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Erdős conjecture

Latest Articles

geometry

The Biggest Smallest Triangle Just Got Smaller

By Leila Sloman
September 8, 2023
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A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

geometry

Mathematicians Solve Long-Standing Coloring Problem

By Anna Kramer
July 19, 2023
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A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

Ramsey theory

The Lawlessness of Large Numbers

By Leila Sloman
July 7, 2023
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Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

graph theory

Mathematicians Discover Novel Way to Predict Structure in Graphs

By Jordana Cepelewicz
June 22, 2023
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Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

combinatorics

First-Year Graduate Student Finds Paradoxical Set

By Alex Stone
June 5, 2023
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No two pairs have the same sum; add three numbers together, and you can get any whole number.

A visual argument explaining why the Ramsey number of three is six.
graph theory

A Very Big Small Leap Forward in Graph Theory

By Leila Sloman
May 2, 2023
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Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

An illustration of a sequence that avoid arithmetic progression, shown as a blue staircase jumping among numbers from one to forty.
combinatorics

Surprise Computer Science Proof Stuns Mathematicians

By Leila Sloman
March 21, 2023
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For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

Side-by-side illustrations of the same linear hypergraph. The edges of the hypergraph are colored in the illustration on the right, but not in the illustration on the left.
combinatorics

Mathematicians Settle Erdős Coloring Conjecture

By Kelsey Houston-Edwards
April 5, 2021
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Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

number theory

A Magical Answer to an 80-Year-Old Puzzle

By Erica Klarreich
October 1, 2015
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Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

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