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Graph theory
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Mathematicians Build Long-Awaited Graph Sandwich
The proof of a decades-old conjecture has given researchers a new way to understand complex networks.
The Four-Color Theorem Gets a Rare New Proof
By revisiting the famous problem — which was controversially solved in the 1970s with the help of computers — mathematicians have gained important new insights into the nature of graphs.
‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions
Mathematicians found that a broad class of networks will abruptly shift behavior past a critical point.
A Master of the Traveling Salesperson Problem Finds His Own Path
Shayan Oveis Gharan has won the Abacus Medal for using tools from across mathematics to boost the power of algorithms.
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.
Networks Hold the Key to a Decades-Old Problem About Waves
Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.
A New Bridge Links the Strange Math of Infinity to Computer Science
Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.
New Method Is the Fastest Way To Find the Best Routes
A canonical problem in computer science is to find the shortest route to every point in a network. A new approach beats the classic algorithm taught in textbooks.
Why the Key to a Mathematical Life is Collaboration
Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.