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AI isn’t outthinking mathematicians, it’s out-remembering them

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Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#461

Post by exe34 »

yesco wrote: post #243
grahamburger wrote: post #210

Earlier quoted context omitted.

People have told me I was smart since I was a kid, but I can't remember for shit. I had a thought when I was fairly young that the only reason I was (maybe, sometimes) outperforming others intellectually is that I was habitually compensating for my poor memory by working things out on the fly, while others could rely more on rote memorization. Anyway, takes all kinds I guess!

Somewhat tangential, but this reminds me of when I took a certain Microbiology midterm in college. I hadn't put much effort into that class leading up to it, as I had some tough CS classes that consumed my focus that semester (also was admittedly not a great student in general). So when I finally went to take the midterm, after cramming like mad before the exam, I quickly realized I basically didn't know the answer t…

> I just kept doing multiple passes through it, each time I noticed one of my answers contradicted one of the others, I would make adjustments to harmonize, which indirectly refined my understanding.

I used to do something somewhat related during exams: I could never find contradictions/mistakes while working forwards, because somehow my brain would make the same mistakes consistently every time I go through something in the same direction, no matter how slowly and methodically I would do it.

So I worked as fast as possible in the forward pass and then reversed the problem in my head and worked backwards just as fast. Except this time I would often find the expected inputs would no longer match the actual inputs, so it helped me identify a lot of mistakes.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#462

Post by throwaway2037 »

hibikir wrote: post #198

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

    > it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or self study, and being able to apply it to the problem at hand.
From my personal experience, a few times I have worked in the "low latency" area of computer science. (Before anybody gets too excited on HN, I am talking about around 100ms per transaction, so the FPGA crowd can ignore my comments! I always say: If you ask 10 programmers what is the definition [limit] of low latency, you will get 10 different answers.) There are many, many programming strategies for low latency that are undocumented in public literature. The only way to discover them is from an existing project or teammate or trial-and-error. I would extend this thought/opinion to massively(?) multi-threaded systems.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#463

Post by tim333 »

a2ff6eeb0 wrote: post #5

Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.

>The age of humans comprehending things is coming to an end

I'm sure humans will comprehend some things and not others just as now. They may be smarter than me but the Einsteins and the like already were. It may be that the cutting edge gets pushed by AI more than humans at some point though.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#465

Post by OroPla »

bhaak wrote: post #280
OroPla wrote: post #197

Earlier quoted context omitted.

I also just keep parroting that the Earth is not flat and a bunch of other things I've been told and then never questioned, since it seems to make sense. When the flath-earth craze started I've been trying to at least get that bit actually personally verified. Haven't managed to do it to this day, though. So I'll just keep parroting various things without properly understanding them. C'est la vie.

Your drive to verify must be very low then. There are hundreds of small logic reasonings or even experiments with which you can easily prove that a flat earth model is at least very complicated or even impossible. Explaining Moon phases gets very complicated in any flat earth model. With binoculars you can see the shadows of craters on the moon's terminator. Or the phases of Venus whereas Mars doesn't have any. Timez…

None of that is an actual verification of round (or kinda potato shaped) Earth. You are just choosing to not think too deeply about it, essentially parroting things, just like I am.

Disproving flat Earth does not verify round Earth, after all. And all your listed refutations of flat Earth do not really disprove anything, either. They might, if you do the actual work, but you did not, choosing to just parrot someone that did put in the work.

Which was my point. It is much easier to speak vaguely and reference things than it is to actual prove something rigorously.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#466

Post by gilrain »

pwython wrote: post #296
jermaustin1 wrote: post #260

Earlier quoted context omitted.

Same. I have bad "factual" memory, but very good "conceptual" memory. I might not remember exactly what someone told me, but I probably gathered a keyword, and a feeling and idea of what they told me. Almost like it takes what they said then compresses it into my mind in a nice little multi-key lookup table.

Yes. "Weak detail recall but strong fluid reasoning, conceptual/gist memory, and adaptive problem-solving" is how GPT sums up what I feel. And "high fluid intelligence" is a label it gave that I won't be using anytime soon... But I like the sound of it.

You asked an LLM to reason about you, for you, and it said you’re an adroit reasoner? It must have context we lack!

