Computer science can be approached as mathematics, as technology, and as a natural science. Turing's foundational contributions opened up all three of these avenues and his lasting imprint on them is still evident. The first two approaches may be the ones that have been most thoroughly explored to date, but this talk will argue that the last is at least as fundamental and was perhaps the one closest to the core of Turing's thinking.

Turing's success in capturing the phenomenon of mechanical mental activity by means of the notion of computability sets the standard as a robust mathematical definition of a natural phenomenon. This talk will review more recent attempts to capture the phenomena of biological evolution, learning, and intelligence by means of definitions that seek to capture these various phenomena by analogously robust mathematical definitions.