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Erdős conjecture
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After 80 Years, Mathematicians Give Famed ‘Erdős Method’ an Upgrade
Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.
Graduate Student Solves Classic Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
Grad Students Find Inevitable Patterns in Big Sets of Numbers
A new proof marks the first progress in decades on a problem about how order emerges from disorder.
The Biggest Smallest Triangle Just Got Smaller
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.
Mathematicians Solve Long-Standing Coloring Problem
A new result shows how much of the plane can be colored by points that are never exactly one unit apart.
The Lawlessness of Large Numbers
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?
Mathematicians Discover Novel Way to Predict Structure in Graphs
Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.
First-Year Graduate Student Finds Paradoxical Set
No two pairs have the same sum; add three numbers together, and you can get any whole number.
A Very Big Small Leap Forward in Graph Theory
Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.