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Terence Tao: At the Erdos problem website, AI assistance now becoming routine

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Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#81

Post by gjm11 »

trauco wrote: post #63
sesm wrote: post #54

Earlier quoted context omitted.

How do you verify that the explanation is accurate? Mathematical definitions can be very subtle.

The answer is you put the top mathematician in the world to do it, easy peasy. “The argument used some p-adic algebraic number theory which was overkill for this problem. I then spent about half an hour converting the proof by hand into a more elementary proof, which I presented on the site.” What’s the exchange rate for 30 minutes of Tao’s brain time in regular researcher’s time? 90 days? A year?

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.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#82

Post by NuclearPM »

fastasucan wrote: post #56
tyre wrote: post #27

Earlier quoted context omitted.

This is where LLMs shine for learning imo: throwing a paper in Claude and getting an overview then being able to ask questions. Especially for fields that I didn’t study at the Bachelors or Masters level, like biology. Getting to engage with deeper research with a knowledgeable tutor assistant has enabled me to go deeper than I otherwise could.

How do you know its correct? And how do you learn to engage with the theory heavy subject doing it this way?

Ask for sources. Easy.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#83

Post by School-Cotton »

gf000 wrote: post #67
School-Cotton wrote: post #65

Earlier quoted context omitted.

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

Unless it's a famous person who lived several centuries ago, probably would leave it as Yáñez, or if I (or more realistically, an average, not too technical user) were to not have an easy way to input the special characters, then as Yanez. Probably not as Yánez, even though we do have the letter 'á', but leaving it as is may be more misleading in terms of pronunciation then the non-accented version.

I think that's roughly similar to how it's done in American English (though Americans are probably less likely to have any idea how to type accented letters). A serious publication would write Yáñez but an average person would be pretty likely to just type "Yanez". Anyway, my point was just that it's not too weird to see someone write "Erdos" if their native language doesn't have the ő character.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#84

Post by tyre »

devin wrote: post #70
tyre wrote: post #27

Earlier quoted context omitted.

This is where LLMs shine for learning imo: throwing a paper in Claude and getting an overview then being able to ask questions. Especially for fields that I didn’t study at the Bachelors or Masters level, like biology. Getting to engage with deeper research with a knowledgeable tutor assistant has enabled me to go deeper than I otherwise could.

If you did not study these topics, the chances are good you do not know what questions to even ask, let alone how to ask them. Add to the fact that you don't even know if the original summary is accurate.

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.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#85

Post by tyre »

SetTheorist wrote: post #68
augment_me wrote: post #47

Earlier quoted context omitted.

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.

Experimenting with LLMs, I've had examples like it providing the Cantor Set (a totally disconnected topological space) as an example of a Continuum immediately after it provides the (correct) definition as a non-empty compact, connected (Hausdorff) topological space. This is immediately obvious as nonsense if you understand the topic, but if one was attempting to learn from this, it could be very confusing and mislea…

I don’t know what any of this means!

But I’m not trying to become an expert in these subjects. If I were, this isn’t the tool I’d use in isolation (which I don’t for these cases anyway.)

Part of reading, questioning, interpreting, and thinking about these things is (a) defining concepts I don’t understand and (b) digging into the levels beneath what I might.

It doesn’t have to be 100% correct to understand the shape and implications of a given study. And I don’t leave any of these interactions thinking, “ah, now I am an expert!”

Even if it were perfectly correct, neither my memory nor understanding is. That’s fine. If I continue to engage with the topic, I’ll make connections and notice inconsistencies. Or I won’t! Which is also fine. It’s right enough to be net (incredibly) useful compared to what I had before.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#86

Post by int_19h »

perching_aix wrote: post #77
gerdesj wrote: post #24

Erdős I was told by a hungarian, that hungarian written spelling and spoken pronunciation is pretty precisely aligned compared to, say, english. Except when it comes to names when it gets a bit random! Why not do the bloke the decency to spell his name correctly? Those diacritics are important. Anyway, I was told that Paul's name is very roughly pronounced by an anglophone as: "airdish".

Ő is just œ (oe), nothing crazy. Certainly not a scenario that would belong to the quirky category. The only weird ones I can think of are the ones that end in -y. For example, Görgey. They're meant to be -i endings. They signify a noble lineage (or at least used to). I guess "ch" might also show up every now and then too (it's just "cs", just like "ch" in English). For example, Széchényi. Since this is a compsci for…

The "weird" part about Hungarian names and words for English speakers is that "y" is a modifier letter in most cases, not a sound in and of itself. So e.g. "Nagy" is pronounced closer to something like "Nahj".

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#87

Post by perching_aix »

int_19h wrote: post #86
perching_aix wrote: post #77

Earlier quoted context omitted.

Ő is just œ (oe), nothing crazy. Certainly not a scenario that would belong to the quirky category. The only weird ones I can think of are the ones that end in -y. For example, Görgey. They're meant to be -i endings. They signify a noble lineage (or at least used to). I guess "ch" might also show up every now and then too (it's just "cs", just like "ch" in English). For example, Széchényi. Since this is a compsci for…

The "weird" part about Hungarian names and words for English speakers is that "y" is a modifier letter in most cases, not a sound in and of itself. So e.g. "Nagy" is pronounced closer to something like "Nahj".

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.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#88

Post by malux85 »

fastasucan wrote: post #56
tyre wrote: post #27

Earlier quoted context omitted.

This is where LLMs shine for learning imo: throwing a paper in Claude and getting an overview then being able to ask questions. Especially for fields that I didn’t study at the Bachelors or Masters level, like biology. Getting to engage with deeper research with a knowledgeable tutor assistant has enabled me to go deeper than I otherwise could.

How do you know its correct? And how do you learn to engage with the theory heavy subject doing it this way?

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.

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#89

Post by an0malous »

bluedel wrote: post #60
niek_pas wrote: post #58

Earlier quoted context omitted.

> Wish we could also do the same for "Beam me up scotty" You might die every time you do, though, so maybe not.

For some definitions of "you" and "die".

You = your body and mind

Die = don’t exist anymore

Re: Terence Tao: At the Erdos problem website, AI assistance now becoming routine

#90

Post by ChicagoBoy11 »

mjcohen wrote: post #29
gerdesj wrote: post #24

Erdős I was told by a hungarian, that hungarian written spelling and spoken pronunciation is pretty precisely aligned compared to, say, english. Except when it comes to names when it gets a bit random! Why not do the bloke the decency to spell his name correctly? Those diacritics are important. Anyway, I was told that Paul's name is very roughly pronounced by an anglophone as: "airdish".

(I saw this on a math department bulletin board about 1960) A theorem both deep and profound States that every circle is round But in a paper by Erdos Written in Kurdish A counterexample is found

I suspect there is a great joke embedded in here, but sadly it went over my head. Any help?
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