[fen11]

> In 1936 both Alan Turing and Alonzo Church independently reached the conclusion, using different methods, that the answer is "no."

I think claiming these efforts were independent is misleading. Church was Turing’s PhD advisor in 1936, and one of the appendices of Turing’s thesis retroactively justifies the lambda calculus definition of computing, by proving it equivalent to his Turing machine definition. That sounds less like competing definitions of computability to me, and instead a story of collaboration to produce a philosophical justification (Turing machines) for Church’s pure mathematical theory (lambda calculus). Which is not to disparage Turing either: creating this philosophical justification was an impressive and fundamentally important achievement. I think Church sometimes gets unfairly maligned in these discussions as an out-of-touch purist who didn’t care to come up with a believable definition, but clearly he cared enough to support his student working on the problem!

Is there some evidence for the independence or competitiveness of their work that I’ve missed?

Anyway, apart from this nitpick about the introduction, I appreciate seeing this foundational stuff explained clearly!

[jarpschop]

I don't think Turing knew about the existence of the lambda calculus when he wrote the paper. It was later that he decided to study his PhD under Church and move to Princeton.

[samwho]

This is correct, they were independent works. It’s spoken about in “The Annotated Turing” by Charles Petzold.