Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

The incompleteness theorem is accepted as part of the mathematical canon today, but columnist Jacob Aron says it was a ...

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all ...

Fermat’s Last Theorem is so simple to state, but so hard to prove. Though the 350-year-old claim is a straightforward one about integers, the proof that University of Oxford mathematician Andrew Wiles ...

Richard Elwes reports on Harvey Friedman’s fascinating work on incompleteness in Boolean relation theory, but it is quite a stretch to extend his work to ask “are the rules of arithmetic… unsound?” ...

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences. In 1931, the Austrian logician Kurt ...