New Math Revives Geometry's Oldest Problems

By JOSEPH HOWLETT

Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.

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Naomi Saphra thinks that most research into language models focuses too much on the finished product. She's mining the history of their training for insights into why these systems work the way they do.

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KNOT THEORY

A Simple Way To Measure Knots Has Come Unraveled

By LEILA SLOMAN

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

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THE QUANTA PODCAST

AI's Dark Side Is Only a Nudge Away

Podcast hosted by SAMIR PATEL
with STEPHEN ORNES

The new science of "emergent misalignment" explores how PG-13 training data — insecure code, superstitious numbers or even extreme-sports advice — can open the door to AI's dark side.

Listen (Apple) | Listen (Spotify)

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QUANTA AUDIO EDITION

A New, Chemical View of Ecosystems

Podcast hosted by SAMIR PATEL
with STEPHEN ORNES

Rare and powerful compounds, known as keystone molecules, can build a web of invisible interactions among species.

Listen (Apple) | Listen (Spotify)

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