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topology

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topology

In Topology, When Are Two Shapes the Same?

By Kevin Hartnett
September 28, 2021
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As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
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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.

graph theory

How Big Data Carried Graph Theory Into New Dimensions

By Stephen Ornes
August 19, 2021
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Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

Illustration of colorful flowchart using raised blocks against a black background
proofs

Proof Assistant Makes Jump to Big-League Math

By Kevin Hartnett
July 28, 2021
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Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

Math Meets QFT

Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

By Kevin Hartnett
June 24, 2021
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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
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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
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The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.

Color photo of Jordan Ellenberg sitting with a laptop by a lake at sunset
Q&A

A Number Theorist Who Connects Math to Other Creative Pursuits

By Steve Nadis
May 27, 2021
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Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

topology

How Mathematicians Use Homology to Make Sense of Topology

By Kelsey Houston-Edwards
May 11, 2021
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Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.


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