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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.
Why Mathematicians Re-Prove What They Already Know
It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.
Coloring by Numbers Reveals Arithmetic Patterns in Fractions
In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.
Math’s ‘Oldest Problem Ever’ Gets a New Answer
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.
Mathematician Hurls Structure and Disorder Into Century-Old Problem
A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”
New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different
Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.
Undergraduate Math Student Pushes Frontier of Graph Theory
At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.
Disorder Persists in Larger Graphs, New Math Proof Finds
David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.
‘Rainbows’ Are a Mathematician’s Best Friend
“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.