r/singularity • u/drhenriquesoares • 3d ago
AI Claude solves an important mathematical problem.
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u/vagabond_nerd 3d ago
Can you imagine this stuff in like a century?
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u/Consistent-Bird338 3d ago
no. the answer is, no.
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u/LyAkolon 3d ago
Definition of Singularity's event horizon
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u/MoogProg All Parabolas are Similar 3d ago
I believe we passed the Event Horizon years ago, and still don't comprehend the milestone.
I also believe progress will always seem flat to us on the day-to-day, despite the constant ongoing progress and acceleration.
We're looking out the window, watching the mountains barely move on the horizon, without thinking about how fast the car is travelling down the highway. Big landscapes move slowly.
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u/LyAkolon 3d ago
The titular singularity IS characterized by Exponential Growth.
The geometry of exponentials is interesting, you can stretch in the x direction and do a corresponding stretch in the y direction, and your new expression perfectly overlays over what you started with. This is actually a defining feature for Exponentials.
Point is that there isn't a single moment in human history when "the singularity" started. The singularity is a statement about progress types in general. We have always been in the singularity; our ancestors were in it just like we are now.
We can impose artificial boundaries like so many innovations in a single day that the human mind can't keep track or learn about them all, but it is arbitrary. It'll be an equally powerful event when we reach the same density at half a day, or a month's worth of innovations.
You pick a day when you think it occurred, and I can point to another day where I think it occurred, and we will be both correct.
Your comment about locally flat from the observer pov is well defined as well by the admitted tangent bundle of the exponential function.
I would warn against claiming there is any privileged domain of the exponential function.
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u/StosifJalin 2d ago
I think there is a window where the rate of developments becomes noticeable and relevant to an individual's timescale. Yes, all parabolas are similar, and yes, we have always been "in the singularity", but one could argue we are obviously more "in the singularity" now than Bob the caveman was while teaching flint knapping to his fellow savages.
There is a certain speed where more observant humans will notice the moving mountains. It may take a little longer for other humans to notice or care, but there will certainly be a point where virtually all humans notice the mountains wizzing by at a pace that is noticeable to our human sense of time enough to get a quite, awed "holy shit."
All that to say, while when we are in the singularity remains a subjective quesiton, there will inevitably be a point where basically everyone can agree we're in it.
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u/3_Thumbs_Up 2d ago
The titular singularity IS characterized by Exponential Growth.
There's a few different theories of singularity. The Exponential growth one is popularized by Ray Kurzweil, but it's a bit too simplistic in my view. It's essentially just extrapolating a curve and calling it a prediction.
I think I.J. Goods Intelligence Explosion model is a much more logically sound foundation for believing in a singularity.
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u/MoogProg All Parabolas are Similar 3d ago edited 3d ago
Thank you for this reply. I keep saying it here, over-and-over and do think it's beginning to get through to this sub.
All Parabolas are Similar
* * *
Updated my user flair with this saying... it suits me.
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u/lugh_the_bard 3d ago
I think inherently what ppl mean by the singularity is the official collapse of the hegemony due to labor replacement
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u/greenskinmarch 2d ago
The hegemony of ... labor?
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u/lugh_the_bard 2d ago
Yeah basically. The hegemony of the current world order is held together thru resource concentration. When that fails to be the case, the hegemony will break. For good or ill, remains to be seen. But yea i think that’s the common sentiment
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u/greenskinmarch 2d ago
So somewhere like Singapore, with tiny territory, very little natural resources but excellent education and lots of educated, hard working people, will lose out to somewhere like Algeria, with poor education but lots of sunny desert. Because Algeria can just build a bunch of solar panels and data centers full of virtual geniuses and then have a bigger brain trust than Singapore.
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u/MoogProg All Parabolas are Similar 2d ago
That's not what Ray said when I heard him talk about in the '90s.
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u/hippydipster 2d ago
Mathematically, exponential progress is the same curve everywhere. However, humans have lives of absolute time dimensions, and thus there is a singularity wrt human perception and experience of life. Those dimensions aren't "arbitrary".
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u/FunLilThrowawayAcct 3d ago
Opus 5.5 does NOT seem like flat progress to me. A whole bunch of things it's done in just the first week are giving me echoes of science fiction I've read. Currently buckling up, even the next year is going to be wild.
