Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of the ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...

Extremal graph theory seeks the largest or smallest structure a graph can exhibit under given constraints, typically by forbidding a particular subgraph. The classical Turán problem determines the ...

Imagine a world where artificial intelligence not only understands language but creates with it, where quantum systems no longer feel like an enigma but a solvable puzzle. It might sound like science ...

A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach. 1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer ...

New results emerging from graph theory prove that the way a population is organized can guarantee the eventual triumph of natural selection — or permanently thwart it. Natural selection has been a ...