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In Lockdown, Mathematicians Crack a Stubborn Geometry Riddle

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In mid-March, mathematicians Joshua Greene and Andrew Lobb both found themselves in lockdown and struggling to adjust to the Covid-19 pandemic. They decided to cope by throwing themselves into their research.

"I think the pandemic was really kind of galvanizing," says Greene, a professor at Boston College. "We each decided it would be best to lean into some collaborations to sustain us."

One of the problems the two friends looked at was a version of a century-old unsolved question in geometry. The "rectangular peg problem" has resisted mathematicians' best efforts for decades. Greene and Lobb, an associate professor at Durham University in England and at the Okinawa Institute of Science and Technology, held weekly Zoom calls and had a quick succession of insights. Then, on May 19, they posted a solution.

The pair solved a problem about closed curves that are both "continuous" and "smooth" by transporting the problem into an entirely new geometric setting.

"It's sort of weird," says Richard Schwartz of Brown University. "It was just the right idea for this problem."

From Quanta Magazine
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