Noam Zeilberger
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noamzoam.mathstodon.xyz.ap.brid.gy
Noam Zeilberger
@noamzoam.mathstodon.xyz.ap.brid.gy
37 followers 2 following 23 posts
Computer science theorist and mathematician interested in the connections between things. Assistant professor in the LIX lab at Ecole Polytechnique.

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noamzoam.mathstodon.xyz.ap.brid.gy
Une autre époque
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
December 5, 2025 at 10:34 AM
noamzoam.mathstodon.xyz.ap.brid.gy
[teaching / functional programming project / Lambek calculus / new AI vs old AI]

Every year in my functional programming course I assign a mini-project for students to complete in small groups, as a significant portion of their course grade. The topic varies […]

[Original post on mathstodon.xyz]
sample Lambek / Montague style lexicon from the project description page. sample Lambek calculus derivation from the project description page.
November 27, 2025 at 4:20 PM
noamzoam.mathstodon.xyz.ap.brid.gy
(the issue also contains some mildly amusing and cringey advertisements.)
2-page advertisement from October 1969 issue of CACM. There is a hand holding a photo of a mainframe computer. Title text "Take a close look at IBM's new computer. You might think we overdid it." The ad includes the line "We built Model 195 so men can study things like they've never been studied before.", among other amusing and cringey lines.
September 26, 2025 at 12:17 AM
noamzoam.mathstodon.xyz.ap.brid.gy
Visited the library of the Institut Henri Poincaré yesterday, and they had a small rack with free-for-taking copies of some old journals. Was delighted to find a copy of the issue of Communications of the ACM containing the original article on Hoare logic!
cover of Communications of the ACM, Volume 12, Number 10, October 1969, with the stamp of the library of the Institut Henri Poincaré table of contents of Communications of the ACM, Volume 12, Number 10, October 1969. There is a small blue line marked next to the article by C. A. R. Hoare, "An Axiomatic Basis for Computer Programming". Perspective view of first two pages of Hoare's "An Axiomatic Basis for Computer Programming".
September 26, 2025 at 12:09 AM
noamzoam.mathstodon.xyz.ap.brid.gy
@andrejbauer definitely one of my favorites, but your comment brought to mind an entry in the encyclopedia appendix to Girard's Locus Solum, which I remembered as a backhanded compliment to Martin-Löf. Looking at it again I see that I was misremembering, and […]

[Original post on mathstodon.xyz]
September 22, 2025 at 4:25 PM
noamzoam.mathstodon.xyz.ap.brid.gy
A lesser known fact about Saunders Mac Lane is that he wrote a thesis in logic, completed in 1933 at Göttingen under the direction of Bernays and Weyl. I'm at the library and pulled out a copy of "Saunders Mac Lane : Selected Papers", which in addition to […]

