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…
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!
AI isn’t outthinking mathematicians, it’s out-remembering them
311–320 of 546 posts
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#312Earlier quoted context omitted.
A smart kid can be anything from not eating rocks anymore to multiplying numbers at an early age. Most of us turn out like the rescued exotic bird which turns out to be a seagull covered in curry.
Sometimes I wish there was a Hacker News comment hall of fame.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#313Earlier quoted context omitted.
If humans have nothing to contribute then shared understanding is a pointless endeavor. It makes sense now in the "centaur" period where human + AI > AI alone, but when AI mathematicians are both more rigorous and more elegant, then taking the time dumbing down their proofs to a human level of understanding is like requiring that we ensure all our current proofs be understandable by a monkey.
> If humans have nothing to contribute then shared understanding is a pointless endeavor. I agree, but as a software engineer this gives me pause because I keep trying to insist on coding standards but I’m unable to come up with a compelling reason why it matters. Ostensibly the reason we cared about things like DRY and code quality was so that it would be easy to understand and easy to maintain and easy to make chan…
IMO it's still a problem with LLMs; we still have to build in a way that makes it easier for an LLM to make changes later and arguably it's the same things that made software development easier for humans. IME LLMs tend to not know how to do that for themselves and instead just amplify/copy patterns that already exist.
If an LLM can't pave the way for itself then ultimately shared understanding is required to take advantage of LLMs in the first place.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#314I 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…
Really, compress. Compression is a useful proxy for intelligence.
To compress data efficiently, an entity must discover the underlying patterns, structures, and regularities within that data. Identifying these structures is precisely what we define as "understanding" or "intelligence.
Anything we put into writing can be thought of as a string of data. The Kolmogorov complexity of a string of data is the length of the shortest possible computer program that can output that string.
A good compressor doesn't just memorize (yes, there's a reason LLM writing features the "it's not just X, it's Y pattern"), it builds a generalized model to handle unseen, similar data. LLMs are trained by compressing the internet into weights, they use this to write new code.
When an LLM is trained, it compresses ...bytes of human text into a few ...bytes of neural network weights. When you ask it a question, it uses that compressed model to generate (decompress) a coherent response.
Consider the dichotomy:
LLMs display emergent reasoning, coding capabilities, and logic because they were forced to compress human language so tightly.
LLMs often suffer from "hallucinations" and struggle with novel logic puzzles because compression encourages mimicking statistical patterns rather than building a true causal model of the physical world.
An algorithm can achieve massive compression if it utilizes a highly complex, slow, or massive decompression engine. If a system takes 10 000 years to decompress a file, or requires an infinite amount of computing power (like Kolmogorov complexity), it cannot function as a practical intelligence. Real intelligence must operate within tight time and energy constraints.
> Maybe there's true brilliance out there
Brilliance is a trope. pg's 2009 "The Anatomy of Determination" deals with it: https://www.paulgraham.com/determination.html
In it, he argues that determination is the single most important predictor of success, surpassing even raw intelligence.
While popular culture loves the narrative of the "brilliant genius," Graham's experience backing hundreds of startups taught him that a highly intelligent person without drive quickly becomes ineffectual. Conversely, a profoundly determined individual can find pathways to success even in ordinary or unglamorous industries. Over time, determination actually starts to look like talent.
I'm going to commit a faux pas (a breach of HN etiquette) and give an AI summary in 3 bullet points because, well, the article deals with 3 points, so it's a good fit and I doubt I can compress it better than AI:
1. Willfulness. The desire to get your way regardless of obstacles or consequences.Being fearless about consequences and pushing through "hellacious" moments when others quit.
2. Discipline. The ability to force yourself to do what you planned to do. Being "hard on yourself" and turning off the background analysis in your mind that questions the plan.
3. Ambition. The grandness of your destination and what you want to achieve. Choosing the right target; if determination is a vector, ambition is the direction it points.
Of these 3, it's quite obvious at this point that LLMs are superior at 1) and 2), as LLM alignment is quite good, and it's ability to spin up sub-agents that can work for over 24 hrs is better than humans. Human limit is basically 1 hackathon's worth of cognitive work. Beyond that, health becomes a concern, and how many people can produce useful work under sleep deprivation? Codex can work for 24-ish hours, as evidenced by today's "Auto-research with codex: How I achieved a 232x Faster Kernel": https://news.ycombinator.com/item?id=49309549
So what's left for mere mortals? Apparently, nourishing your ambition:
"So here in sum is how determination seems to work: it consists of willfulness balanced with discipline, aimed by ambition. And fortunately at least two of these three qualities can be cultivated. You may be able to increase your strength of will somewhat; you can definitely learn self-discipline; and almost everyone is practically malnourished when it comes to ambition."
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#315I 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 wonder practically how useful it is. It should be very useful, right? Say you're a hiring manager, and now you can hire thousands of students who have almost eidetic memory across pretty much all the subjects. The students can produce amazing work if you give them specific instructions. They are also very good at mechanical pattern matching. That is, they are the uttermost crammers. They are like the students who don't really get STEM yet they could, through memorizing all the problem-solving patterns, ace any national college entrance examinations, IMOs, PHOs, Putnams, you name it, and all the way to solving hard problems like Sendov Conjecture - they even found out elegant elementary solutions! Mind you, Terrance Tao proved a weaker conclusion when studying the Sendov Conjecture and got to publish his work on The Big Four. That said, the students won't take initiatives, and they sometimes make very silly or even impossible mistakes, to the point that it requires your supervision and review. Would you hire them to do your company's work? I'd assume that answer is a resounding yes.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#316On 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 their output, but with very diminishing returns. Even if they were perfect, there will be an ongoing cost to little or no human awareness and understanding of the codebase.
It may take some time for people to recognize the cost of AI code generation and their value for virtually everything else, but I believe we'll get there.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#317Earlier quoted context omitted.
No, not morons, but people who have built a career on string theory. At this point, even if they regret their decisions, it’s too late to turn back now.
I don't think it's a good argument. String theory is just "one application" of advanced mathematical physics. It's like saying that software developers specialised in ReactJS would lose their career if ReactJS is suddenly abandoned.
ReactJS devs will retrain when the market dies. Professors still publishing theories/experiments costing large amounts of public monies better spent elsewhere.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#318Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#3191. remembering all the different information to remember all the tricks
2. trying all the different tricks in the problem
3. optimizing deciding which to try based on different information
4. trying random things to discover patterns (and hence new tricks)
5. explaining your tricks to others so that they can do the first 4 steps independently and come up with even better tricsk
6. refactoring tricks into common and special parts to create a well organized theory
7. documenting for future generation in a language they can understand
that's all thinking is.