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Erdős conjecture

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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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