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Mathematics

Latest Articles

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.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
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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
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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.

foundations of mathematics

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

By Natalie Wolchover
July 15, 2021
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For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

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
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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
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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
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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.


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