\tFriday February 6 2026 \t<\/p>\n
Ruby Jackson for Varsity<\/p>\n
One of the most prolific mathematicians of the 20th century, Paul Erd\u0151s, proposed over a thousand mathematical conjectures throughout his career: the Erd\u0151s problems. Around 40% have been solved, but none by AI \u2013 until last month. To the surprise of many mathematicians, it was in fact the world\u2019s first fully autonomous AI solution to an open mathematical problem (a problem recognised by researchers yet to be solved). And the mathematician that solved it? Kevin Barreto, a second-year Queen\u2019s Mathmo.<\/p>\n
Kevin began tackling Erd\u0151s problems in earnest in November 2025, after seeing that an AI startup, Harmonic, had obtained<\/a> a partial solution to an Erd\u0151s problem using their AI system, Aristotle. \u201cYou know, maybe there\u2019s some low-hanging-fruit problems that would be within reach of an undergrad,\u201d Kevin said he thought at the time.<\/p>\n By early December, he\u2019d already solved one Erd\u0151s problem without using AI, in his field of specialty, number theory, and obtained a partial result on another. His work quickly gained<\/a> attention on a forum dedicated to cataloguing Erd\u0151s problems, earning him congratulations from Terence Tao, whom many consider to be the greatest living mathematician \u2013 although Kevin was \u201cactually rather nonchalant\u201d about it. \u201cWhen one is entirely confident in their proof, no congratulations are needed; the mathematics speaks for itself.\u201d Encouraged, he began experimenting with using AI to solve these problems.<\/p>\n
<\/p>\n \u201cWhen one is entirely confident in their proof, no congratulations are needed\u201d<\/p>\n
<\/p>\n Collaborating online with a hobbyist mathematician, Liam Price, the pair eventually identified a promising candidate problem that ChatGPT-5.2 solved entirely without human intervention. Kevin then fed the proof into Aristotle, which automatically formalised it in Lean \u2013 a programming language used to quickly verify the logic of mathematical proofs.<\/p>\n After Kevin excitedly posted<\/a> the result on Twitter on Christmas Day, another forum user quickly discovered the problem had actually already been solved. Undeterred, the pair continued their work and within weeks, achieved a fully autonomous AI proof to a genuinely unsolved problem, Erd\u0151s problem #728\u2013albeit using arguments similar to earlier work. Since then, AI has gone on to fully solve several more Erd\u0151s problems and contributed<\/a> to many others. For some of the problems which Erd\u0151s considered more interesting or difficult, he offered prizes of up to $10,000, but Kevin believes these are currently far out of reach for today\u2019s models.<\/p>\n Directly solving problems is not the only way AI can assist mathematicians. Large Language Models\u2019 (LLMs) \u2018deep research\u2019 modes have also proved transformative for literature review, unearthing obscure but relevant results that might otherwise be missed, and helping researchers avoid retreading old ground. The rapid progress of LLMs over the past year has made their potential in maths and science increasingly clear. Systems that once struggled with basic reasoning are now highly capable of undergraduate and even competition mathematics \u2013 as any Mathmo or Natsci behind on their problem sheets will know. However, Kevin\u2019s work marks a further step.<\/p>\n
<\/p>\n \u201cUndeterred, the pair continued their work and within weeks, achieved a fully autonomous AI proof to a genuinely unsolved problem, Erd\u0151s problem #728\u201d<\/p>\n
<\/p>\n While these models will undoubtedly continue to improve, Kevin argues that a \u201cfundamentally new architecture\u201d is needed to achieve true mathematical superintelligence \u2013 one capable of tackling the deepest unsolved problems in mathematics, such as the Millennium Prize problems. Trained on existing work, today\u2019s LLMs are adept at cleverly combining known ideas. This may be enough to solve Erd\u0151s problems, but cannot produce the completely novel concepts required for the hardest problems; partly because these ideas are so foreign that they would require entirely new mathematical language, which LLMs are inherently incapable of creating, to even express.<\/p>\n Kevin\u2019s work is striking but equally compelling is Kevin himself. He may look like a typical Mathmo, but his path into research is far from conventional. He comes from a working-class immigrant background and is the first in his family to attend university, with parents who left school early. He has always had a clear passion for mathematics \u2013 by thirteen, he knew he wanted to be a mathematician, and by seventeen he was obsessively reading the newest research in analytic number theory. Yet he has no Olympiad background, having been comparatively average at school maths competitions, and entered Cambridge only after being accepted into Queen\u2019s through the summer pool, after a rejection from Trinity.