{"id":937556,"date":"2026-10-18T11:18:29","date_gmt":"2026-10-18T11:18:29","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/937556\/"},"modified":"2026-10-18T11:18:29","modified_gmt":"2026-10-18T11:18:29","slug":"is-this-the-end-of-math-as-we-know-it-2","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/937556\/","title":{"rendered":"Is this the end of math as we know it?"},"content":{"rendered":"

OpenAI\u2019s models solved hundreds of major math problems last week. One professor tells us what it means for the future of the field<\/p>\n

Reprinted with permission from Be Giant<\/a>, a non-profit, non-partisan media outlet reporting on the people, places, ideas and breakthroughs shaping Canada’s future. Sign up for their weekly newsletter<\/a>.<\/p>\n

On October 6, OpenAI released a raft of documents that shook the math world<\/a> \u2013 372 results that claim to resolve well-known open questions in mathematics and theoretical computer science that researchers have been studying for years. Mathematicians told The New York Times that the release was \u201cbreathtaking\u201d and \u201ddevastating,\u201d<\/a> adding that \u201cuntil very recently, it would have been impossible to imagine that the frontiers of mathematics could move so far in one day.\u201d According to OpenAI, the results were achieved with a single prompt to a single AI agent. Be Giant asked Michael Groechenig, vice-chair at U of T Mississauga\u2019s department of mathematical and computational sciences and a winner of the New Horizons Prize in Mathematics, what this development means for the field \u2014 and whether the result is a canary in the coal mine.<\/p>\n

Was October 6 Judgment Day for the field of mathematics?<\/p>\n

It was not. The mathematical landscape is vast. There are so many problems out there. The ones that OpenAI tackled are problems that people have actively worked on, so they come with a certain prestige \u2013 that\u2019s what companies like Anthropic and OpenAI are piggybacking on. I think they\u2019re betting that a lot of people will conflate being good at mathematics with intelligence.<\/p>\n

To non-mathematicians reading the headlines, it sounds like OpenAI has accomplished something groundbreaking. Is there reason to be skeptical of the results?<\/p>\n

I take a very critical point of view of the recent announcement. For 42 per cent of the main results, they provided complementary Lean formalizations of the arguments. Lean is a programming language that allows you to explain a proof, a mathematical argument, to a computer, and then the computer can check whether it\u2019s complete and rigorous.<\/p>\n

So the rest of the results haven\u2019t been formally guaranteed yet?<\/p>\n

That\u2019s correct. I think it\u2019s very important not to abandon the usual precautions, because when a colleague of mine releases a new paper, no matter how famous he is, I don\u2019t instantly say, \u201cOh, this is probably true or wrong.\u201d I say, “Time will tell.\u201d<\/p>\n<\/p>\n

In the papers you\u2019ve written, and with your New Horizons Prize, you credit other people\u2019s work, because pure mathematics can be very collaborative. It\u2019s been described<\/a> as each of you being a link in a chain.<\/p>\n

Absolutely, yes. Prior to AI, people would just share ideas openly, sometimes years in advance of the actual release of their papers. Nowadays, people have more reserve with respect to sharing ideas openly because sometimes just the term of a good idea, a single prompt, can be enough for an AI system to complete a reasonable-looking preprint, and so then that idea is gone out of the window.<\/p>\n

\"_dc83126\"
\nGroechenig contemplating a proof in Euclid’s Elements, a book he says ‘played a major role in the development of mathematical exposition.’ (Duane Cole\/Be Giant) <\/p>\n

Meaning you lose the opportunity to work on it.<\/p>\n

Yes. In the case of this particular release, the problems that OpenAI claims to have solved could have made a career for a young and upcoming researcher; this could have been a way to recognize a new rising star, or graduate students could have contributed to small portions that would have become a part of the solution or maybe even solved one of these problems. The way we nurture new talent in the community is by having researchers work on open problems and see whether they can solve them. It\u2019s not so much the successful resolution that counts; it\u2019s more the intellectual watershed or undercurrent that is created by humans deliberately [working on] these big open questions.<\/p>\n

I can understand that. I like solving puzzles, so I like reading murder mysteries, but I never flip to the end of the book to find out who\u2019s the murderer. No spoilers. Did OpenAI just release 372 spoilers?<\/p>\n