[Original post on mathstodon.xyz]
After a year I left Chicago to go to Göttingen where I hoped that the environment of Hilbert would give more encouragement to my study of logic and rigor. By then I must have vaguely begun to see that a good proof consisted of more than just rigorous detail, because there was also an important element of plan for the proof -- the crucial ideas, which, over and above the careful detail, really make the proof function and get to the desired end. I clearly recall sitting in a vast lecture room listening to Edmund Landau lecture on Dirichlet series. As always, Landau's proofs were simply careful lists of one detail after another, but he gave this detail with such exemplary care that I could both copy down in my notebook all the needed detail and enter in the margin some overarching description of the plan of his proof (a plan which he never directly revealed). Then I came gradually to the insight that proofs in mathematics combined rigorous detail and overall plan -- and that overweening attention to the precision of detail could, as in the case of \emph{Principia}, wholly hide the plan. There arose with me the notion that the necessary rigor could be codified and simplified, so as to be made almost automatic. If only the automatic could be properly described and organized, then the essential ideas of the proof would come through. This idea of organizing the \emph{plan} of a proof in a formal way was evidently the germ of my thesis. I explained it to them in Vienna, where I thought that Rudolph Carnap would be more sympathetic. Instead, I thought very hard in spurts about a thesis. A decisive spurt came on April 18--22, when I finally worked out a plan of the final thesis. In an exuberant letter of April 26th to my mother I wrote: \begin{quote} ``Perhaps I have time to tell you a bit about my new discovery. It's a new symbolic logic for \emph{mathematical proofs.} It applies, as far as I can see now, to all proofs in all branches of mathematics (a rather big order!). It makes it possible to write down the proof of a theorem in a very much shorter space than by the usual methods, and at the same time it makes the proof very much clearer. In essence, it eliminates practically \emph{all} the long mechanical manipulations necessary to prove a theorem. It is only necessary to give \emph{leading ideas} of the \emph{proof.} In fact, once these leading ideas are given -- together with a few directions -- then it becomes possible to compute \emph{from} the leading ideas just what the \emph{proof} of the theorem will be. In other words, once these leading ideas are given, all the rest is a purely mechanical sort of job. It is possible to define once and for all how the job is to be carried out (the general definition depends essentially upon the abstract methods I have been developing for the past year).'' \end{quote} On this basis, I described exactly a number of the routine steps in a proof, giving each a label, as for example: \begin{quote} \emph{Inf schrumpf}: To prove a theorem $L \supset P$, search for a prior theorem of the form $M\supset N$, where $L$ is a ``special case'' of $M$ and $P$ the corresponding special case of $M$. \emph{Sub inf schrumpf}: Given a prior theorem $M\supset N$, one can conclude that $L\supset L'$, where $L'$ is obtained from $L$ by replacing every ``positive'' component of the form $M$ by a new component $N$. \emph{Sub Def}: Substitute the definitions. \emph{Identität}: Use one of the standard identities of algebra (or of the propositional calculus). \emph{Sub Theorem \#20.43}: Use the cited theorem, in the (only) possible way. \emph{$x = C$ fixieren}: Given a premise $(\exists x)L(x)$, assert $L(C)$ for some suitable ``constant'' $C$. \emph{Halbnorm}: Move a quantifier $\exists x$ or $\forall x$ to the front of an expression. \end{quote} All told the thesis gives twenty or twenty-five of such rules (listed at the start of Chapter VII), and then observes that many proofs can be ``abbreviated'' by listing in order the rules to be applied. In this sense, the thesis gives a formal definition of a routine proof.
July 25, 2025 at 12:10 PM
noamzoam.mathstodon.xyz.ap.brid.gy
Somehow ended up clicking to the "Donald Knuth" page on "Celebrity Birthdays", and I wonder how these things are generated.
[dubious text from "Celebrity Birthdays" site.] Donald Knuth is one of the most popular and richest Mathematician who was born on January 10, 1938 in Wisconsin, Wisconsin, United States. Mathematician and engineer who was arguably most recognized as the Professor Emeritus at Stanford in Palo Alto, California. Henry Suzzallo once studied at Stanford University, where he served as the Professor Emeritus. [dubious text from "Celebrity Birthdays" site.] Donald Knuth Net Worth Net Worth $5 Million Source Of Income Mathematician House Living in own house. Donald Knuth is one of the richest Mathematician from United States. According to our analysis, Wikipedia, Forbes & Business Insider, Donald Knuth 's net worth $5 Million. (Last Update: December 11, 2023) [dubious text from "Celebrity Birthdays" site.] Height, Weight & Body Measurements Donald Knuth height Not available right now. Donald weight Not Known & body measurements will update soon. Who is Donald Knuth Dating? According to our records, Donald Knuth is possibily single & has not been previously engaged. As of December 1, 2023, Donald Knuth’s is not dating anyone. Relationships Record : We have no records of past relationships for Donald Knuth. You may help us to build the dating records for Donald Knuth!
May 3, 2025 at 6:48 AM
noamzoam.mathstodon.xyz.ap.brid.gy
I really enjoyed this "Public Address on Generative Linguistics" by Matilde Marcolli:

https://www.youtube.com/watch?v=-gx3SK7FvKk

Marcolli is a mathematical physicist and recent [!] collaborator of Noam Chomsky. This lecture from Oct 2023 is broadly about […]

[Original post on mathstodon.xyz]
slide from Matilde Marcolli talk What does one gain from the use of mathematical formalism in Generative Linguistics? * mathematics is a powerful explanatory tool, because it is concise and flexible * this is why it is the language of science (or as Galileo had it, the language in which the universe is written) * it allows you to recognize when similar fundamental structures arise in different contexts: those are a sign of _universal laws of nature_ The purpose of science is to obtain a concise conceptual explanation of natural phenomena, that should be testable, predictive, and essential (entia non sunt multiplicanda praeter necessitatem) Generative linguistics aims at producing such models of the structure and functioning of language slide from talk by Matilde Marcolli, title: "Where is the explanatory power? Where is the understanding?" * do LLMs disprove Generative Linguistics, as some claim? ... No: quite the opposite, as the generative process of syntax is robust enough to emerge in keys and queries from a probabilistic smear of semantic relatedness * do LLMs dispense with the need for theoretical linguistics? ... No: successes of LLMs as language-handling machines do not provide us with a fundamental, coincise, explanatory, conceptual understanding of the structure of language * can LLMs be useful to theoretical linguistics? .... Possibly, as an experimental apparatus for the investigation of inverse problems in the syntax-semantics interface * if we have a functioning technology, do we need science?
December 20, 2024 at 5:04 PM