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geometry

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
Read Later

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.

Insights puzzle

Math Can, in Theory, Help You Escape a Hungry Bear

By Pradeep Mutalik
August 25, 2021
Read Later

How readers used their geometry skills to survive a dangerous puzzle.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
Read Later

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

Illustration showing geometric figures at left connected via wormhole to numbers at right.
Langlands program

New Shape Opens ‘Wormhole’ Between Numbers and Geometry

By Kevin Hartnett
July 19, 2021
Read Later

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

A pixelated black and white animation of a model of percolation.
mathematical physics

Mathematicians Prove Symmetry of Phase Transitions

By Allison Whitten
July 8, 2021
Read Later

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Insights puzzle

Can Math Help You Escape a Hungry Bear?

By Pradeep Mutalik
June 29, 2021
Read Later

In this month’s puzzle, math is a question of life or death.

Math Meets QFT

Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

By Kevin Hartnett
June 24, 2021
Read Later

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.

Math Meets QFT

Mathematicians Prove 2D Version of Quantum Gravity Really Works

By Charlie Wood
June 17, 2021
Read Later

In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.

Math Meets QFT

The Mystery at the Heart of Physics That Only Math Can Solve

By Kevin Hartnett
June 10, 2021
Read Later

The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.


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