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 ...

If you buy something using links in our stories, we may earn a commission. This helps support our journalism. Learn more. Please also consider subscribing to WIRED In 1931, the Austrian logician Kurt ...

One of the basic theorems in universal algebra is Birkhoff's variety theorem: the smallest equationally axiomatizable class containing a class K of algebras coincides with the class obtained by taking ...

The reticent and relentlessly abstract logician Kurt Gödel might seem an unlikely candidate for popular appreciation. But that’s what Rebecca Goldstein aims for in her new book Incompleteness, an ...

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 ...

Kurt Gödel (second from right) receives the first Albert Einstein Award in 1951. In the esoteric world of mathematical logic, a dramatic discovery has been made. Previously unnoticed gaps have been ...

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?” ...

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 ...