Resumo:
In this talk I will review some historical aspects of the momentous time during the 1930s when Turing, Church, Goedel, and Kleene were laying the foundations of our field. I will describe how the concepts of universality and self-reference play out in the formalisms of the time and how the Y combinator, the recursion theorem of Kleene, and Goedel's fixpoint lemma are all essentially the same phenomenon. I will also discuss Turing's definition of the computable reals and its implications for constructive analysis.