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#467

Post by quickthrowman »

groundzeros2015 wrote: post #399
breezybottom wrote: post #398

Earlier quoted context omitted.

I don't know where you're getting that from. The sorting of students into "gifted" and "non-gifted" categories is very common. You don't need to look further than your local school district for proof.

> don't need to look further than your local school district for proof. Yeah mine didn't have it. And the teachers fought every attempt to do so because it hurt their metrics (who gets stuck with the lower class average). Are you by chance part of the PMC and your local school district is of similar demographics?

You can just say “upper middle class”, PMC means ‘private military contractor.’

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#468

Post by alexpotato »

hibikir wrote: post #198

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

> I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us

There is a great episode of Inside the Actor's Studio where there is a Q&A with Mike Myers.

He was asked if going to college/getting more education was helpful to being a comedian.

He responded:

"Many times in writing comedy, you are on an 'island' and you are trying to figure out how to get to the next 'island'. Having more education and knowing more about the world can definitely help you do that"

I like the above quote because to me intelligence is a combination of remembering useful information but also being able to "connect the dots" between those facts and apply to them to the current situation.

As another example, I was watching a documentary about LIGO. One of the engineers had memorized the entire system in his head. The other engineers would come to him and ask "Will this change to component A affect anything else?". He would pause and think and then say "Yes, component F touches that so it will be affected." The other engineers mentioned how useful it was to haves someone who had the entire system in "one brain".

I've seen this in finance technology too where someone, usually a woman, has large parts of the system memorized and performs a similar function.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#469

Post by swat535 »

groundzeros2015 wrote: post #390
bragr wrote: post #220

Earlier quoted context omitted.

We sort kids into the smart and non-smart labels when they are young, and those labels tend to stick, even when what we're measuring isn't raw intelligence but just variance in childhood development that wash out in the long term. I don't think either group is well served by this.

No we don't. Public schools are incentivized not to help high performers. It actually hurts their metrics and budget. The widespread gifted/talented experience in public school ended in the late 90s. The actual intelligence segregation is self-selected. PMC parents live together in the same neighborhoods. Whether you believe in genetic or social factors, the smart kids come from here. In the 80s and 90s there was an…

> No we don't. Public schools are incentivized not to help high performers

This is actually true.. in my country we used to have 3 different tiers for Mathematics like 416, 426, 436, etc for high school students. You would get the right class for how good you were.

They dropped this and made a simple "sciences" vs "humanity" path. Then they also removed percentage grades and replaced with alphabets A, B, C, etc. There used to special awards for high performers with medals and gifts and the end of year, those events also got the shaft.

The idea was to reduce stress on students..

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#470

Post by doginasuit »

smj-edison wrote: post #321
doginasuit wrote: post #316

A superhuman working memory is exactly how I've been describing the LLM advantage. Paired with the unreliability of its reasoning and judgment, it is what makes AI a supplement to human intelligence, not a replacement. On the other side, LLMs make random mistakes and wrong choices and they have a bias toward writing more code instead of less. You can make up for this to some degree by running another LLM against thei…

I also find them bad at what I call "abstraction compression." They're really bad at noticing when a helper function is needed, when some structure they repeated five times slightly differently can become a struct, when a whole section of code can be encapsulated in a simpler design. I'm lucky that for my side project (an interpreter) I've written all the code myself, so I've built up its design in my mind over the p…

I have that issue too. One thing I suspect they are amazing at is documentation generation, maybe a good solution is to have it generate a concise summary of helper functions that are available for any given context. Then have it use the same doc when you call in some code generation.

You touched on another baked-in limitation of LLMs: their inability to follow Don't Repeat Yourself. To anthropomorphize a little, LLMs love to repeat themselves. I remember in the early days before reasoning algorithms came along, you could ask an LLM a question and it would often explain the same answer two or three times in a slightly different way. You also see this in image generation with multiple people, they will often do essentially the same person several times with minimal variation. Applied to code, in your functions they saw an earlier pattern and they can't help but write it the same way.

This isn't entirely at odds with producing good code, I often force myself to wait for another occurrence of where a helper function is needed before I write it, lest I create a slew of utilities that are easy to forget about. Maybe it just needs an additional pass: "analyze your output and create a set of helper functions where logic is repeated or the abstraction is wanted."

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