OpenAI model solves 10 long-standing math problems, sparks anxiety

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OpenAI revealed it had produced solutions to 10 long-standing mathematics problems using an advanced unreleased model called Astra, with some of the problems having confounded academics for decades.

The solved problems span a wide range of mathematical fields. One concerns how tightly spheres can be packed in more than three dimensions - a question linked to how efficiently data can be encoded and transmitted. Another pushed the limits of error-correcting codes used to recover information from noisy signals. A third resolved two open questions about how complex connected networks can become before structural patterns emerge. Other results touched on quantum game theory and the search for targets inside high-dimensional grids, with implications for post-quantum cybersecurity. Among the most discussed was a proof regarding non-sofic groups - infinite mathematical structures that cannot be approximated by finite ones - whose existence had been an open question for decades.

The announcement has drawn a disputed reception. Francesco Fournier-Facio, a mathematician at the University of Cambridge, told The Verge that researchers in the non-sofic groups area believed OpenAI’s original announcement minimized the contributions of human mathematicians whose recent work the model built upon. James Maynard, a professor at the University of Oxford and Fields Medal winner, described spending the past year in “soul searching” over the future of his discipline.

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