"A Taxonomy of Omnicidal Futures Involving Artificial Intelligence"
(Jacob Tsimerman, Andrew Critch)
We should not be surprised if AI solves the Millenium problems very soon and advances to a level that is barely comprehensible, or even incomprehensible, to the best humans.
We can expect this not by curve fitting to recent progress but by reasoning from first principles about where the progress has come from (synthetic data, non-human corpus) that has no obvious upper bound on capabilities.
I'm not sure there is another profession in the world where it's impossible to explain to a layman on what the winners of their most prestigious award have worked on.
- Yu Deng: IMO gold [1]
- Jacob Tsimerman: 2x IMO gold [2]
- John Pardon: 3x IOI gold [3]
Fun fact: Tsimerman and Deng both overlapped with Peter Scholze (another Fields Medal recipient) at the IMO
[1] https://www.imo-official.org/results/contestant/8824/
Hackernews: Next time it'll all be LLMs. AI's going to kill us all, though, one of the mathematicians said so! Maths is useless anyway, what a bunch of nerds. Ooh, one of them likes lesbian fanfic.
Oddly. specific. Sorry, I don't get the reference, could you please tell me what/who does that refer to (which fanfic and person, and why said person and fact is relevant to this question)
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i’d like to revise my earlier comment: 2022 may have been the last time we had pure humans win a Fields Medal.
I’m fairly certain this batch's winners used LLMs for research, lit-revews, reviewing work, and calculations... perhaps not enough to count as a co-author, but still enough to handle a lot of the grunt work.
Who would have imagined the pace of progress in LLM-powered math..
https://www.quantamagazine.org/yu-deng-wins-the-fields-medal...
> For comfort, Deng turned to manga. “I remember him at Courant. He was always holding a manga,” said Jalal Shatah, a professor there who formerly chaired the math department. Deng particularly liked stories about deep friendship and romance and found himself drawn to a genre known as yuri, which focuses on those kinds of relationships between women — stories that “feel nice and warm and beautiful,” as he put it. They helped him be kinder to himself, “more comfortable with life.”
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Note that while the description "anime lesbian" might sound weird to western audiences, within asian nerd subcultures it's relatively a common thingy.
fwiw, I feel the same way about biology "Lysing action of the (1,2)b-carotene receptive encephalopathy pathway" type shit.
High school biology is enough to get a vague idea of this though.
Despite my degree being in engineering, which involved 4 semesters of calculus, and 3 other semesters of math, (7 total) I have absolutely no fucking clue what’s going on in the Fields Medal description above. It’s only barely more intelligible than if it had been written in Chinese (which I truly cannot read at all).
I genuinely don’t understand it at all. Even words that I think I recognize like “harmonic” or “geometric” are useless to me because the actual terms are “harmonic analysis” and “geometric measure theory” and I have 0% clue what those are.
I don’t have to google any of the words in the example biology title.
I work in something related to Image Compression, so when the computer has to download the image from Internet it's smaller and use less data. Anyway, I study the mathematical part, not the programming part.
The idea is that images usually have big plain parts like the sky or the wall of a house, so you use big blobs of "ink" to paint them. For the border you use smaller blobs of "ink". And very close to the border you use smaller and smaller blobs of "ink". In this method, all the blobs of "ink" has the same shape, the only difference is the size. Also, the plain parts are not perfectly plain, so you use some small blobs of "ink" there.
In a typical image, you need very few blobs of "ink" if you pick the shape of the blobs of "ink" correctly. So you can only send the position and size of the blobs of "ink", that is much smaller than sending all the information of the image. The hard part is choosing a shape of the blobs of "ink" to make this conversion automatically and very fast, without asking the computer to do something smart to select the positions.
If the listener has more technical background:
The blobs of "ink" have white "ink" in some parts and black "ink" in other parts. This correspond to positive and negative values and actually all the blobs of "ink" are an orthonormal base so the calculation is only a orthonormal base change, that is super easy and fast. There is no smart selection of the position of the blobs of "ink" positions, just a boring orthonormal base change.
If the listener has even more technical background:
Something something Fourier Transform.
I don't want to count how many lies that description has. Also, all the parts in this description were done by other persons perhaps 10 year before me. I think I only once compressed an image, just for fun, and got a tiny compression because it was a toy method (¿Haar base?).
https://www.quantamagazine.org/series/fields-and-abacus-meda...
Dating or maybe a significant other, parents, siblings, any BBQ event IE any social event outside academia where someone asks "So what do you do?"
Yes we do have plenty of practice adjusting our explanations to the audience.
Other fields do it, but it is almost systematic in math, and arguably, it makes things even harder to understand as people names are not descriptive.
Omitting the human history of a field does not automatically make it easier.
Same with their ability to summarize and explain things
And their ability to create mathematical objects that are similar, but weird in a funky way, to the actual real objects.
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He jumps, but the bunch still escapes.
So he goes away sour;
And, 'tis said, to this hour
Declares that he's no taste for grapes.
