The Condensed Mathematics of Peter Scholze and Dustin Clausen

“That’s wrong,” it pierces the silence. The chalk dust reflects in the rays of light that make their way through the imposing stained glass windows. In the lecture hall in Bonn, which is lined with dark wood paneling, about a dozen students raise their heads and stare at the screen. Squeakingly, the lecturer scribbles cryptic symbols on a blackboard – and falters. In Copenhagen, almost 800 kilometers away, he scratches his head and traces the last thing he wrote with his finger.

“Actually, I was thinking about something about this…” He pauses again. You could practically hear a pin drop. The troublemaker sits in the first row, he is confusingly similar to the lecturer: mid-30s, long, dark hair, tall stature, slim figure. You hardly stand out from the students present. And yet they are the professors – and they are no strangers either: Dustin Clausen is giving the lecture at the University of Copenhagen, while Peter Scholze and the other listeners in Bonn are listening intently to him.

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“That’s not true,” says Scholze and leans back. Then he blurts out what restrictions are necessary to make Clausen’s statement correct. He nods: »I have to think about it for a moment.« Another few moments of silence. “Okay, I’ll fix it later,” he concludes, and continues the lecture: definition, theorem, proof.

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