Noam Zeilberger

From: Maggie McLoughlin <mam@CS.Stanford.EDU> To: noam.zeilberger@polytechnique.edu Subject: from Prof Knuth re your letter of 11 Feb 20256 Reply-to: knuth-bug@cs.stanford.edu Date: Fri, 27 Feb 2026 13:10:27 -0800 Hi Noam. [Are you any relation to my friend Doron?] Many thanks for your flattering letter. I fear that you have an exaggerated view of my competence; yet of course I'm delighted to know that somebody understands what I was trying to say. I'd forgotten about deleting those paragraphs from the original preface to Volume 1. In the desk copy of the 33rd printing of the second edition, I'd marked only one change (besides additions to the list of abbreviations for commonly cited journals): pure mathematical problems historically have always developed from -> pure mathematical problems almost always owe their origins to [Probably that change went into one of the published errata.] Evidently in 1997, after Silvio Levy had presented me with TeX versions of the various parts of Volume 1 so that I could finally make a third edition, I edited the preface by first adding a paragraph (apologizing for being forced to leave things out because CS had been growing so rapidly). Naturally I also then looked for parts of the preface that no longer needed to be said. And I guess I'd come to the conclusion that mathematicians had by then come to understand the material that you've quoted from the earlier prefaces.

About Ulam's article: I don't actually recall reading any articles in the September 1964 Scientific American except Martin Gardner's column [which Martin intentionally made "as unmathematical as possible" that month ... it's about puns and palindromes]. No doubt if I had time today, I'd find the articles by Courant, Davis, Kline, Sawyer, Kac, Quine, Dyson, Bellman, and Ulam quite inspiring. [wow, what a collection of great expositors and thinkers!] I wouldn't have written many of the sentences of Ulam that you quoted. ("It is preferable to regard the computer as a handy device for manipulating and displaying symbols.") An interesting thought, but it's never entered my head. I met Stan (and visited his Sante De home) in 1976, and we got along great. He's wonderfully creative, and by now I've read many of his books and papers. I think the main other person who influenced my original preface, besides my mentor de Bruijn (a frequent visitor to Caltech), was George Forsythe. You can get an idea of the ideas that I thank him for the most by looking at the bio that I wrote in CACM when he died suddenly in 1972. Cordially, Don Knuth PS You say you're "eagerly looking forward to reading Volumes 5 and 6". But I'm currently in the midst of 4C, and that will by no means be the end of Volume 4...

I wrote a letter to Knuth asking about this, and he wrote back!

From: Maggie McLoughlin <mam@CS.Stanford.EDU> To: noam.zeilberger@polytechnique.edu Subject: from Prof Knuth re your letter of 11 Feb 20256 Reply-to: knuth-bug@cs.stanford.edu Date: Fri, 27 Feb 2026 13:10:27 -0800 Hi Noam. [Are you any relation to my friend Doron?] Many thanks for your flattering letter. I fear that you have an exaggerated view of my competence; yet of course I'm delighted to know that somebody understands what I was trying to say. I'd forgotten about deleting those paragraphs from the original preface to Volume 1. In the desk copy of the 33rd printing of the second edition, I'd marked only one change (besides additions to the list of abbreviations for commonly cited journals): pure mathematical problems historically have always developed from -> pure mathematical problems almost always owe their origins to [Probably that change went into one of the published errata.] Evidently in 1997, after Silvio Levy had presented me with TeX versions of the various parts of Volume 1 so that I could finally make a third edition, I edited the preface by first adding a paragraph (apologizing for being forced to leave things out because CS had been growing so rapidly). Naturally I also then looked for parts of the preface that no longer needed to be said. And I guess I'd come to the conclusion that mathematicians had by then come to understand the material that you've quoted from the earlier prefaces.

About Ulam's article: I don't actually recall reading any articles in the September 1964 Scientific American except Martin Gardner's column [which Martin intentionally made "as unmathematical as possible" that month ... it's about puns and palindromes]. No doubt if I had time today, I'd find the articles by Courant, Davis, Kline, Sawyer, Kac, Quine, Dyson, Bellman, and Ulam quite inspiring. [wow, what a collection of great expositors and thinkers!] I wouldn't have written many of the sentences of Ulam that you quoted. ("It is preferable to regard the computer as a handy device for manipulating and displaying symbols.") An interesting thought, but it's never entered my head. I met Stan (and visited his Sante De home) in 1976, and we got along great. He's wonderfully creative, and by now I've read many of his books and papers. I think the main other person who influenced my original preface, besides my mentor de Bruijn (a frequent visitor to Caltech), was George Forsythe. You can get an idea of the ideas that I thank him for the most by looking at the bio that I wrote in CACM when he died suddenly in 1972. Cordially, Don Knuth PS You say you're "eagerly looking forward to reading Volumes 5 and 6". But I'm currently in the midst of 4C, and that will by no means be the end of Volume 4...

I wrote a letter to Knuth asking about this, and he wrote back!

Very interesting, and characteristically careful and hype-free, from Daniel Litt on how good current AI models really are or aren't at mathematical research.

(He cautiously decides that they're probably a bit better than he thought.) […]

@julesh oops, yes you are right! (Set,+) is an ordinary co-multicategory (the representable co-multicategory of the underlying monoidal category), so the problem only arises from the combination with (Set,x), i.e., the not-quite-linearly distributive structure that you point out.

