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Leila Sloman

Contributing Correspondent

Latest Articles

combinatorics

Hypergraphs Reveal Solution to 50-Year-Old Problem

By Leila Sloman
July 14, 2022
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In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

Points connected by lines.
graph theory

Mathematical Connect-the-Dots Reveals How Structure Emerges

By Leila Sloman
June 23, 2022
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A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

An illustration of a person walking across a surface with many holes.
topology

Unimaginable Surfaces Discovered After Decades-Long Search

By Leila Sloman
June 2, 2022
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Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

Two red loops connected by a ghostly tube.
topology

How Complex Is a Knot? New Proof Reveals Ranking System That Works.

By Leila Sloman
May 18, 2022
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“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

A ring of bubbles in blue water.
fluid dynamics

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

By Leila Sloman
May 2, 2022
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The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

A mathematical graph with plant roots.
number theory

New Proof Illuminates the Hidden Structure of Common Equations

By Leila Sloman
April 21, 2022
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Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

A fictitious 8-bit video game called “counterexample quest.”
machine learning

In New Math Proofs, Artificial Intelligence Plays to Win

By Leila Sloman
March 7, 2022
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A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

combinatorics

Mathematician Answers Chess Problem About Attacking Queens

By Leila Sloman
September 21, 2021
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The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.


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