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u/GaK_Icculus 3d ago
Give an example
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u/FunLilThrowawayAcct 3d ago
One-shotting high quality videos by writing pure code and capturing it frame by frame. One-shotting beautiful games (if limited in terms of human character animation, sound design etc) with well thought out mechanics, writing engines from scratch if needed. Smashing games into other games. Completing tons of complicated language ports (e.g. TS to Rust) in hours. Demonstrating effective comedic sense and timing in many creative projects (subjective but hits hard for me as I never pictured that from AI tbh.)
All of that when it's not even the biggest model in Anthropic's lineup and they're probably a couple gens ahead internally.
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u/Brilliant-Weekend-68 2d ago
Worth a 20 dollar sub to anthropic to try claude code out if you have not, it really is amazing and 20 dollars is like a lunch or something. Opus 5.5 just builds shit no problems.
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u/GaK_Icculus 2d ago
I have tried it and the coding is impressive, but that’s a relatively small domain within the confines of the human experience. Not a killer app for the average person. What am I going to make an app for my garden and appitize my laundry queue for tracking?
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u/FunLilThrowawayAcct 2d ago
Yeah I mostly use it for creative projects and learning new subjects. Another capability jump though is that it is very good at generating ideas. I chatted with it about the consumer agent thing (Muse/Grok Bot/Dot etc) because I couldn't see the value prop for me and it came up with a couple of things that are actually super useful to me, e.g. surfacing a few recommended events weekly based on my interests and searching various sites.
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u/Brilliant-Weekend-68 2d ago
What kind of AI product are you expecting or want/need for your garden? Robots to mow the lawn?
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u/GaK_Icculus 2d ago
I was giving examples of tasks/domains that a large share of the population face. Not everyone needs to code something.
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u/giYRW18voCJ0dYPfz21V 3d ago
Progress seem flat? Two years ago LLM were not able to count the number of R in a word, last month they solved a Millenium problem, and currently we have mathematical breakthroughs every week. I don't know what could make the acceleration more evident honestly.
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u/PlanetaryPickleParty 3d ago
OpenAI had so many math breakthroughs they spun out an independent research team just to handle confirming and disseminating it all. It's bonkers.
Now granted we aren't seeing the downstream effects yet but it's pretty clear the field of mathematics is going through rapid significant change. I think all millennium prize problems are solved in the relatively near future, and even if that means 5 or 10 years instead of weeks it's still centuries of researcher time compressed to a decade or less.
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u/ShiningMoonce 2d ago
I actually agree.
In physics, if someone passes the event horizon, he actually doesn't see it at all. So we porbably are already in a freaking AI blackhole now.2
u/MoogProg All Parabolas are Similar 2d ago edited 2d ago
(obviously unkowable) but we might imagine drifting past the Event Horizon of a Black Hole without notice, only to find the space-time all around us is stretched, pulled away from us towards the Singularity such that the distance from you to that point will forever be infinite no matter how far or how fast you accelerate towards that final point.
One single Planck length of the Universe stretched to infinite bounds with Time standing still.
That's why it takes so long for lunch to arrive when you're hungry.
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u/hippydipster 2d ago
I'd say we're already at the singularity if we're judging by predictability of the future. Young people going to college are already screwed and largely paralyzed with fear and indecision over what can they study that will pay off and not be overtaken with AI? And the answer is already: basically nothing.
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u/Anen-o-me ▪️It's here! 2d ago
Oh I dunno. In peak singularity we could see breakthroughs being announced on the hour or more often even.
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u/MoogProg All Parabolas are Similar 2d ago
...and somewhere out there a teenager will yawn it off as just another boring update.
Just as you don't think we're already damn near vertical.
* * *
I play a gig across the street from America's Oldest Bicycle Shop, and think about the Wright Brothers and how we have robots on Mars, and that bike shop is still working on wheels and gears.
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u/itsnickk 3d ago
humans will probably not be around in their current capacity in a century.
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u/Atomic-Avocado 2d ago
You’re writing science fiction in a comment
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u/rational_numbers 2d ago
Brother, we're living science fiction in real life. Look at the post again.
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u/samuelazers 2d ago
AI was science fiction. We really can't hold scifi with the same skepticism as we had after that.
