J.M.E. Hyland est professeur de logique mathématique au King’s College à Cambridge.

## Logic, abstract mathematics and the science of information: an

unappreciated aspect of the heritage of Turing.

*The science of information was born in the 1930s in the midst of* *the great discoveries of modern logic. In his famous 1937 paper* *Turing gave a definitive analysis of the notion of computability.* *The fact that this intuitive notion has a precise counterpart still* *seems remarkable today. Turing’s analysis has had an evident impact* *on practical computing. Computers are the most visible aspect of* *information science and even today we think of them as Turing* *machines. As a result perhaps the dominant idea of our time* *is that information science is information technology, that is to* *say that it is only concerned with practical questions.*

*However there is another aspect to computability. One should not* *forget that the notion first appeared within logic. Many links* *between logic, abstract mathematics and programming have since* *emerged and these form an important component of information* *science. Moreover information science itself has been a source of* *new mathematical structures. One example is given by the interplay* *between the Theory of Types from logic and Category Theory. I shall* *say something about this area and about Turing’s largely forgotten* *interest in related questions.*