--- title: 'The Summer Math Fell to the Machines' source: 'https://youtube.com/watch?v=iuZPTE5qsJY' video_id: 'iuZPTE5qsJY' date: 2026-08-19 duration_sec: 334 channel: 'Fireship' --- # The Summer Math Fell to the Machines > Source: [The Summer Math Fell to the Machines](https://youtube.com/watch?v=iuZPTE5qsJY) ## Summary The video reports on the summer of 2026, when AI systems solved or disproved numerous open mathematical problems, including the Jacobian conjecture and the dense garments conjecture, at an unprecedented pace. It highlights the reactions from the mathematical community, including Terrence Tao's warning, and discusses the implications for the future of mathematics. ### Key Points - **AI's unprecedented pace** [00:15] — AI has solved more open math problems in the last 3 weeks than humans did in the previous decade, including an 87-year-old conjecture and a 30-year-old graph theory problem. - **Tao's warning** [00:41] — Terrence Tao, a renowned mathematician, warned of a crisis in the foundations of mathematical values and practices at the International Congress of Mathematicians. - **First major disproof** [01:08] — In May, an OpenAI model disproved an 80-year-old Erdős–Erdős conjecture, causing sleepless nights for researchers. - **Leiden Declaration** [01:34] — 16 researchers from 15 universities published the Leiden Declaration, asking for guardrails around AI in mathematics research, but it was ignored. - **Jacobian conjecture disproved** [01:46] — Levent Alpe, with help from Fable, disproved the Jacobian conjecture, a famous problem in algebraic geometry on Smale's list. - **Dense garments conjecture falls** [02:25] — GPT-5.6 disproved the dense garments conjecture, a 30-year-old graph theory problem, with a tiny network of seven nodes and nine edges. - **Amateurs and students join in** [03:03] — A Colombia PhD student solved six open problems in 5 days, and a 23-year-old amateur solved another, showing AI's democratizing effect. - **OpenAI's internal breakthroughs** [03:29] — OpenAI's next major model solved 10 open problems, including improving the sphere packing bound (unchanged since 1978) and disproving Con's rigidity conjecture. - **Riemann hypothesis progress** [04:08] — Jared Sumar, creator of BunJS, used Claude to make progress on the Riemann hypothesis, raising the fraction of provably satisfying solutions from 41% to 67%. ## Transcript to put up with hearing about how AI is going to make them obsolete and steal family. But besides the occasional identity crisis, I feel like most of us are actually doing pretty well. Sadly, our mathematician friends may not be so lucky because over the last 3 weeks, AI has killed more open math problems than the entire human race managed in the previous decade. One 87y old conjecture from a list of the hardest problems of the 21st century got disproven during the World Cup final. Another 30-year-old graph theory conjecture fell to four prompts in 58 words. Things have gotten so bad that Terrence Tao, a man who won an International Math Olympiad medal at age 10 while the rest of us were making cinnamon sugar sandwiches and watching rocket power, stood up at the International Congress of Mathematicians and warned of a crisis in the foundations of mathematical values and practices. In today's video, we'll look back at the summer mathematics fell to machines and find out what that may mean for the rest of us. It is August 19th, 2026, and you're watching the code started about a year ago when some models solved five of the six problems at the International Math Olympiad. But at the time it felt mostly harmless because competition math is the leak code of math problems. Then back in May, an open AI model disproved an 80-year-old Edos Eridish conjecture didn't feel so harmless anymore. >> Couldn't believe it. I I had trouble sleeping for the first couple of nights I was out. In June, 16 researchers from 15 universities published what they called the Leiden Declaration, which politely asked the world to establish some guard rails around AI and mathematics research, which the world then politely ignored. And last month, while Americans were pretending to like soccer and Europeans were pretending to like medieval infrastructure without air conditioning, mathematician Levent Alpe opposed a counter example to X that disproved the Jacobian conjecture, which is one of the most famous problems in algebraic geometry. The idea is that if you have a polomial function whose derivative checks out at every single point, meaning it's perfectly reversible anywhere you zoom in, then the entire I know that probably doesn't mean much to you, but since 1939, that felt so obviously true to mathematicians that it made Smile's list of the hardest problems of the 21st century because nobody could actually prove or disprove it. That is until Levent did last month with some help from Fable. And just 2 days later, it happened again with a 30-year-old graph theory problem called the dense garments conjecture, which you can think of like a delivery routing split across multiple routes, the question is whether you can always bundle them into single unsplit routes without the total delivery cost going up. And for 30 years, everyone assumed that you could. They just couldn't prove it. Then a researcher named Dimmitri Ryben pointed GPT 5.6 at it and basically told it to make a breakthrough. The model responded with a tiny network of just seven nodes and nine edges where forcing every shipment into a single route was always more expensive than letting them split. Disproving the conjecture. And it's not just the pros doing this. That same week, a Colombia PhD student knocked out six open ed problems in 5 days, and a 23-year-old amateur banged out another. And this is mostly before any of the big tech labs took their own shots. But then just two weeks ago, OpenAI got in on the bullying when they revealed that internally their next major model solved 10 open problems across math and theoretical computer science. And they a lean certificate, which is a formal proof the compiler can check list is one I know some of you have thought about a lot, which is how tightly you can cram identical sized balls into a space. The general bound on this problem hasn't moved since 1978, but OpenAI just improved it. The other nine problems include things like the first explicit construction of a non-sopic group and a disproof of con's rigidity conjecture, which I won't mathematicians have been chasing some of them since the '90s. But of course, Daario couldn't just sit by and get big derivative by Sam. So, just last week, Anthropic fired back by announcing that one of its own unreleased models made progress on the Reman hypothesis, which is one of the most famous unsolved problems in all of mathematics. It's a 167-year-old question about the distribution of prime numbers, and it's one of the seven Millennium Prize bounty on its head. The best part is that it wasn't an anthropic mathematician who discovered it. It was Jared Sumar, the creator of BunJS, as he was on his jog for his I'm filthy rich now and need to get fit too era. During his run, Jared asked Claude to take a real stab at proving it. So, it did and generated 650 wrong ideas for solving the problem. Jared then told it to try again, and this time the model spent a day and a half coordinating 60 sub agents inside claude code, running 2400 shell commands, writing hundreds of Python scripts, and burning 31 million output tokens. Now, that still didn't lead to it proving the hypothesis, but it did bump the fraction of solutions that provably satisfy the hypothesis from 41% to 67%, which I'm told is validated by two mathematicians at Anthropic, checked by two outside number theory experts, and formalized and lean. 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