Terence Tao: At the Erdos problem website, AI assistance now becoming routine
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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.
Perhaps in low stakes situations it could at least guarantee some entertainment value. Though I worry that folks will get into high stakes situations without the tools to distinguish facts from smoothly worded slop.
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.
The texts have to be short and high-level for the assistants to have any chance of accurately explaining them.
You won't be able to verify everything taught from first principles, so do have to at some point give different sources different credibility I think.
No it isnt.
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.
And there’s always some risk.
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.
You use your brain and cross-reference multiple sources.
Even traditional research methods return bogus information. People are just wrong sometimes and you as a researcher have to deal with that.
The way to deal with LLM accuracy is to not trust it blindly. Same as everything. The LLM will try to convince you and itself that it's right even when it isn't. But you can say the same for a shockingly large number of historic works written by explorers and people who had no clue what they were talking about.
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.
“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?
... 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.
Even imperfect assistants increase leverage.
https://aristotle.harmonic.fun/
TIL: startup founded by Robin Hood CEO
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".
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
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).
In general, if the source language has a latin alphabet, we try to stick to the original spelling in most cases, but it is not uncommon to replace non-Hungarian letters with the closest one. It's a bit more complicated in case of non-latin alphabets, especially Cyrillic due to a lot of shared history.
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 forum to some extent, maybe I should also mention that the so-called Lanczos-interpolation is "actually" Lánczos. Took even me a while to pick up on that one! Thinking about it, I now see that it features a "cz", another letter (digraph) that is longer part of the alphabet.
Also note that Paul is a "translated" name. His actual name was Pál Erdős. He got lucky with that one, it's an easy swap. Edward Teller (Ede Teller) was the same way, and so was John (von) Neumann (János Neumann).
As a bonus trivia, the Hungarian name order is big endian, like the Japanese. So it would be "Erdős Pál", "Teller Ede", "Neumann János", and "Lánczos Kornél". Though just like with Japanese, I would not recommend trying to adhere to this order in most English speaking contexts.
> 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.
> 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.
is not actually surprising to an English speaker.
It's not very credible. There are individual fragments that make sense but it's not consistent when taken together.
For example, by making reference to Godelian problems and his overall mistrust of infinitary structures, he's implicitly endorsing ultrafinitism (not just finitism because e.g. PRA which is the usual theory for finitary proofs also falls prey to Godel's incompleteness theorems). But this is inconsistent with his expressed support for CASes, which very happily manipulate structures that are meant to be infinitary.
He tries to justify this on the grounds that CASes only perform a finite number of symbol manipulations to arrive at an answer, but so too is true for Lean, otherwise typechecking would never terminate. Indeed this is true of any formal system you could run on a computer.
Leaving aside his inconsistent set of arguments for CAS over Lean (and there isn't really a strong distinction between the two honestly; you could argue that Lean and other dependently types proof assistants are just another kind of CAS), his implicit support of ultrafinitism already would require a huge amount of work to make applicable to a computer system. There isn't a consensus on the logical foundations of ultrafinitism yet so building out a proof checker that satisfies ultrafinitistic demands isn't even really well-defined and requires a huge amount of theory crafting.
And just for clarity, finitism is the notion that unboundedness is okay but actual infinities are suspect. E.g. it's okay to say "there are an infinite number of natural numbers" which is understood to be shorthand for "there is no bound on natural numbers" but it's not okay to treat the infinitary object N of all natural numbers as a real thing. So e.g. some finitists are okay with PA over PRA.
On the other hand ultrafinitists deny unboundedness and say that sufficiently large natural numbers simply do not exist (most commonly the operationalization of this is that the question of whether a number exists or not is a matter of computation that scales with the size of the number, if the computation has not completed we cannot have confidence the number exists, and hence sufficiently large numbers for which the relevant computations have not been completed do not exist). This means e.g. quantification or statements of the form "for all natural numbers..." are very dangerous and there's not a complete consensus yet on the correct formalization of this from an ultrafinitistic point of view (or whether such statements would ever be considered coherent).
The classical mathematician would respond that the theorems are clearly meaningful and you can easily test them against any natural numbers you care about to see empirically they are meaningful.
The ultrafinitist would respond that they are only coincidentally correct, in the same way that pre-modern mathematical reasoning was often very sloppy, featured regular abuse of notation, and had no coherent foundations, but nonetheless still often arrived at correct conclusions by "coincidence."
The classical mathematician might then go over how strong the intuition of something like "there exists a number that..." is and how it is an easily empirically validated statement...
And so the debate would keep going.
Or the author is not natively fluent in English.
So I agree. I think these tools are very helpful, but I also think it is unhelpful that people are trying to sell them as much more than they are. The over hype of them not only legitimizes any pushback but provides ammunition. I believe the truth is that they're helpful tools, but are still far from replacing expertise. I believe that if we try to oversell them then we run the risk of ruining their utility. If you promise the moon you have the deliver the moon. That's different from aiming for the moon and landing in the trees.
You might die every time you do, though, so maybe not.
Die = don’t exist anymore