Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. The method can be extended to prove statements about more ...

Analysis was founded in 1933 to provide a forum for short discussions of topics in philosophy. It quickly established itself as one of the characteristic journals of philosophy within the analytic ...

But now Google’s DeepMind team has built AlphaProof, an AI system that matched silver medalists’ performance at the 2024 ...

Dave Richeson at Division By Zero wrote recently about a “proof technique” for proving equalities or inequalities that is far too common: Starting with the equality to be proven and working backwards ...

In 2024, an AI entered the fray of the International Mathematical Olympiad (IMO). Google’s AlphaProof is part of the same Alpha group that also created AlphaFold and AlphaGo. It solved problems that ...

Let us assume what most mathematical readers would take for granted anyway: There are mathematical objects such as numbers and functions and there are objective facts about these objects, such as 3 < ...

Herbert Simon, the Nobel-prize winning economist, was a techno-enthusiast. In 1956 he predicted that, “within 10 years, computers would beat the world chess champion, compose ‘aesthetically satisfying ...