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New Proof Settles How to Approximate Numbers Like Pi
The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.
A 53-Year-Old Network Coloring Conjecture Is Disproved
In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.
Computer Scientists Expand the Frontier of Verifiable Knowledge
The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.
Why Mathematicians Can’t Find the Hay in a Haystack
In math, sometimes the most common things are the hardest to find.
Universal Method to Sort Complex Information Found
The nearest neighbor problem asks where a new point fits into an existing data set. A few researchers set out to prove that there was no universal way to solve it. Instead, they found such a way.
First Big Steps Toward Proving the Unique Games Conjecture
The latest in a new series of proofs brings theoretical computer scientists within striking distance of one of the great conjectures of their discipline.
Decades-Old Graph Problem Yields to Amateur Mathematician
By making the first progress on the “chromatic number of the plane” problem in over 60 years, an anti-aging pundit has achieved mathematical immortality.