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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.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.

In math, sometimes the most common things are the hardest to find.

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

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.

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

The latest in a new series of proofs brings theoretical computer scientists within striking distance of one of the great conjectures of their discipline.

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.

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