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mathematics

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a small human figure stands on a golden geometric structure while the sky is full of curving pink and purple grids
graph theory

Quantum Field Theory Pries Open Mathematical Puzzle

By Leila Sloman
February 16, 2023
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Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

A human speaks to a neural network, which produces mathematical equations, against a starry background
artificial intelligence

To Teach Computers Math, Researchers Merge AI Approaches

By Kevin Hartnett
February 15, 2023
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Large language models still struggle with basic reasoning tasks. Two new papers that apply machine learning to math provide a blueprint for how that could change.

geometry

Mathematicians Complete Quest to Build ‘Spherical Cubes’

By Jordana Cepelewicz
February 10, 2023
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Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

The Joy of Why

The Joy of Asking About Infinity, Jellyfish and the End of the Universe

By Polly Stryker
February 9, 2023
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As The Joy of Why podcast returns for a second season, producer Polly Stryker and host Steven Strogatz invite listeners to join them and their brilliant new guests on another voyage of discovery.

topology

Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

By Leila Sloman
February 2, 2023
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A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

Fanciful illustration of galaxies with various geometric shapes at their centers.
mathematical physics

Mathematicians Find an Infinity of Possible Black Hole Shapes

By Steve Nadis
January 24, 2023
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In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.

cartoon illustration of a female teacher surrounded by students throwing paper airplanes covered in equations against a bright orange background
Quantized Academy

The Basic Algebra Behind Secret Codes and Space Communication

By Patrick Honner
January 23, 2023
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Whether you’re passing secret notes in class or downloading images from a space probe, Reed-Solomon codes offer an ingenious way to embed information and correct for errors.

illustration of four six-sided green dice covered in different numbers, with orange arrows connecting some of the dice
combinatorics

Mathematicians Roll Dice and Get Rock-Paper-Scissors

By Erica Klarreich
January 19, 2023
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Mathematicians have uncovered a surprising wealth of rock-paper-scissors-like patterns in randomly chosen dice.

graph theory

Finally, a Fast Algorithm for Shortest Paths on Negative Graphs

By Ben Brubaker
January 18, 2023
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Researchers can now find the shortest route through a network nearly as fast as theoretically possible, even when some steps can cancel out others.


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