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Mathematics

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Quantized Academy

The Simple Math Problem We Still Can’t Solve

By Patrick Honner
September 22, 2020
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Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

Photo of students sitting at desks competing in the International Mathematical Olympiad
Abstractions blog

At the Math Olympiad, Computers Prepare to Go for the Gold

By Kevin Hartnett
September 21, 2020
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Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

Aerial image of a complicated road network.
Abstractions blog

A New Algorithm for Graph Crossings, Hiding in Plain Sight

By Stephanie DeMarco
September 15, 2020
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Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

By David S. Richeson
September 14, 2020
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Mathematicians have long grappled with the reality that some problems just don’t have solutions.

A comically long “missing persons” poster for an odd perfect number that shows all the restrictions it has to satisfy.
number theory

Mathematicians Open a New Front on an Ancient Number Problem

By Steve Nadis
September 10, 2020
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For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Q&A

Conducting the Mathematical Orchestra From the Middle

By Rachel Crowell
September 2, 2020
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Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

An illustration of an ant walking in a straight line around a dodecahedron.
Abstractions blog

Mathematicians Report New Discovery About the Dodecahedron

By Erica Klarreich
August 31, 2020
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Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

Illustration of a robot and a human furiously doing math next to each other
artificial intelligence

How Close Are Computers to Automating Mathematical Reasoning?

By Stephen Ornes
August 27, 2020
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AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

Photo of Marijn Heule walking among computer processors
Abstractions blog

Computer Scientists Attempt to Corner the Collatz Conjecture

By Kevin Hartnett
August 26, 2020
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A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.


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