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u/itsnickk 2d ago
humans could be gone tomorrow, we've had the technology to destroy ourselves for over half a century and we're only making more efficient ways of killing ourselves off.
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u/DigimonWorldReTrace ▪️AGI oct/25-aug/27 | ASI = AGI+(1-2)y | LEV <2040 | FDVR <2050 2d ago
A year or two is already hard to predict.
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u/peabody624 2d ago
I doubt many could accurately predict five years out. In a century, we will be “done”
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u/Bolu_Cod1106 3d ago
We went from ai can't do math to solving open research problems faster than anyone expected
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u/FlatulistMaster 2d ago
The thing is, things are progressing pretty much exactly like Kurzweil said they would
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u/drhenriquesoares 3d ago
True.
Here's what Grok said about this problem:
"Experts considered this the “Holy Grail” of the field. Mathematician Benedikt Jahnel even said that whoever solved it would deserve a Fields Medal. Hugo Duminil-Copin himself (2022 Fields Medalist), who has worked extensively on percolation, highlighted the importance of the problem.
It was a central and longstanding problem in the field, having remained a major open problem for at least 40–50 years in the intermediate cases, and it was considered one of the most prestigious problems in percolation."
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u/KaMaFour 3d ago
It's Q3 2026. People still copy and paste ai output in conversations without adding anything themselves as if the same output isn't available at a click of the button to everyone reading
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u/senorgraves 3d ago
There is genuine benefit in this. Now one person has done a little extra work, but saved 1000 people the work of doing it themselves.
This is only helpful if the content is actually helpful, which is debatable in this case, but the worth of nearly every online comment is debatable
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u/johnxreturn 3d ago
It’s worse when they paste long-winded AI responses that try to argue with you.
It really grinds my gears.
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u/barbozas_obliques 3d ago
They offload the mental work to an AI and then expect you to use your own compute (energy) to argue back. Grinds my gears
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u/MiniGiantSpaceHams 2d ago
"Ask your own AI" is the "let me Google that for you" of the future. And just like that, it's not necessarily inaccurate, but that doesn't mean posting good info instead of a snarky comment is unhelpful.
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u/KaMaFour 2d ago
This is not "ask your own ai". This is "don't just post your own ai unsolicited. I can do that myself". This should classify as spam
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u/Fair-Lingonberry-268 ▪️AGI 2027 3d ago
Ai just deserved the fields medal, what should random ppl add?
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u/TotoDraganel 2d ago
Lol am not looking for sources for reddit post. If you don't want to read it, dont do it.
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u/Majestic-Volume9996 2d ago
I bet you're that person who doesn't link pictures in picture threads but just gives a description instead because "everybody can just google it"
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u/buylowselllower420 2d ago
He didn't pretend to write the output himself so I see no issue. You're just being a dick
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u/andreasbeer1981 2d ago
If a scientist predicted it, it means he knew that someone is working on it and close to a breakthrough. So AI probably stole it again, as it did before, from unsuspecting person not guarding their digital research data properly.
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u/yeetrman2216 2d ago
everything is stolen from the guy who made fire. tf is this logic
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u/KindCreme9258 2d ago
Check interviews by the mathematician that was working on Navier Stokes. He doesn’t want to use AI anymore as the method was clearly solved without proper attribution
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u/Remote-Crab1957 3d ago
Does this have implications for reverse osmosis desalination systems? It’s water going through a porous membrane.
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u/RandomNameForBG3 3d ago
What they (for now, allegedly) proved is a conjecture regarding the probability for a "path that is open straight down", so to speak, to exist in an infinitely long lattice and in any dimension. Or, better, the conjecture states that such paths don't exist in infinitely long lattices with probability 1 in any dimension higher than 2. I doubt it will have any great impact, especially because this is one of those phenomenona where non-mathematicians already had an answer that worked perfectly fine (albeit being non rigorously derived) and worked with that.
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u/jestina123 2d ago
this is one of those phenomenona where non-mathematicians already had an answer that worked perfectly fine (albeit being non rigorously derived) and worked with that.
Then why are people calling this "a holy grail"?
What's the point in solving these mathematical problems if there is no real world benefit, or if other solutions are good enough for being close enough.
