Algorithmic randomness and computability theory inhabit a crossroads between mathematics and computer science, providing a rigorous framework for understanding randomness in infinite sequences and ...

The field of Reverse Mathematics explores the minimal axiomatic frameworks necessary to prove classical theorems, seeking to elucidate the logical foundations of mathematics. In parallel, ...

Quantum theory describes events that take place on extremely short time scales. In the past, such events were regarded as 'momentary' or 'instantaneous': An electron orbits the nucleus of an atom—in ...

Initially discussed are some of Alan Turing's wonderfully profound and influential ideas about mind and mechanism—including regarding their connection to the main topic of the present study, which is ...

We show that to every recursive total continuous functional Φ there is a PCF-definable representative Ψ of Φ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming ...

This course gives an introduction to the mathematical foundations of computation. The course will look at Turing machines, universal computation, the Church-Turing thesis, the halting problem and ...

Lawrence Krauss is quite right that we need to be much clearer about the role of falsifiability in making a theory “scientific” (3 December, p 23). Despite taking mostly science subjects at school and ...

What is the best way for a group of individuals to cooperate? This is a longstanding question with roots in game theory, a branch of science which uses mathematical models of how individuals should ...

This course gives an introduction to the mathematical foundations of computation. The course will look at Turing machines, universal computation, the Church-Turing thesis, the halting problem and ...