100+ reactions to 100+ solutions

Posted on 8 October 2026, last updated with new reactions on 9 October 2026 6:35 pm (CEST). The newest reactions are below, write to us at [email protected] if you want to contribute one! Many of us are grappling with OpenAI’s announcement on 6 October. We feel that it is useful to have a snapshot of the community’s gut feeling today, and this is what you see below. We will keep it open for another week, and you are welcome to send us further short reactions. To make sure it is clear that we are all in this together, each reaction is signed only by name, without reference to affiliation or career stage. You’ll find all types of reactions: general reflections as well as problem-specific comments. Tim Santens The results of OpenAI are almost unbelievable, Quasi-Riemann is a result that I thought was complete science fiction. Much can be said about the behavior of the AI labs, but given the existence of these models mathematics as a research discipline will have to undergo a massive transformation. Roman Sauer A common piece of wisdom is that mathematicians only have a few tricks in their bag – which they skillfully apply again and again. I have such trick whose unreasonable effectiveness surprised me a few times: replacing a manifold by a certain measurable foliated object, a construction that comes from ergodic theory, and using it in unexpected contexts. More recently, I relied on this trick in a paper with Sabine Braun on macroscopic scalar curvature, which was further extended by Hannah Alpert. This trick and these two papers now appear in OpenAI’s deeply creative solutions of problems 207 and 335 – problems so different, they could not be farther apart! I am stunned. What do I take away from this night? We cannot defensively narrow our focus to what we currently regard as human qualities in mathematics. This will force us into a diminishing role. Instead, we have to radically expand our view of what a mathematician is and does. Xiaolei Wu It is the last day of a week-long national holiday here in China. We had just taken a short family trip to a nearby coastal city. After waking up, I followed my usual routine and checked my phone. I was surprised to find many messages containing the same PDF file. Apparently, OpenAI had solved many open problems. So I took a look at the group theory section. It looked unreal. These were almost all the major open problems in my field! How is it possible? So I sent a message asking where the file had come from. The answer was that OpenAI had just officially announced it. I checked the group theory section again. Yes, these really were almost all of them. So Thompson’s group F is non-amenable. OK, I had tried it many times using ChatGPT, but I guess I didn’t have the newest model or enough tokens. Eilenberg–Ganea is false—not so surprising, perhaps, but how? OK, at least the Whitehead Conjecture has not fallen. And what? They had completely solved the Boone–Higman conjecture? And the ambient simple group could even be of type (F∞F_\infty)…\ldots I had expected this day to arrive, but maybe something like one year later. After a while, I started to look at other sessions, starting from topology. So the Borel conjecture fails in dimension 4, the coarse Baum-Connes also fails…\ldots The rest of the day felt long. More messages came in. My social media feeds were flooded with discussions about the list. Some people were still claiming that the problems solved in their fields were actually not so important. But I guess I had already passed that stage. Nicholas Williams We’ve certainly learnt a lot of new facts from this release. At the same time, it will take a while for us mathematicians to digest all of these papers. There’s no doubt that large language models have changed things enormously, but the end goal must always be human understanding. It feels important to point out that mathematicians do more than just solve open problems from the literature: we also have to grapple with the subject matter and think about what the good conjectures should be in the first place. But on the other hand, it does feel like the end of an era where the ability to solve problems was a distinguishing feature of being a mathematician. And this feels sad for those of us who like to solve problems. Henry Bradford Today my chief feelings are disorientation and bewilderment. It’s as if the pace of events has outstripped us by such a margin, that it is impossible to know how one should respond, or even how to start finding out how to respond. My greatest worry is for the prospects for bringing through the next generation of mathematicians: we know how much time and effort it takes to refine one’s craft in our subject to the point where one can meaningfully contribute to the advancement of knowledge, and I’m anxious that the necessary incentives may no longer exist for bright young people to invest that effort. I am holding on to hope that a bright future for the practice of mathematics is possible, in which our understanding of the mathematical universe is enriched, rather than undermined, by the ubiquity of AI tools. To get there though, we need as a community to agree what a realistic pathway should look like for a young scholar to establish themselves in our subject. Henry Wilton There are many problems on OpenAI’s list that I care a lot about: the Cannon conjecture, the non-residually-finite hyperbolic group, the Boone—Higman conjecture and at least ten others. I haven’t looked at any of them in detail yet, although a cursory glance suggests that the write-ups vary wildly in quality. It will take months of work to go through the proofs of all of them, to check if the proofs are correct and to try to digest them. But I think it’s important to focus on the big picture. If OpenAI wanted to destroy the mathematical community, this would be a great way to go about it. Open problems are a resource that the mathematical community developed over decades or even centuries. The value they have is the value we have given them. They provide structure, a yardstick for progress and long-term goals. The advent of AI was always going to be a seismic shock, but this huge dump of papers is a tsunami that we have no time to prepare for. It’s clear that OpenAI will happily wash away our community’s structures to further their financial interests. There is a long list of mathematical structures and norms that OpenAI seems to be intent on damaging. By refusing to name the authors of their papers, they imply that mathematics is no longer a human endeavour. They don’t submit their results to journals, which both implies that the norms of the mathematical community are defunct and makes it impossible for the community to digest their results. OpenAI haven’t shared fundamental information about how the problems are selected or the failure rates of their attempts. This information should be a necessary requirement for any serious scientific discussion of their tools. And of course there is the basic financial injustice that their hugely valuable models learned to reason by copying the very reasoning that our community made available for free through the Open Access movement. I hope the mathematical community can adjust our practices and norms quickly enough to survive the shock of these developments, but I am fearful. Macarena Arenas Perhaps the AI companies could, if they wanted to, do something to benefit humankind and the planet we live on (ending world hunger, solving global warming, curing cancer…), but this is not it, and it is not being done for altruistic purposes. Regarding the mathematics, some of it is unverified, most of it is badly written, and (probably) none of it is transparent in documenting how it was produced, who was involved, and what was its cost (in every sense). All of it is of course impressive. Some of it might come to benefit mathematics and mathematicians, but overall I think it is an example of a corporation trying to exert manipulative pressure on a field of knowledge, and I think it has been done irresponsibly. I hope that we as a community can find our way through this mess, but for the time being, it is a mess, and it causes more harm than good. It will distract a lot of people from working on their own ideas; it will disrupt many existing research agendas; it will create conflict in the mathematical community; it will encourage a lot of opportunistic, ill-informed use of these technologies (thus adding to the “slop” and creating more noise for us to navigate through); and it will discourage many, many people from doing mathematics. Johannes Schmitt One thing to keep in mind about this drop of papers is that they were not created by OpenAI with the main goal of making progress in mathematical research, or even primarily for PR (there were some PR posts, but e.g. the final announcement was comparatively restrained). The main reason these papers exist is that OpenAI used unsolved math problems to evaluate their internal models for the purpose of improving their capabilities. They had to use hard open problems because these are the only ones still posing a challenge to frontier AI models. I believe that, from OpenAI’s point of view, the papers are essentially a byproduct of their internal development. Thus the company could just have remained silent, or picked a few flashy results for another blog post. I think it is to their credit that instead they reached out to the math community for guidance on how to proceed, leading to the formation of the Advisory Group on Mathematics and Artificial Intelligence. They followed some of the advice by this group, such as a timely release and (partial) Lean certificates, but not all of it, and in particular announced that they will continue to use open math problems for model development. In my view, the most pressing need of the math community right now is to have a central platform to discuss the results, start digesting the (by multiple