@julesh this bigger class are related to so-called "premulticategories" as considered by Sam Staton and Paul Levy in "Universal Properties of Impure Programming Languages" (https://doi.org/10.1145/2429069.2429091). Basically, premulticategories are what you get by starting from the […]

With apologies for the delay, the recordings of the talks at the Types and Topology Workshop in celebration of @MartinEscardo's 60th birthday (https://tdejong.com/mhe60) are now on YouTube (where available) 📺

https://www.youtube.com/@mhe60/videos (also linked from the workshop webpage)

Many […]

The arXiv's new "make everyone write in English to promote linguistic diversity" policy went into effect yesterday (https://blog.arxiv.org/2026/01/13/non-english-paper-submission-guidelines/), and they have now released a feedback survey […]

@joey here's a link to Ryoma's homepage http://www.math.akita-u.ac.jp/~ryoma/, in particular my counterexample was inspired by the construction used in Theorem 23 of this paper: https://arxiv.org/abs/2008.01413.

But looking again at your original post, I think the argument you gave works as an […]

@joey (this example is inspired by Ryoma Sinya's work on approximation of languages by regular languages.)

@joey indeed I think not, the forgetful functor from REG to Lang does not have a left adjoint. It should be possible to construct a counterexample using the fact that the non-regular language L = {0^n 1^n|n} is the intersection of the infinite family of regular languages Rk = {0^n 1^m | m=n mod […]

The CNRS is breaking free from the Web of Science From January 1st 2026, the CNRS will cut access to one of the largest commercial bibliometric databases, Clarivate Analytics'

The CNRS is breaking free from the Web of Science | CNRS https://www.cnrs.fr/en/update/cnrs-breaking-free-web-science

[knuth, ulam, computers + math]

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 […]

[knuth, ulam, computers + math]

Here is the opening of Ulam's article:

> Although to many people the electronic computer has come to symbolize the importance of mathematics in the modern world, few professional mathematicians are closely acquainted with the machine. Some, in fact, seem even to […]

[knuth, ulam, computers + math]

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 […]

[knuth, ulam, computers + math]

> I wish to show that the connection between computers and mathematics is far deeper and more intimate than these traditional relationships would imply. The construction of a computer program from a set of basic instructions is very similar to the construction of […]

[knuth, ulam, computers + math]

While looking for some sources to help motivate the study of computer programming to very young undergraduate students, I ended up reading the preface to Volume 1 of Knuth's _The Art of Computer Programming_ -- in an electronic copy of the Second Printing from […]

Giving University Exams in the Age of Chatbots Giving University Exams in the Age of Chatbots par Ploum - Lionel Dricot.

Giving University Exams in the Age of Chatbots

How I managed to give an exam while giving the students the choice to use a chatbot or not.

And what I learned in the process.

https://ploum.net/2026-01-19-exam-with-chatbots.html

RE: https://mastoxiv.page/@arXiv_mathCT_bot/115899102956428600

Another article uploaded to the arXiv (technically, being updated) in a non-English language, making me think about how this policy change will soon go into effect […]

RE: https://mathstodon.xyz/@slava/115822631093391345

I for one am eagerly looking forward to Volume 5 of The Art of Computer Programming, on "Lexical scanning" and "Parsing techniques". Hopefully Knuth will get around to finishing it in the next couple years, before he's 90! […]

@robinhouston So you can distinguish Q(M) from Q(M*) by viewing it as being equipped with a 2-coloring and not just being 2-colorable. In map enumeration people usually consider rooted maps. I believe that Q defines a bijection between half-edge rooted general maps and corner-rooted bipartite […]

@robinhouston about the question of whether it defines a bijection, you're right that a map M and the dual map M* have essentially the same incidence/radial map, but here is the precise statement of from Schaeffer's article: "The mapping Q and R are bijections from maps with n edges respectively […]

@robinhouston note that M*, Q(M), and R(M) are defined in a uniform way for maps on arbitrary surfaces, not just on the sphere.

Figure from Gilles Schaeffer's chapter on "Planar maps" in the CRC Handbook of enumerative combinatorics. It shows a planar map M, the dual map M*, the incidence map Q(M) (a quadrangulation), and the edge map R(M) (a 4-valent map).

@robinhouston Gilles Schaeffer calls it the "incidence map" Q(M) of a map M in https://www.lix.polytechnique.fr/~schaeffe/Biblio/HB.pdf, but yes, I think it is essentially the same thing as what you call the radial graph. Here is a figure from his article.

@robinhouston oh, now I see what you mean but that's hard for me to visualize. Could you draw a picture?

@robinhouston (corresponding OEIS entry: https://oeis.org/A007137)

@robinhouston just to clarify, in one place you wrote "non-bipartite" and in another "bipartite" -- which is it? I suppose you mean bipartite in the standard sense, i.e., admitting a proper 2-coloring of the vertices?

And what sizes are you looking at to do exhaustive enumeration? This paper ( […]

The slides for Types and Topology (https://tdejong.com/mhe60) are all up on the website now (where available)!

@MartinEscardo

I just spent a fun few days in Glasgow, where I was in town for Malin Altenmüller's (https://maltenmuller.github.io/) successful viva at Strathclyde! I really enjoyed Malin's thesis work and it's always a pleasure to visit the @mspstrath.

Book cover "Programmes d'intelligence artificielle en BASIC"

Title page, "Programmes d'intelligence artificielle en BASIC" by Marie Gaëlle MONTEIL and Richard SCHOMBERG, 1985

A glance at the table of contents, including chapter sections such as "Les Tours de Hanoï" and a chapter on Tic-Tac-Toe

BASIC code for towers of Hanoi

Une autre époque

@noamzoam The blog post is a delightful read. True the policy change took longer than it should have, but it is a story of perseverance and eventual success (and some great stories of how mathematicians were able to balance career and family).