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The Useful Unknowable

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Copyright: Sanjay Basu   How Godel’s ghost is quietly rewriting cryptography, AI, and physics. A graduate student just used the limits of mathematics itself to hide secrets. Across four fields this week, researchers are discovering that what we cannot know is becoming our most powerful resource. In 1931, a twenty-five year old Austrian logician named Kurt Godel proved that any sufficiently rich system of mathematics contains true statements it can never prove. For most of the twentieth century that result was treated like a tombstone laid over a particular kind of dream, the dream of complete and tidy knowledge. Hilbert wanted everything decidable. Godel handed him a polite shrug and a counterexample. This past week, on a server quietly maintained by the International Association for Cryptologic Research, an MIT graduate student showed that Godel’s so called limit can be turned into a key. Once you start looking, the same trick is showing up in physics, in AI, and in the philosophy...
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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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