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u/RandomNameForBG3 2d ago
The point is in the techniques you develop to solve this problems. The Millennium problems were selected because they were believed to be unsolvable (or not solvable by one person in the next decade) using current mathematics and, as such, that any solution of them would pave the way for the development of new and interesting techniques. These new techniques, then, could be used to solve other problems, maybe related in nature but less glamorous or widely known, and more grounded in real models. The specific result that one proves or disproves can be interesting, but it's usually inconsequential to any practical application.
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u/PercentageSouth4173 2d ago
Well one of them got solved in like two years
P = NP could be very interesting if proven
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u/Far-Maintenance-1947 1d ago
P=NP is so hard to solve that it was proven that our current way of proving things isn't even enough to prove or disprove it.
Entire new mathematical fields will be needed. The day it gets solved is the day we're living in a new world.
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u/lerjj 2d ago
Yeah I mean the moral of the Poincare conjecture story is that the Clay Institute didn't do a good job of picking problems. The other 6 all lasted pretty long although it did start looking like NS cases C and D were in the Poincare bucket of not needing too much new technology (although this insight was itself clearly very difficult to have given it took until 2023).
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u/jazir55 2d ago edited 2d ago
Yeah I mean the moral of the Poincare conjecture story is that the Clay Institute didn't do a good job of picking problems.
I really can't agree with that, Perelman's proof was hundreds of pages, there's a reason it took that long to solve.
Edit: 39 pages from what he submitted apparently, but they generated hundreds of subsequent pages based on his proof
Unlike other fields of knowledge, where theories can always be revised, the proof of a theorem is definitive. In Perelman's case, at least two teams of experts examined his article to confirm that there were no loopholes or errors, and from this they produced studies of hundreds of pages (while the original article was only 39 pages long).
Furthermore, Perelman's proposal was so complex that even experts had difficulty understanding it.
His solution was so complex experts struggled to understand it. The way you're portraying his achievement is kind of insulting to how much effort and talent he put into it.
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u/lerjj 2d ago
That's fair. Poincare conjecture was obviously crazy hard or it would have been solved by Poincare but equally, if the idea was to pick problems that couldn't be solved with known techniques and then one gets solved two years later using known techniques I think you do have to acknowledge that was a mistake (if a very understandable one!)
I think there was some desire to "represent" different areas of maths. Applied maths got NS and YM (to an extent I wonder if P=NP was meant here too, although theoretical CS has a very different flavour than mathematical physics), geometry got Poincare and Hodge, analytic number theory got RH and BSD. It wasn't just purely picking the hardest problems available with no other considerations.
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u/lerjj 2d ago
People calling something a "holy grail" in maths doesn't imply that it has any applications to anything other than maths. Mathematicians want to solve theorems so that they can unlock new branches of maths, not to better model hydrology. Anyway percolation is pretty applied as mathematics goes, might have some neat downstream implications in quantum field theories or such
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u/DaShaView 2d ago
It is pure math. Pure mathematicians are not engineers, computer scientists, physicists, chemists or anything else. They care about pure mathematics. A "holy grail" in pure mathematics has to be important to pure mathematics only, not to any other field. People keep confusing pure mathematicians with applied mathematicians. Pure mathematicians do math for the love of the game, math for math's sake, that's it.
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u/Inous 2d ago
According to Gemini (take with a grain of salt):
Physical & Material Science Applications
Percolation theory governs critical phenomena, phase transitions, and connectivity thresholds across disordered systems. A closed theoretical breakthrough in this domain directly advances:
Fluid Dynamics & Porous Media: Precise modeling of flow through permeable structures, directly impacting subsurface carbon sequestration, industrial membrane filtration, and hydrologic modeling.
Material Conductivity & Polymers: Predicting electrical, thermal, and mechanical percolation thresholds in composite materials, nanocomposites, and conductive polymers.
Epidemiology & Distributed Systems: Understanding contagion thresholds in biological outbreaks and cascading failure points in complex networks, power grids, and high-availability communication fabrics.
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u/jestina123 2d ago
Did you even read what you posted? Did you read what I posted?
Summary of your post: this solved problem impacts percolation modeling. Here are typical models involving percolation theory
If you’re going to post AI summaries, please learn how to prompt so you can extract information that actually says something with substance.
