As I mentioned before, Menzler-Trott’s biography of Gentzen has a number of appendices, including a fifty page essay “Hilbert’s Programme” by Craig Smorynski. (A better title might have been “The slow emergence of Hilbert’s Programme from Hilbert’s intermittent work on foundational questions up to 1930/31, and in particular from his disputes with Brouwer and Weyl.” But I can see why Smorynski stuck to his snappy title!)
I found this essay a terrific read, very helpful and illuminating, at least for someone who makes no pretence of knowing much about the history here. This should now go on any reading list for philosophy of maths students touching on Hilbert’s Programme. And so spread the word: it would be a great pity if Smorynski’s efforts went largely unread because buried at the back of a rather oddly written biography. (The rationale for having this piece appended to the biography is that it sets the scene for Gentzen’s work — but actually, as I noted, Menzler-Trott doesn’t engage very closely with that work, so he doesn’t really join up the dots. An opportunity missed.)