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The Co-Mathematician's Question

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Copyright: Sanjay Basu I n late April, an Oxford topologist named Marc Lackenby fed a problem from a battered Russian notebook to an AI that DeepMind had been quietly building for the better part of a year. The notebook is the Kourovka Notebook, and it has been collecting unsolved questions in group theory since 1965, passed mathematician to mathematician across continents and editions, like an open-mic list nobody quite knows how to close. The question Lackenby chose, problem 21.10, had outlived two generations of mathematicians. A few days and one caught-out flawed proof later, the problem was closed. The strange part isn’t that the machine solved it. The strange part is what happened in between. Most reporting on the result settled into the predictable register. Machine cracks human problem. The expected think pieces filed themselves. What got less airtime, and what is actually the story, is the workflow that did the cracking, and a small philosophical pinch point it produced almost...
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The Math of Less

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Why this week’s biggest breakthroughs all worked by taking things away, and what a fringe philosophy of mathematics has to do with any of it. Copyright: Sanjay Basu F or most of the last decade, the headlines in physics, AI, and computing have all rhymed with the same dull tune. More. More parameters. More qubits. More compute. More data. More layers. More floors on the same skyscraper, and another floor again next quarter, because what else are you going to put in a press release. But this week, four very different research stories shared an unsettling subtext, and it is the opposite one. The next jump forward might come from doing brilliantly less. From a Caltech team showing that a useful quantum computer needs ten thousand qubits instead of a million, to a Google paper that crushes a transformer’s memory using a forty-year-old trick from pure mathematics, science is having a quiet subtractive moment. And tucked behind it, almost embarrassed to be there, is a philosopher’s question ...
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