Noam Zeilberger

I wrote a letter to Knuth asking about this, and he wrote back! [Edited to add a link to the original letter I sent: https://noamz.org/misc/letter-to-knuth-11-feb-2026.pdf]

@mjd@mathstodon.xyz Doron is my uncle!

Possibly the reason that neither paragraph is cited more often is that they were both eventually removed -- at least, they do not appear in the preface to the 3rd edition of Volume 1. I am not sure why, or whether they were still there in the 2nd edition. The version of the preface above is dated October 1967. Adding to the mystery, while trying to find references to the passage online, for fun I tried copying the text of the first paragraph into ChatGPT and asked it to identify the quote. It authoritatively answered that the quotation is from Stanisław Ulam's essay "Computers in mathematics" appearing in the book _Science, Computers, and People_ edited by M. C. Reynolds and Gian-Carlo Rota [https://doi.org/10.1007/978-1-4615-9819-0_6] Of course it isn't. But that essay is actually a reprint of an article by Ulam in the September 1964 issue of Scientific American [https://www.jstor.org/stable/24931634] which opens with strikingly similar language to the paragraph of Knuth's preface. (3/4)

@gjm@mathstodon.xyz @dougmerritt@mathstodon.xyz but to be clear, I think the question of explaining the similarity here is curious but of really minor significance. I was delighted to receive such a kind response from Knuth, especially for all the extra historical context and interesting pointers.

@gjm@mathstodon.xyz I agree that it looks unlikely to be a coincidence, but also extremely uncharacteristic of Knuth to lift a passage without attribution. A guess is that Knuth was subconsciously influenced to reconstruct this wording after having read Ulam's article a few years earlier. But that's just speculation, and probably the right person to ask is Knuth himself.

@MartinEscardo@mathstodon.xyz yes I already knew that Knuth had interacted with de Bruijn about the Automath project and mentioned it in my letter to him (which I guess I should have included for more context). I knew this from William Lovas, who got to chat with Knuth once when he was visiting at CMU. William told Knuth about his then thesis work on an extension of the LF logical framework with subtyping, and Knuth mentioned that he had proposed something similar to de Bruijn!

I just checked and the original preface with these two paragraphs still appears in the second edition of Volume 1. On Knuth's TAOCP page [https://www-cs-faculty.stanford.edu/~knuth/taocp.html] in the "Errata for Volume 1 (2nd ed.)" he mentions that "In the third edition I will revise this preface extensively, so that it will reflect the actual scope of these books instead of the state they were in when Volume 1 was first published." But I don't see anything else about the preface on that page.

@gjm@mathstodon.xyz @dougmerritt@mathstodon.xyz from Knuth's response I draw the inference that it is very likely that he *had* actually read Ulam's article in Scientific American, since he recalls reading Martin Gardner's article in the same issue, and it is normal not to remember every single thing you read 60 years ago (I have trouble remembering what I had for breakfast!). My running hypothesis is still that there could have been some subconscious incorporation of elements of Ulam's phrasing after such an exposure, or else that it is just a pure coincidence.