Combinatorics and discrete mathematics form a vibrant and expansive branch of modern mathematics, dedicated to the study of finite or countable structures and the methods used to count, classify, and ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.” Within a month, a loose collaboration verified it ...

After previously discussing permutations, Dr. James McCaffrey of Microsoft Research uses step-by-step examples and full code presentations to explore combinations. A zero-based mathematical (n, k) ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

Princeton mathematician Noga Alon has received the 2024 Wolf Prize in Mathematics “for pioneering contributions to mathematical cryptography, combinatorics, and the theory of computer science.” He ...