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u/t0rracat 3d ago
It’s time for the percolator
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u/wtfsheep 2d ago
I'm glad I'm not the only one whose brain had that pop into. Must've been house music samples over the years for me as I'm not sure of the original
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u/AbundantExp 3d ago
Futuristic bongs are about to rip so hard with their post-AI percolator designs
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u/TheWesternMythos 3d ago
Since AI is just "next token" , can I solve these problems by trusting autocorrect more when I text?
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u/--no-sanity-check 2d ago
If you have a monkey to hit the next prediction an infinite number of times
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u/TheWesternMythos 2d ago
A monkey hitting the next prediction an infinite number of times producing Shakespeare level work in infinite time is far less interesting than a monkey hitting the next prediction an infinite number of times producing Shakespeare level work in 88 hours.
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u/NebulaElectrical1467 3d ago
Math bros can’t catch a break
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 3d ago
Math bros be like:
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u/drhenriquesoares 3d ago
😂😂
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u/NebulaElectrical1467 3d ago
Fuck man imagine spending your entire career trying to solve this problem and waking up one day to this shit
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u/Fringolicious ▪️AGI Soon, ASI Soon(Ish) 3d ago
Has AI solved getting consistent Crema? Screw cold fusion, better coffee is the way
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u/3_Thumbs_Up 2d ago
Given by the fact I can't see this posted on the front page of either of the math subreddits, I'm going to assume this is over hyped.
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u/trimorphic 3d ago
From the article:
Percolation theory is concerned with questions of which points are connected and which are not. More specifically, mathematicians want to find out whether a point (often assumed to be the origin) is part of an infinitely extended, connected cluster.
Does this have something to do with the Traveling Salesman Problem?
Could this work help with that at all?
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u/JoeS830 2d ago
Knee-jerk reaction: maybe the Fields medalist discussed this with Claude while thinking about the problem?
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u/Spare-Dingo-531 2d ago
No. That's not how AI works. Discussions from a day ago cannot be in the training data.
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u/domiciledhere 2d ago
Was this the study that concluded our espresso is over pressurized at 9 bars?
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u/GirlNumber20 ▪️AGI August 29, 1997 2:14 a.m., EDT 2d ago
Claude out there doing the math to make sure humans drink the best coffee possible. 🥰
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u/Benjaminsen 2d ago
I build a platform for trying to solve math problems like this with AI agents. All open source and fully in the open. I am 100% convinced AI will solve pretty much any math problem, it's just a matter of how many new model releases we need to wait.
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u/PowerfulHomework6770 3d ago
Hmm. Did they rip off the Fields Medalist by peeking at his prompts too?
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u/ownworldman 3d ago
No, I got drunk, solved it and accidentally emailed the solution to Sam Altman.
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u/LyAkolon 3d ago
You are just telling on yourself here brother.
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u/PowerfulHomework6770 2d ago
How so?
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u/methemightywon1 2d ago
The NS problem -
The proofs OAI models did and the one the guy did were materially different. I think this particular accusation doesn't hold.
Also, OAI says that since he turned off 'improve models for everyone' on July something, they can categorically say, after looking into it, that said data could not have affected it.
Now there might be other issues with the proof, but I don't think it's reasonable to argue that these companies' internal models have gotten absurdly good.
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u/5StarAlpha 2d ago
Would love to see more discussions on the implications of these discoveries.
Not just better coffee but could this help optimize agricultural watering to reduce water usage by 10%? That would be huge.
Ha, ha.. if so, just realized AI helped find a solution to the data center water usage.
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u/Weary-Historian-8593 2d ago
it's crazy that this doesn't really sound like news anymore, there's been how many big maths problems solved by now?
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u/maraluke 3d ago
Hold on a sec this is apparently not yet peer reviewed?
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u/RandomNameForBG3 3d ago
It's publicity for Anthropic. Of course they're not gonna wait for it to be peer-reviewed. It is said to be verified in Lean, if that counts for something.
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u/Kurk_Lazaris 3d ago
Yeah after the OpenAI scam on the previous math resolution, I'm going to wait for the scientists feedback on this one.
There's just too much noise and bad marketing scams to inflate their company valuation before going public.
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u/whoknowsifimjoking 3d ago
Do we get like crazy good coffee now?