'Stunning' percolation proof solves decades-old puzzle about phase transitions
quantamagazine.org47 points by tzury 6 hours ago
47 points by tzury 6 hours ago
> The week before Christmas 2025, five mathematicians were holed up in a classroom at ETH Zurich.
So happy this didn’t end with, “tweaking their prompt for ChatGPT Sol” or whatever.
> He, Diskin, and Radhakrishnan made some progress and brought their results to Sudakov and Tassion. As Tassion took in their work, an idea — perhaps an outrageous one — formed in his mind. … Over those weeks, the collaboration became frenzied. The mathematicians traded ideas constantly, often texting late at night.
It will be a truly sad world if we automate this away.
I understand the sentiment and even feel it myself as a software engineer because there is/was so much ego wrapped up in these kind of skills. However, I have kind of gotten over it because I am now hopeful that AI may now help us solve problems at a much faster rate now that we could before and I think this is actually exactly what we need right now to solve things like climate change etc. If that means that humans don't get all the credit anymore then oh well, at least we may actually have the chance to solve some big issues now.
I'm totally in favor of the pursuit of knowledge for its own sake. But if a non-human agent had been one of those participants, does that subtract from the value of the result? I don't think so.
>It will be a truly sad world if we automate this away.
In my opinion, research can't be fully automated because the space of possible problems is too large. You need humans to decide which problems are worth spending time on, and to evaluate which results are important. We might expect AI to automate some of the routine aspects like searching for counter-examples or formalizing proofs, but that will free up resources for humans to focus on the big ideas and the direction of research.
> You need humans to decide which problems are worth spending time on, and to evaluate which results are important
Why?
Because they likely have a better sense of what could and/or will be fruitful. Same reason an experienced mathematician likely is better at this than a random person off the street.
Incidentally, Duminil-Copin, who also works in percolation theory, wrote an essay on the impact of AI on math.
https://proofsandprompts.com/2026/08/30/care-for-a-little-mo...
What’s so awesome about this? People texting about their ideas?
They are performing cognitive labor. Good for them I suppose but what is so romantic about this particular type to deserve these types of responses?
I think the "romanticism" is literally... romanticism. E.g.,:
(often Romanticism) a movement in the arts and literature that originated in the late 18th century, emphasizing inspiration, subjectivity, and the primacy of the individual.
Literally, we're saying, "humans interacting with humans and being subjective is what brings joy and creativity to people."
That sounds pretty dead on to me. Automating it to a process is the exact opposite so.. I think you're asking the wrong question. If you're trying to ask "why would people want to do this" I don't have an answer for you that isn't a study in the humanities.
Any type of "cognitive labor" i.e. learning and thinking and reasoning, is cause for celebration. It grows the individual as well as our culture. I cheer when I see children do it, and I will surely cheer when academics do it.
It's just workism with rose tinted glasses. All the perpetuation of the current "knowledge economy" would actually mean for most people's children (few of which whom will be blessed to do such erudite forms of cognitive labor - as has always been the case) is more time sitting at a desk, filling out spreadsheets, more psychosis from having humans be an interface where belongs a machine.
The irony is allowing machines to automate the economy will allow more people to have more enjoyable lives. For every nerd plugging away at something like this there are millions of ancestors who fought and died and clawed to do what for most humans for most of history was the only thing that qualified as labor - participating in brutish endeavors (hunting/farming/murdering) that barely sustained their short lives.
LLMs over the next century (probably in China given the retrograde impulses dominating both sides of the political aisle in the US) will likely assist (if not autonomously) solve cancer and other diseases, invent new alloys and forms for manufacturing, automate away all labor (including most if not all military service), travel farther into our universe than any human ever plausibly could, and other breakthroughs.
