Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a computer.
Although most mathematicians doubt that machines will replace the creative aspects of their profession anytime soon, some acknowledge that technology will play an increasingly important role in their research — and this particular feat could be a turning point towards its acceptance.
Scholze, a number theorist, set forth the ambitious plan — which he co-created with his collaborator Dustin Clausen from the University of Copenhagen — in a series of lectures in 2019 at the University of Bonn, Germany, where he is based. The two researchers dubbed it 'condensed mathematics', and they say it promises to bring new insights and connections between fields ranging from geometry to number theory.
Other researchers are paying attention: Scholze is considered one of mathematics' brightest stars and has a track record of introducing revolutionary concepts. Emily Riehl, a mathematician at Johns Hopkins University in Baltimore, Maryland, says that if Scholze and Clausen's vision is realized, the way mathematics is taught to graduate students in 50 years' time could be very different than it is today. "There are a lot of areas of mathematics that I think in the future will be affected by his ideas," she says.
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