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 ...

A new physics paper takes a step toward creating a long-sought "theory of everything" by uniting gravity with the quantum world. However, the new theory remains far from being proven observationally.

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...