> Except when it comes to names when it gets a bit random!

The letters "gy", "ty", and "ly" are not exclusive to names, nor are they significantly more common in names.

It's not that I disagree people would struggle with these, just that it's not unique to names, so it couldn't have been what they were referring to there.

How would you write e.g. the Spanish surname Yáñez ?

More like "for enders", innit?

Totally true! But also, there users like Tao don't feed trolls, and everyone has the option to block them.

I wonder what the ultrafinist argument against theorems about the natural numbers as defined in Coq would be.

> the appearance of the word "metaphysics" in the output suggests the prompt author didn't know what they were talking about to begin with.

Or the author is not natively fluent in English.

You = your body and mind

Die = don’t exist anymore

Thinking about such questions before we are capable of doing such an experiment at least with small animals is like discussing how many angels can stand on the point of a pin.

The embarrassing failures or misconceptions of math experts with regards to research level mathematics? Definitely a serious problem.

Though by your "Perelman and Wiles didn't need "AI" assistance" comment, you'd surely be there on the sidelines to ridicule them for each and every single one. I guess maybe that's where your concerns are coming from?

I can practically see how these concerns of yours would suddenly evaporate if they started using self-hosted models instead... ... yeah, right, who are we kidding?

Wiles's initial presentation of the proof had a serious flaw that killed the whole thing until he found a workaround. I don't remember how long it took him to get out of the jam, but I'm sure he would have handed his credit card to the Devil himself if he thought it might help.

People who don't take advantage of the best available tools and techniques don't get to that level to begin with.

It's fine, at least you admit that what you wrote was just to insult.

For people who at least pretend to care to not think in strawmans, it's been nearly six years, and their deus has never exited said machina (if it's ever been in there to begin with, or anywhere else).