The tempting clusters were too high to gain;
Grieved in his heart he forced a careless smile,
And cried, 'They’re sharp and hardly worth my while.'
"But the Emperor has nothing at all on!" said a little child.
"Listen to the voice of innocence!" exclaimed his father; and what the child had said was whispered from one to another.
"But he has nothing at all on!" at last cried out all the people. The Emperor was vexed, for he knew that the people were right; but he thought the procession must go on now! And the lords of the bedchamber took greater pains than ever, to appear holding up a train, although, in reality, there was no train to hold.
Calculus was invented in 1670, it was about 1680-1700 till it started actually being used in astronomy. The uptake was probably faster because at that time a lot of mathematicians were Astronomers as well.
There is a lot of mathematics created but we don’t yet know how to use it. My hope is that AI can bridge the search gap to accelerate this.
This isn't really a good argument. The assumption here is that the "applications" were possible because of the math itself, but it leaves out the possibility if the math didn't exist somehow it will be discovered/invented because the applications demand so.
> There is a lot of mathematics created but we don’t yet know how to use it.
The vast majority of mathematical work is complete useless. Only a small percentage finds use in the real world (even if you consider the maths from centuries back).
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- winners in the 30s were the last time we have pure human to win (before computer)
- winners in the 70s were the last time we have pure human to win (before internet)
- winners in the 90s were the last time we have pure human to win (before search engine)
Why can't we treat LLMs as just another tool like computers, search engines, computing libraries? Why do people keep trying to anthropomorphizing these binaries?
People in the 1800s used to win awards and acclamation by simply hand-cranking numbers for popular calculations (Pi, error functions, etc.) and printing them in a book. This will just be the same thing.
"The homogeneity in x is an intertwining between a dilation (x,r,u) to (lambda x, r,u) and a dilation (P,Q,R) to (lambda^-2 P, lambda^-1 Q, lambda R) which seems to collapse the 3d jacobian to a sort of twisted 2d jacobian. Is there a general theory of such twisted jacobians and do you have any sense why those particular dilation weights were used?"
"I can see why the five-dimensional Jacobian has a nice monomial form in rho. Why does this make the three-dimensional Jacobian after restricting to c_2 = rho = 1 and eliminating the delta, eps variables also a monomial (now in x)? Is there some block-diagonal structure or something in the 5D Hessian that allows for a nice reduction? I would have expected some sort of Schur's complement type operation to appear."
I, and probably most people on here, won't be able to get the LLM to write such a detailed conversation, because we are not experts in this field. They are tools.
Or are you saying that’s what happened in this case. Because that’s not the way I understand it.
Original comment Source: https://news.ycombinator.com/item?id=48906573
Hey @netvarun, sorry about that. I originally read it in one of your comments, and I should have credited you when I mentioned it. My apologies.
There was never my intention to plagiarize. That's also why I wrote "this prediction" rather than "my prediction" but I still should have mentioned the source. My apologies again.Hope you understand.
But Tsimerman in particular is very AI pilled and has talked about how he thinks LLMs will be doing better work that most mathematicians in 2 years: https://x.com/gbrl_dick/status/2080416238606717052
(He's just been hired by OpenAI)
This is not as radical as it sounds. People did stuff like that all the time pre-LLM. It's just a question of how fussy the journal's editor is. See https://www.wired.com/2013/03/computers-and-math/ for examples in math.
HN discussion on that article: https://news.ycombinator.com/item?id=5322313
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They might not be officials, they not might represent the official organizations, but those things do happen.
I don't know, maybe. I would not put Clankers on the same level (or category / level of importance) as people but if they produce the work maybe they should get the credit.
But that's not what the Fields Medal is for.
If you're a 41 year old mathematician and do amazing groundbreaking world shifting math, you can't get a Fields Medal either.
For example, a single upper-division undergrad level course on probability will expose you to measure theory.
Similarly, harmonic analysis is something that you can take as a reasonably good senior in mathematics.
I didn't take those courses you're talking about, but that's my point. I have a top <1% education in math in the nation, maybe top 2-3% of all college grads, and that's not enough to even scratch the surface of the summary.
typically when I see mentions of harmonic analysis together with differential geometry I start thinking of fourier transform on more fancy shapes (on the sphere, for example, the replacements for complex exponentials are called spherical harmonics)
my PhD was EE in signal processing and I took some extra math classes at the graduate level, and continue to read some of this for fun and profit.
I still cant understand most of the terminology in the fields medal citations. that probably requires a more thorough couple of years of graduate education in mathematics.
math is by far the furthest of the sciences in terms of depth of human discovery.
Can anyone here not involved in theoretical math name 5 Fields Medalists? Take out Terry Tao or Andrew Wiles or Gigori Perelman and can you name any Pure Mathematicians from the last century at all?
