The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures. Hofstadter was ...

Quantum entanglement occurs when two subatomic particles become linked in such a way that their properties remain connected, no matter how far apart they are. A change to one particle seems to ...

Olival Freire Jr is a professor of physics and the history of physics at the Federal University of Bahia, Brazil. What makes matter stable? Why are atoms as they are? Why do different materials vary ...