A huge concentration of the actual talent of our world is already enmeshed in this endeavor. The majority of the detractors aren't cut out to compete, so they cling to their "bullshit jobs"[1] instead of leveraging the democratic processes their ancestors bled for to simply convince enough of their fellow humans to engineer an equitable redistribution of gains. Why do so many people want to eliminate the only chance their kids will have to not have to work? Is it some desire to inflict our modern masochisms onto future generations? It's like watching these colonies of men sign up to get screamed at to prove they are masculine [2]. The West seems to have entered a state of mass delirium. It's the same thing. Pining for the past. One is even more distant - where the labor of raw strength mattered. Another is I guess pining for the more recent past where if you could write or manage powerpoint or excel effectively enough you could have the "American Dream."
Most of the people applauding this particular mathematical breakthrough are unlikely to be able to understand it. It's the same irony that has led man for centuries to use romanticism about human nature selectively. For most of history these conceptions were used to draw arbitrary lines around which homo sapiens were and were not worthy of basic dignity - who was citizen and who was slave. The same capacity for cognitive dissonance is alive and well in modern man.
Don't curse your children. If you don't like who owns LLMs in the United States, the democratic tools to nationalize or redistribute the gains are at your disposal. If you were to actually engage in this battle you will quickly learn the "enemy" is not the machines - it's what it has always been, your fellow man. The past is not coming back, and it was never that great to begin with. It was not so many generations ago that most children who were born died shortly thereafter, and more children were born in general because children were a source of labor to keep the household afloat.
Stop romanticizing labor.
[1] https://en.wikipedia.org/wiki/Bullshit_Jobs [2] https://www.newyorker.com/magazine/2026/04/06/the-camps-prom...
This is hilarious because you are criticizing people spending their time tackling hard knowledge issues, but meanwhile the tech that you hail as your savior is a product of that very effort you criticize, and the continued progress of that tech depends on people continuing to plug away at these hard science, math, and physics problems.
You must have misread me. I'm attacking the romanticization of said labor in the context where it was contrasted with LLM automation, where the former was valued over the latter. Said condemnations of LLMs are not exactly a novel framing in modern discourse, and as you may have surmised, I find these framings tired at best, and on the whole harmful to humanity on the actual merits.
Of course, I applaud the humans doing the hard work to ensure no human has to ever labor again. Apologies if I was unclear on that perspective. I suggest a second look at my reply will however convey this to you.
The case for the "bullshit jobs" theory seems extremely weak to me. If a job is pointless and not adding value, there is an incentive to eliminate it. Markets aren't perfectly efficient of course, but they're not so inefficient as to create millions of jobs that serve no purpose.
The truth is that many people enjoy working. It's satisfying and fulfilling to build something useful or to make a discovery that contributes to human knowledge. We can acknowledge that and then consider the entirely separate question of the ideal level of resource redistibution.
As another comment mentions, this objection has already been dealt with numerous times.
But you then go even beyond the already answered market efficiency/plausibility objection that comes up ad nauseam when Bullshit Jobs is mentioned to make a positive assertion that:
> The truth is that many people enjoy working
On what basis? What is "many"? Do you think a majority of the workforce would elect to keep working if they could maintain their current standard of living without any work? Do you think this would maintain independent of any standard of living? Do you think people would no longer find fulfillment in performing some work (whatever they choose) if it was not economically required of them to perform some labor? I mean presumably the people who do not want to sit around and do nothing will act accordingly. Let them do whatever they want. Why does it follow from that to say that most people "enjoy" having to exchange their labor to earn a paycheck?
It seems to me you are making a rather remarkable claim, with little attempt at substantiation. Maybe you could answer some of my questions to flesh out your point a little more?
You're defining "work" as exchanging labor for a paycheck. I don't agree with that definition. I would define "work" as putting time and energy into a project to meet personal or organizational needs. One of those needs is sustenance, but that's not the only one. In the absence of the need to make a living, I still think a majority of people would work on things like artistic projects, scientific research, philosophical inquiry, creating entertainment, raising children, and providing for their community.
I feel like I can almost see the shape of this, but that it's still very blurry for me. Seems like it could be used for some cool stuff, but I can't quite make out what. Procedural generation? Shader effects? Beyond the more important physical stuff they describe in the article, seems like there's some potential for fun with this?
Refreshing to read about a proof where the critical part is not how they cheered Claude to solve it.