{"slug": "conjecture-sniping", "title": "Conjecture sniping", "summary": "A researcher criticizes the shallow use of large language models (LLMs) to disprove famous mathematical conjectures like the Jacobian and unit distance conjectures, arguing that the true value of mathematics lies in crafting definitions and generating conjectures, not merely solving them. The author points to Grant Sanderson's video as a better explanation of the deeper purpose of mathematical research.", "body_md": "There has been a bit of excitement recently as LLMs have been delivering consequential results in mathematics. First the headline result in May that the unit distance conjecture had been refuted, and just now Fable was prompted into apparently disproving the Jacobian conjecture. During the World Cup final. In a tweet.\n\nErdős conjectures have become the favoured target of a legion of citizen scientists one-shitting (sorry, shotting) proof attempts into the Poissonian shooting gallery that is combinatorics.\n\nTwitter bros are breathlessly losing their minds: “math is dead!!!”, “math factories!!!”\n\nI must confess it all leaves me feeling more than a bit disheartened. But not for the reasons you might think.\n\nTo be clear: I am *extremely* activated about the potential of LLM-assisted research. What I want to say takes aim at what I feel is a gaping misunderstanding about what research science is all about.\n\nThe collective media twitter-meme-bro artificial (un)intelligent consciousness is just so shallow, so trivial, so… unimaginative. Why is it that everyone, so predictably, so spiritlessly, does exactly the same thing: “let’s prove the Collatz conjecture”. Wtf is it with the Collatz conjecture!? Is that like the only thing you ever heard of!? (And don’t you even dare say the Riemann hypothesis. That is the LLM-mathematics equivalent of playing Smoke on the Water in a guitar store.) Oh, the Collatz conjecture can’t be proved in one chat? Ok, Erdős it is then.\n\nI wanted to write something persuasive, and stirring, about how maths, and science in general, is so much more than just pinging off conjectures one at a time. Luckily, I don’t have to. Grant Sanderson explained it all about a million times more eloquently than I could ever hope to. Stop reading right this instant.\n\nGo watch it now: [https://youtu.be/TfyPshgMbug?si=KFyANwDvcBQaIB6a](https://youtu.be/TfyPshgMbug?si=KFyANwDvcBQaIB6a)\n\nOh, you are back? So, please just insert “what he said” right here.\n\nWe now have a common understanding (thank you once again Grant, who has such a deep feel for the mathematics profession, and for *why* it is the way it is). So you get it now, right? You get that proving conjectures isn’t the sole goal of mathematics, of physics, of science. There is far more to it. You appreciate now that *coming up with* a good conjecture is more highly prized. (It really fucking is. I have sat on multiple hiring committees for maths professorships where a candidate’s ability to generate interesting and productive conjectures was openly praised *far* above their ability to solve them.) And you see now that crafting a good definition is the profoundest thing of all.\n\n*Books* are written about a single definition (take, e.g., the whole field of topology). Whole research schools work on definitions. Careers are made by good conjectures.\n\nThis is why I am so underwhelmed, so demoralised, so disheartened by the droves mindlessly swarming famous conjectures. It is not that LLMs aren’t useful. OMG, far from it. Their capabilities are frankly mind altering.\n\nIt is the arrogant crassness of it all: ignorantly dispatching an army of LLM clankers off to prove Erdős conjectures without ever grasping the “why”.\n\nFor many understandable reasons LLMs are going to be pretty good at disproving conjectures. But there is one thing they are bad at: coming up with conjectures. And you know what they truly, deeply suck at? Definitions.\n\nI have spent the better part of a year putting deliberate practice into utilising LLMs for scientific research. I have stared directly into the abyss, at the eldritch horrors of definition slop concocted by uncontrolled LLMs let loose on exploratory research.\n\nThis is where the hard work is. I have enduring respect for anyone who can tame an LLM into building new theory with agents beyond the horizon of a single chat window. Everything comes into play at this scale: orchestration, validation, exploration, exploitation. I have spent agonising and often frustrating months trying to crack these gnarly workflow problems, to harness the power of LLMs to do *actually new research*. You know, that stuff involving conjectures, and new definitions. I have not come close to this challenge.\n\nThe software engineering field has started to talk a lot about “taste” recently. They were the first to see what happens when you turn off the lights in a software factory. This fate is ploughing towards us, like a supertanker with no one at the helm. It dismays me that everyone has to go through this learning curve first, to see that you can’t just turn the lights off on a factory of agents building new theory. Antediluvian nightmares await you down there.", "url": "https://wpnews.pro/news/conjecture-sniping", "canonical_source": "https://tjoresearchnotes.wordpress.com/2026/07/20/conjecture-sniping/", "published_at": "2026-07-20 20:12:30+00:00", "updated_at": "2026-07-28 12:58:41.112589+00:00", "lang": "en", "topics": ["large-language-models", "artificial-intelligence", "ai-research"], "entities": ["Grant Sanderson", "Jacobian conjecture", "unit distance conjecture", "Collatz conjecture", "Riemann hypothesis", "Erdős conjectures"], "alternates": {"html": "https://wpnews.pro/news/conjecture-sniping", "markdown": "https://wpnews.pro/news/conjecture-sniping.md", "text": "https://wpnews.pro/news/conjecture-sniping.txt", "jsonld": "https://wpnews.pro/news/conjecture-sniping.jsonld"}}