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New math revives geometry's oldest problems
Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.
In 2015, Kass was passing through Atlanta, where Wickelgren lived, and decided to approach her with his latest obsession: He wanted to revisit enumerative questions in restricted number systems, that long-abandoned endeavor. “At this point,” said Aravind Asok of the University of Southern California, trying to glean information about enumerative geometry problems from quadratic forms “is an entire industry.” It’s also concrete and accessible, which has attracted the attention of young mathematicians, he added. “The math keeps going one level higher in abstraction, and then sometimes I feel like I don’t know what I’m talking about anymore,” said Sabrina Pauli, who was Wickelgren’s first graduate student and is now a professor at the Technical University of Darmstadt in Germany.
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