Dear Mr. Turing,

We regret to inform you that your submission

"On Computable Numbers, With an Application to the Entscheidungsproblem"

was not accepted to appear in FOCS 1936. The Program Committee received a record 4 submissions this year, many of them of high quality, and scheduling constraints unfortunately made it impossible to accept all of them.

Below please find some reviews on your submission. The reviews are *not* intended as an explanation for why your paper was rejected. This decision depended on many factors, including discussions at the PC meeting and competition from other papers.

Best wishes,

FOCS 1936 Program Committee

---------------------------------------- review 1 ----------------------------------------

seems like a trivial modification of godel's result from STOC'31

---------------------------------------- review 2 ----------------------------------------

The author shows that Hilbert's Entscheidungsproblem (given a mathematical statement, decide whether it admits a formal proof) is unsolvable by any finite means. While this seems like an important result, I have several concerns/criticisms:

1. The author defines a new "Turing machine" model for the specific purpose of proving his result. This model was not defined in any previous papers; thus, the motivation is unclear.

2. I doubt Hilbert's goal of "automating mathematical thought" was ever really taken seriously by anyone (including Hilbert himself). Given this, the negative result comes as no surprise -- a positive result would have been much more interesting.

3. It's hard to find any technical "meat" in this paper. Once the author sets up the problem, the main result follows immediately by a standard diagonalization argument.

4. The whole philosophical discussion in Section 9, about what it means to compute something, is out of place (even slightly embarrassing) and should be deleted entirely.

Summary: While this paper deserves to be published somewhere -- SODA? ICALP? FSTTCS? -- it certainly isn't FOCS caliber.

---------------------------------------- review 3 ----------------------------------------

merge with alonzo church's submission?

---------------------------------------- review 4 ----------------------------------------

while i agree with the other reviewers' concerns about triviality, i confess to liking this paper anyway. one reason is that, along the way to the main result, the author proves a lemma stating that there exists a "universal machine" (a machine able to simulate any other machine given a suitable choice of input). the claim that this lemma could have "practical" applications is clearly exaggerated -- but even so, it seems like it could be a useful ingredient for other results.

Recommendation: Borderline Accept.