<\/p>\n Arriving in Cambridge, Kevin hoped to eventually pursue a PhD under James Maynard, a Fields medallist in the field of analytic number theory. But his first year was derailed by mental health struggles, and he failed the Tripos exams. After taking a gap year, he was allowed to resit first year, this time achieving a 2:ii. He is blunt about the experience: \u201cTripos is not my thing,\u201d a judgment he attributes to having very specific mathematical interests and being someone who is \u201cnot very good at thinking of ideas on the spot.\u201d<\/p>\n
<\/p>\n \u201cI think there is a far too competitive atmosphere in Cambridge\u201d<\/p>\n
<\/p>\n At Cambridge, it becomes ingrained in students that Tripos ranks reflect mathematical potential, making it unthinkable that someone outside the top of the cohort could already be capable of original research. I confess that I was expecting Kevin to be someone who flew through the tripos with ease and thus had time on his hands to do such work. Kevin describes how this attitude can turn toxic, recalling instances of top-ranked students deriding those lower down the Tripos despite their deep passion for the subject. \u201cI think there is a far too competitive atmosphere in Cambridge. [\u2026] I have felt that the words I speak are dismissed by peers or faculty simply because I am not as well-performed on Tripos as they\u00a0are. It\u2019s like people will tactfully refuse to help each other, such as on example sheets, just to help secure their ranking above that person.\u201d<\/p>\n Kevin is not the first to show that Tripos rank is an imperfect predictor of research ability. He points to the example of Klaus Roth, Britain\u2019s first Fields medallist, who graduated with a third-class degree and was advised by his supervisor to abandon mathematics altogether. \u201cThe Tripos is genuinely a good way to test mathematical ability,\u201d Kevin reflects, \u201cbut it\u2019s a form of mathematical ability I don\u2019t possess.\u201d His struggles with the tripos also pushed his turn to AI: \u201cit got to a point where I felt like I could make a bigger contribution to maths by trying to make a machine that can do what I can\u2019t.\u201d<\/p>\n After being allowed to return to Cambridge following his gap year, Kevin now faces the opposite problem: securing approval to take another year out to continue his work at a leading AI research\u00a0lab. Companies including OpenAI and DeepMind, as well as specialist maths AI startups such as Harmonic, have approached him directly, actively courting him, something Kevin says is \u201cactually rather overwhelming [\u2026] it has been a long-time dream of mine to eventually work at DeepMind after seeing the revolutionary accomplishments they\u2019ve made.\u201d He is quick to add, however, that xAI is off the table \u2013 he \u201cwill not be helping Elon Muskrat.\u201d<\/p>\n
<\/p>\n \u201cI felt like I could make a bigger contribution to maths by trying to make a machine that can do what I can\u2019t\u201d<\/p>\n
<\/p>\n For many in STEM, these labs are the ultimate place to work, akin to a modern-day Manhattan Project or Bell Labs. Unsurprisingly, positions are so competitive that they\u2019re effectively inaccessible to most students, and undergraduate placements are essentially unheard\u00a0of. Again, unsurprisingly, Kevin is being considered as a special exception. He is now weighing whether to drop out to pursue this work, although he is worried that eventually he \u201cmay get bored of this AI for maths stuff\u201d and want to return to his original dream of doing a PhD \u2013 a path that would almost certainly require finishing his degree.<\/p>\n It has been a transformative few months for Kevin whose work has now been featured in the New York Times<\/a> and the New Scientist<\/a>. As recently as last November, he wrote that it would be a dream of his to simply make a minor contribution to an Erd\u0151s problem. Despite this, he remains very humble. \u201cI\u2019m not cracked,\u201d he insists, adding that \u201canyone interested in these problems could have done this.\u201d I\u2019m still deciding whether I believe\u00a0him.<\/p>\n New HTML Container\n <\/p>\n Speaking to Kevin, I found myself genuinely inspired \u2013 not only as a physicist increasingly weary of the Tripos grind \u2013 but by the picture he paints of the extraordinary years that lie ahead of us in science and mathematics.<\/p>\n