That\u2019s exactly what it is. And it\u2019s not just spoilers. Many mathematicians feel threatened by the capabilities of AI systems and also by the behaviour of these AI companies. It\u2019s ironic, because AI wouldn\u2019t exist without a large body of mathematical knowledge that mathematicians have maintained over generations.<\/p>\n

You\u2019re a researcher, but you\u2019re also a teacher. In a field like mathematics, where an apprentice-master relationship has always been the learning model, what happens now?<\/p>\n

That\u2019s an excellent question. That\u2019s what I and many of my colleagues want to fight for, because without that relationship and without a collaborative community, there\u2019s no point in mathematics. The problems that OpenAI has claimed to have resolved, those are important questions, but they\u2019re not urgent. It\u2019s not urgent for humanity to know the answer to these problems, and having open problems can be a good thing. We don\u2019t have to understand absolutely everything. But urgent questions \u2013 we have many of those. Everyone would like to see a remedy for cancer, climate change and many other open problems that require urgent solutions. I think it\u2019s important to emphasize that AI currently can\u2019t propose any reasonable solutions to those.<\/p>\n

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\nWhen it comes to advising students on using AI in their math work, Groechenig says, ‘I want them to make their own decision because I know as little as them what the future is going to be like.’ (Duane Cole\/Be Giant) <\/p>\n

What do we lose if AI takes over advanced math work?<\/p>\n

I think there\u2019s always been a benefit to society maintaining a community of people who are capable of reasoning mathematically and passing that knowledge on to future generations, because otherwise we wouldn\u2019t have seen things like GPS or even AI itself.<\/p>\n

You have colleagues who have gone to work for OpenAI recently<\/a>. You must have some interesting debates in the faculty lounge.<\/p>\n

Oh, absolutely. There\u2019s a very diverse set of opinions with respect to AI use in mathematics. I\u2019ve decided, at least for the time being, to just continue doing math the way I was trained because I think it\u2019s important to maintain that knowledge, but I don\u2019t force this sort of vision onto my students. I want them to make their own decision because I know as little as them what the future is going to be like.<\/p>\n

It\u2019s the next generation of researchers who should have the bigger say in what the future looks like. We should listen to post-docs and graduate students and even undergrads. Some colleagues have decided to interact with AI systems in a legitimate and meaningful way, and then other colleagues on the far end of the AI-adaptation spectrum have become complete button pushers, sort of fully automated mathematicians. There\u2019s a whole spectrum of opinions, and I think that\u2019s what academia should be like. It\u2019s an example of peaceful coexistence of sometimes conflicting opinions.<\/p>\n

My personal slogan is just to keep calm and carry on. Also try to talk to junior mathematicians who seem to be in distress about the situation. That should be a responsibility for everyone \u2013 to actually make sure that people don\u2019t feel threatened by what AI is doing.<\/p>\n

That\u2019s interesting, because most of us can\u2019t wrap our heads around advanced mathematics, so we think people like you who can, are, by definition, geniuses. What\u2019s your definition of intelligence?<\/p>\n

Honestly, I feel it\u2019s a very difficult question to answer. The study of mathematics mostly requires resilience; it\u2019s a painstaking process. You repetitively think about the same problem until you understand it. It\u2019s filled with moments of frustration but also incredible insight. Mathematicians are mostly just people who take joy in solving problems. It is related to a particular aspect of human intelligence, but it\u2019s definitely not all of it.<\/p>\n

To give an example, something that AI labs find very difficult is to build a robot and tell it to go to a person\u2019s house and make a cup of tea. This is a task you could assign to any 10-year-old, and they\u2019ll probably succeed. That requires intelligence, right? You need to go to a house you\u2019ve never been to, locate the kitchen, then locate the drawers with the tea bags and the cups and so on and get the kettle to work, which could be a different model from any you\u2019ve seen before. It\u2019s the kind of intelligence that is ubiquitous in everyday life. We constantly rely on it, and it\u2019s just very difficult to reproduce artificially because it\u2019s the sort of training that people don\u2019t record. I think the hardest part of intelligence to emulate is the part we simply take for granted.<\/p>\n

Lisa Hrabluk is an award-winning journalist focused on reporting from the ground up, explaining how complex issues are reshaping everyday life. She\u2019s written for Time, The Canadian Press, Progress and CanWest Global, was a reporter, columnist and editor with the New Brunswick Telegraph-Journal, and is a weekly commentator on CBC Radio.<\/p>\n

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