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Apr 20 at 18:23 comment added usr1234567 Thanks for the link. Indeed, than the fuss is more about publishing first. Intersting!
Apr 20 at 17:05 comment added Liviu Nicolaescu @usr1234567 George Birkhoff acknoledges the work of von Neumann on the first page of of his paper on ergodic theory. pnas.org/doi/full/10.1073/pnas.17.2.656
Apr 20 at 14:02 comment added Dan Romik It’s a great answer and story, upvoted. And thanks for the cool reference @usr1234567, I agree with you that the relevance to OP’s actual question is limited, both because it appears Birkhoff was not the reviewer for von Neumann’s paper, and (perhaps more importantly) because von Neumann did not upload his paper to arXiv.
Apr 20 at 10:37 comment added Liviu Nicolaescu Birkhoff's theorem is several orders more complicated than vin Neumann's mean ergodic theorem . Birkhoff's proof was so complicated that over the years several illustrious mathematicians provided gradually simpler proofs.
Apr 20 at 1:33 comment added paul garrett For context, in some circles, G.D. Birkhoff has reputation for being ... "ingenerous". Oh, ok, yeah, also vocally anti-semitic (von Neumann was ethnically jewish...) I do think that this taints some of these situations...
Apr 19 at 22:28 comment added usr1234567 @GEdgar The source from my last comment does not support your statement that Birkhoff was the reviewer. He got to know von Neumann's result and surpassed him by publishing a paper. It does not work as an example for OP's fear.
Apr 19 at 20:51 comment added usr1234567 @DanRomik From the abstract, this paper might answer your question (I am to tired to read it right now): Joseph D. Zund, Historia Mathematica 29 (2002), 138–156, doi:10.1006/hmat.2001.2338 (core.ac.uk/download/pdf/82378876.pdf)
Apr 19 at 20:32 comment added Dan Romik Very interesting. Do you have a reference where this story is told, or where Birkhoff made the admission you mention?
Apr 19 at 15:20 history answered GEdgar CC BY-SA 4.0