[FOM] History of computable functions

[Andrej Bauer]

A student of mine is working on a seminar in which he will show in
excruciating detail that the general recursive functions embed in
untyped lambda calculus (this is at undergraduate level). He would
like to know more about the history of computable functions, lambda
calculus, Turing machines, etc., with a reasonably correct timeline of
who did what when. Can someone please suggest some reading material?

Thanks!

Andrej Bauer