Welcome to Quantum Magazine's podcast.

Each episode we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another.

Now that it's been disproved, the universe

of shapes has exploded. That's next.

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In early June of 2023, Buzz built as mathematicians landed at London's Heathrow Airport.

Their destination was the University of Oxford and a conference in

honor of the 65th birthday of Michael Hopkins. He's a mathematician at Harvard University, who'd served

as a mentor to many of the attendees. Hopkins made a name for himself in the late 1980s for work

on seven conjectures that Doug Ravenel of the

University of Rochester had formulated a decade earlier. They had to do with techniques for

determining when two shapes or spaces that might look different are really the same. Hopkins and

his collaborators proved all of Ravenel's conjectures,

except for one, the telescope conjecture. At the time, Hopkins laid his work on Ravenel's

conjectures to rest. For decades afterward, the telescope conjecture seemed all but impossible to

solve. Here's Hopkins. That kind of a theorem was untouchably

...