Discrete mathematics is about precision in reasoning as much as it is about solving problems. Proof techniques like induction, contradiction, and direct reasoning are used to establish results in ...

Deep in the heart of Microsoft, Jennifer Chayes and Christian Borgs lead a who's who of mathematics and computer science. The goal? To explore anything they please Every weekday afternoon some 20 ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

An innovative approach to solving a stubborn, but elementary, question in graph theory — the mathematical study of networks of nodes and their connections — may signal the first major theoretical ...

It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major ...

Graph theory is moving from textbooks to traffic lights, powering smarter transportation networks worldwide. From retail deliveries to freight corridors and urban commuting, it helps planners cut ...

In the race toward practical quantum computers and networks, photons—fundamental particles of light—hold intriguing possibilities as fast carriers of information at room temperature. Researchers at ...