Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

Mathematician Kenneth I. Appel used an I.B.M. computer in 1976 to prove a century-old problem concerning colors on a map, and from there computers were used to provide proofs for higher and higher ...

2025’s most surprising computational revelations included a new fundamental relationship between time and space, an undergraduate who overthrew a 40-year-old conjecture, and an important milestone in ...