Saunders Mac Lane says he attended Hilbert's weekly lectures on "matters of general intellectual interest" around 1931 or 1933 (Saunders Mac Lane: A Mathematical Autobiography p. 44). I believe these are the same as Mac Lane elsewhere called Hilbert's "general lecture course on the philosophy of science which I heard him give in late 1931'' (1995 "A matter of temperament", letter, with reply by Freeman J. Dyson. New York Review of Books, 42(15):56.

Are there any published descriptions of these lectures, beyond Mac Lane's remark that the topics included "the overall importance of the discovery of the Americas"?

Hel Braun probably means these same lectures in her autobiography when she refers to Hilbert's legendary crepe de chine lectures (sagenhaften Crepe de Chine-Vorlesungen) (Eine Frau und die Mathematik 1933–1940). That is lectures given to a rather posh audience from beyond the university. But she says nothing about content.


1 Answer 1


Here is MacLane's sentence about the lectures in its entirety:

"Although the leading mathematician, David Hilbert, had retired and came only once a week to lecture on matters of general intellectual interest - for instance on the overall importance of the discovery of the Americas - many young stars had appeared".

It is unclear if he actually attended a lecture or is referring a second hand account, or, if he did attend, whether he attended more than once. His shift of focus at the end of the sentence, and switching to Weyl, "Hilbert's successor", in the next one suggest only passing familiarity with them. MacLane also mentions winter of 1933 on the same page as the sentence, it seems likely but not entirely certain that the lectures referred to are contemporaneous.

According to the McTutor biography:

"In 1930 Hilbert retired but only a few years later, in 1933, life in Göttingen changed completely when the Nazis came to power and Jewish lecturers were dismissed. By the autumn of 1933 most had left or were dismissed. Hilbert, although retired, had still been giving a few lectures. In the winter semester of 1933-34 he gave one lecture a week on the foundations of geometry".

Unfortunately, McTutor's O'Connor and Robertson do not disclose their source of information on the content of the lectures either. But in 1932 Springer published Hilbert's and Cohn-Vossen's Intuitive Geometry (Geometry and the Imagination in English translation), which Nuno and Romao in Hilbert as Outreacher describe as "widely acknowledged as one of the highest achievements in mathematical exposition to the general public, and it provides the layperson with an accurate (and timeless) impression of what the spirit of mathematics is about".

This is confirmed by the list of Hilbert's lecture courses printed in David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917-1933, see below. However, the only lecture in the volume from 1933 is called On the Infinite, which I suppose also could be of "general intellectual interest". The editors' comments in the introduction on the general state of Hilbert's Nachlaß suggest that they prioritized mathematics and science related lecture notes for publication. So if there was something on the discovery of the Americas it would still sit handwritten in the archives:

"The present Volume is the third in a series of six presenting a selection from Hilbert’s previously unpublished lecture notes on the foundations of mathematics and physics during the period 1890 to 1933. The Hilbert Nachlaß contains approximately eighty lecture notebooks, covering all aspects of his mathematical activity, and spanning almost the entirety of his teaching career; some are in his own hand, others were carefully worked out by his assistants as official protocols of his lectures... The structure of this Edition, the nature, location, and condition of the Hilbert lecture notes, their provenance, and what we have been able to reconstruct of their history, are all described in the general ‘Introduction to the Edition’, which is to be found at the beginning of Volume 1."

Googlebooks displays the relevant part of the volume 1 introduction, with few exceptions the manuscripts are kept in the library of the Mathematics Institute, and the manuscript division of the university, both in Göttingen.

List of Hilbert's lecture courses in 1931-34 (from David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917-1933, p.991)

SS 1931 Grundlagen der Mathematik, 1st.67 [Foundations of Mathematics]

WS 1931/32 Einleitung in die Philosophie auf Grund moderner Naturwissenschaft (für Hörer aller Fakultäten), 1st. [Introduction to Philosophy of Modern Natural Science (for students of all departments)]

SS 1932 Grundlagenfragen der Geometrie, 1st. [Foundational Questions of Geometry]

WS 1932/33 Grundlagen der Logik, allgemeinverständlich (für Hörer aller Fakultäten), 1st. [Foundations of Logic, intelligibly (for students of all departments)]

SS 1933 Wissen und Denken (für Hörer aller Fakultäten), 1st. [Knowledge and Thinking (for students of all departments)]

WS 1933/34 Grundlagen der Geometrie, mit Schmidt 2st. [Foundations of Geometry]

  • $\begingroup$ He says elsewhere he attended Hilbert's lectures. I added that to the question. I would not be entirely sure of Mac Lane's memory of the dates 60 years later, although he did have letters he had written to his mother at the time and he may have checked those. $\endgroup$ Sep 11, 2016 at 7:28
  • 3
    $\begingroup$ @Colin I confirmed foundations of geometry for the winter of 1933, see edit. But from what I read the editors saying, the notes on general topics, if any, might only be available in handwritten originals at this time. Hope this helps. By the way, I am a big fan of your papers on Grothendieck and MacLane! $\endgroup$
    – Conifold
    Sep 11, 2016 at 23:21

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