Hey, Alberto here! 👋 Each week, I publish long-form AI analysis covering culture, philosophy, and business. Paid subscribers get Monday how-to guides and Friday news commentary. If you’d like to become a paid subscriber, here’s a button for that:Second deep-dive in a row! Today’s topic—how AI is impacting mathematics—deserves a long treatment, so I wrote 10,000 words on it.I recommend taking it slowly and even dedicating several days. It took me around two weeks to write (too much has happened!), so I hope the effort was worth it.P.S.: Read the footnotes if you have the time.If what’s happening to mathematics right now were happening to literature instead, I might stop writing altogether and then stop getting out of bed.“What if the library of Babel was being constructed before our eyes and there was some mechanism for separating the masterpieces from the random strings of text, and all the masterpieces were dropping as fast as publishers could scoop them up?” asks Kirwin Hampshire in a haunting essay. And now I understand why I owe mathematicians some tenderness here because my answer to his question is: screw you for even picturing that nightmare.1Thanks, but I don’t want my AI models to “churn masterpieces,” as if that were not an oxymoron. If some Anthropic staffer tweeted tomorrow, “hello there fable’s reportage on Can Humans Really Think? took twenty-three point six seconds and has won the Pulitzer Prize in the feature writing category,” I’d be mad. If OpenAI’s newsroom published a blog post listing ten contenders to the “Great American novel” and subsequently ChatGPT won the Nobel Prize in Literature, I’d be sad.Only then—mad, sad, depressed—would we writers understand how mathematicians feel right now.At least some of them. Others feel the exact opposite.But why the disparity?2026 was not too good a year for enthusiasts of number theory; neither a perfect square like 2025 nor a prime like 2027, it had to be happy as a semiprime (both “happy” and “semiprime” are actual categories). And even if mathematicians are not known for being superstitious, no one ever wants to deal with the rare unlucky year with three “Friday 13th”s. Still, 2026 has proven even worse than that: it is, if we are to believe the rumors, the year mathematics either dies or is reborn, and, because god has a sense of humor, trying to make a forecast feels like tossing a coin.By the end of 2025, AI was better at math than students but worse than professors. It could get an IMO gold score here, solve a lesser-known Erdős open problem there, but nothing too hard. In January 2026, Daniel Litt, assistant professor of mathematics at the University of Toronto—and a close follower of AI’s progress on his trade—said in the EpochAI podcast that “with some work, one can probably elicit better performance from current-gen models, but overall, it’s about the level of a contest problem.” By May 2026, four months later, his take was already obsolete.That’s when the first signs that something big was happening started to appear.A mysterious internal OpenAI model made an unusually important breakthrough during the usual evaluation procedures. It disproved a long-standing conjecture on the unit-distance problem proposed by Paul Erdős in 1946, which can be stated as follows: “How often can the same distance occur among n points in the plane?” Easy to pose, hard to solve. OpenAI reported that the AI provided “an infinite family of examples that yield a polynomial improvement” over the existing best solution, meaning that the consensus belief among mathematicians was not true. I don’t want to go into the details, but it suffices to say that this finding marked “the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI.”2Notable mathematicians called this “an outstanding achievement,” an “impressive piece of work,” proof that “AI [is] capable of having original ingenious ideas,” and a “milestone in AI mathematics.” Here’s something that Thomas Bloom, one of them, wrote in the companion remarks piece:The frontiers of knowledge are very spiky, and no doubt the coming months and years will see similar successes in many other areas of mathematics . . . AI is helping us to more fully explore the cathedral of mathematics we have build over the centuries; what other unseen wonders are waiting in the wings?After two months of slow digestion by the math community, Bloom’s prediction was fulfilled on July 10th. But surprisingly, this time it was not “some mysterious internal model” but OpenAI’s GPT-5.6 Sol Ultra model—a public model. After being prompted to “spend at least 8 hours on this before even thinking of returning or giving up,” GPT-5.6 Sol came back one hour later with a proof of the Cycle Double Cover Conjecture (50 years old).Ethan Knight@__eknight__Yesterday, we made GPT-5.6 Sol Ultra generally available. Today, we're sharing that it produced a proof of the 50-year-old Cycle Double Cover Conjecture using 64 subagents in just under one hour. We're sharing the prompt and proof below. We're excited to see what you all do with6:08 PM · Jul 10, 2026 · 2.44M Views232 Replies · 542 Reposts · 6.81K LikesFor the entire month of July, this would be the pattern. A tweet would be published, and some decades-old conjecture would suddenly be solved. On July 20th, Anthropic’s Levent Alpöge tweeted:levent@__alpoge__hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final