Banach-Tarski and the Paradox of Infinite Cloning | Quanta Magazine

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

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Quanta Magazine

How Terry Tao Became an Evangelist for AI in Math

With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research. The post How Terry Tao Became an Evangelist for AI in Math first appeared on Quanta Magazine

Kevin Hartnett·Jun 8, 2026

Quanta Magazine

More Conversations, Complex Questions, and Bold Ideas in Season Five of ‘The Joy of Why’

The podcast returns with 12 all-new episodes that explore the biggest questions in basic science and mathematics. The post More Conversations, Complex Questions, and Bold Ideas in Season Five of ‘The Joy of Why’ first appeared on Quanta Magazine

Simon Frantz·Jun 4, 2026

Quanta Magazine

Plasmid, Virus or Other? DNA ‘Borgs’ Blur Boundaries. | Quanta Magazine

Scientists have reported large DNA structures in some archaea that defy easy categorization.

Jul 21, 2021·8 min read

Quanta Magazine

How to Find Rational Points Like Your Job Depends on It | Quanta Magazine

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Jul 22, 2021·15 min read

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The ‘Weirdest’ Matter, Made of Partial Particles, Defies Description | Quanta Magazine

Theorists are in a frenzy over “fractons,” bizarre, but potentially useful, hypothetical particles that can only move in combination with one another.

Jul 26, 2021·7 min read

Quanta Magazine

A Soil-Science Revolution Upends Plans to Fight Climate Change | Quanta Magazine

A centuries-old concept in soil science has recently been thrown out. Yet it remains a key ingredient in everything from climate models to advanced carbon-capture projects.

Jul 27, 2021·14 min read