In his article Stephen Cole Kleene - a reminescence, Saunders Mac Lane quotes a letter from Kleene to his mother. In that letter, Kleene wrote:
"Rosser and my article is deadly. It is only 8 pages typed....,but it would require reading a couple of hundred pages perhaps to make full check up on it all. One sentence takes 10 pages to prove."
Alas, the piece does not say what paper of Kleene's the letter refers to. However, no matter what paper it was, I do not believe that that type of distillation is ever useful when writing a paper. Who could claim to understand those 8 pages after all?
Addendum: One of my readers pointed out that the essay does point out the title of the paper. It is
Kleene, S. C.; Rosser, J. B.
The inconsistency of certain formal logics.
Ann. of Math. (2) 36 (1935), no. 3, 630--636.
The paper is available online from: http://www.jstor.org/view/0003486x/di961655/96p00874/0.
Thanks to the anonymous reader, and shame on me for not checking my sources as thoroughly as I should have done, and trusting my untrustworthy memory.
3 comments:
If I am not mistaken, it indeed mentions the name of the paper. It seems to be: The Inconsistencies of Certain Forms of Formal Logic. It is available online from: http://www.jstor.org/view/0003486x/di961655/96p00874/0 (It appears to be even one page less, thus 7 pages, in the end!)
Thanks for pointing out my mistake! I read those reminscences of Mac Lane's a long time ago, and had made a note to write a post about it then. I'll add this remark to the post.
Lesson: One should always go back and check the sources before citing anything.
I failed to pay heed to this lesson, and it showed.
Someday mathematicians will use computers to overcome proofs complexity in the same way as chess players of nowadays do to analyze chess openings.
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