I’ll just say it: What the hell is going on with AI “reasoning”? Sorry for the air quotes. That punctuational side-eye was more common in 2024, when the specially trained cousins of LLMs now known as “large reasoning models,” or LRMs, were still new. Nowadays it may seem downright churlish, though, given that a “general-purpose reasoning model” from OpenAI solved a famous open mathematical…

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In 1992, mathematicians famously proved that seven “riffle shuffles” — the kind where a player splits a deck of cards into two piles, then uses their thumbs to interleave them back together in a zipperlike motion — are enough to mix up the deck. When Dave Bayer and Persi Diaconis came up with this proof, they also revealed something surprising about what happens along the way: At first…

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