I wouldn't be the least bit surprised if work done on the behavior of vectors in high-dimensional space by Hong and her colleagues someday becomes relevant to practical neural-net R&D. You never know what you might need in the future, but it will suck if engineers have to stop and figure this stuff out from first principles when they do need it.
von Neumann did a lot of theoretical work, e.g. https://www.academia.edu/download/38046446/Ohta_15_von_Neuma... where he was hanging out intellectually with McCullough and Pitts. He not only wouldn't be surprised at the ANN renaissance under way now, he'd ask us what took so long. He even cited M&P in his EDVAC report. Way ahead of his time, envisioning how hardware that wouldn't be practical for another 80 years might work.
Terence Tao's work (with Emmanuel Candès and Justin Romberg) on compressed sensing. Published in 2004-05. By 2007 that was being used for in-vivo MRI reconstruction with substantially undersampled data
June Huh's work on combinatorial Hodge theory was used within 3 years to improve sampling for random spanning forests.
Note that this is only Fields medalists (not all pure mathematics). There have been huge improvements in zero knowledge proofs and homomorphic encryption over the last ~5 years that are also directly applicable to pure mathematics, but no one has a Fields medal for it.
I have argued exact claim before and from what I recall, Tao maybe contributed 1% to MRI improvements in the last 20 to 30 years. You are way over exaggerating the importance of what he did.
Take category theory for example. The initial mathematics appeared in 1942. The application to social sciences started in about 1970 and I’m not sure of the level of uptake at the current time but a quick AI search says applications have accelerated in the past decade (needs verification).
https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...
This happened because Rudi was persistent and Einstein was kind enough.
In future, citizen scientists have a chance to work on their ideas using AI, eventhough they don't have the deep domain skills. Of course, an expert would still need to review it as usual. But it is a useful tool to democratize science further.
https://www.sciencenews.org/blog/context/amateur-who-helped-...
Yes, I do feel that. Make of it what you will.
If I were to anthromorphize my experience with frontier models, it would be as a mentally challenged child with complete memorization of an encyclopedia and thesaurus. It has the ability to rapidly experiment and potentially succeed at tasks through trial-and-error, but not without constantly corralling it in the correct direction because it would stick a fork in an outlet if unattended for five minutes.
Tao's chat certainly doesn't give me a vibe of talking with a peer. Do you much often have conversations with colleagues where you write one sentence and then get five pages dumped on you, repeating ad infinitum? LLMs can be useful for rubber ducking, and sometimes the plausibly-related word-soup it generates so quickly will help your thinking along faster, but that's not the same thing as a genuine conversation. And it mostly looked like Tao was using it as an advanced calculator, firing off his own ideas for it to quickly do calculations on. I don't know why we need to anthromorphize these tools just because they generate sentences.
https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...
While there was a bunch of human effort - it is not that hard to imagine this whole pipeline becoming fully autonomous in the coming months.
I asked chatgpt to write a poem about my mothers dog a while back. It spit out a poem that my mother likes and keeps around. When asked, I say chatgpt wrote it. If I asked chatgpt for a proof of the Goldbach Conjecture and it spit out a verifiable proof, I think I would go ahead and give chatgpt credit. Not that I think it is likely. It would be more of some ability (like a robot end effector is able to hold an egg) and monkeys at typewriters.
Maybe not Fields Medal worthy, but worthy of some credit.
The stuff you mentioned is first year business for most math undergraduates. You should not expect to know most things in senior level math after taking just first-year math.
It’s like expecting to know computational complexity theory, or distributed systems theory, after taking first year CS.
This is ahistorical. Elliptic curves had been around for a long time, but elliptic curve cryptography was applied from its birth in 1985. Also the reasons elliptic curves had been studied for so long (Mordell-Weil Theorem, Falting's Theorem, Sato-Tate, etc) didn't really have much to do with the reason it was proposed, which was that its group probably wasn't vulnerable to the same kinds of attacks as DH.
> When the problem eventually came along, the solution was obvious thanks to pure math.
Also ahistorical. ECC wasn't proposed until almost a decade after DHKE (possibly only that early because it was hot at the time thanks to Lenstra (https://www.math.uwaterloo.ca/~ajmeneze/publications/ecc.pdf)) and it took decades to get in common use. Doesn't seem all that obvious.
Memorizing an encyclopedia is not going to help you solve open high-level math problems, is it?
It kind of could, given the above. Part of an LLM's advantage is that, much like a calculator or a Chess engine, it can iterate over a finite problem space far, far faster than a human can. That much is expected of a useful computing tool.
It is worth noting that we know literally nothing about how the counterexample was achieved. Technically speaking, the person who tweeted it could have solved it themselves with zero LLM assistance and then attributed it to Fable to boost their IPO and ensuing payday. I'm not saying that's actually what happened, but it's hard to draw conclusions without any transparency about the degree of human involvement.
My daily experience certainly does not reflect that of prompting a superhuman intelligence when it routinely flubs commands and destructively drops the PATH of its vm, or bypasses an instruction about passing tests by burning millions of tokens constructing a completely new test suite that rubberstamps its own work when it can't pass the real tests.
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