Georg Cantor? Galileo Galilei? Rudy Rucker? David Foster Wallace? Apocryphal?
Question for Quote Investigator: The careless use of infinity in mathematical and scientific reasoning produces confusion and contradictions. Hence, mathematicians in the 1800s often placed tight restrictions on the use of infinity within mathematical proofs.
The theory of transfinite numbers was pioneered by mathematician Georg Cantor who envisioned an extraordinary hierarchy of infinite sets. Influential colleagues reacted with disbelief and scorn to Cantor’s mind-stretching ideas. Apparently, Cantor responded by saying something like the following:
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us.
Oddly, this statement has also been attributed to the famous Italian Renaissance astronomer Galileo Galilei. Would you please help me to find an accurate version of the quotation together with a citation identifying the originator?
Reply from Quote Investigator: QI has found no substantive support for the attribution to Galileo Galilei who died in 1642. A contributor to the Goodreads website implausibly linked the quotation to Galileo in 2017.1
The earliest close match in English known to QI appeared in 1982 within the book “Infinity and the Mind: The Science and Philosophy of the Infinite” by mathematician and science fiction author Rudy Rucker. Boldface added to excerpts by QI:2
In mathematics no other subject has led to more polemics than the issue of the existence or nonexistence of mathematical infinities. We will return to some of these polemics in the last chapter. For now, let us reprint Cantor’s opening salvo in the modern phase of this age-old debate:
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
The accompanying footnote pointed to a letter by Georg Cantor published within a collection of his essays.
Below are details and additional selected citations in chronological order.
Georg Cantor sent a letter to G. Eneström in Stockholm dated November 4, 1885. The letter was reprinted in 1932 within “Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts” (“Collected Treatises of Mathematical and Philosophical Content”) of Cantor edited by mathematician Ernst Zermelo. The title was “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“On the different points of view regarding the actual infinite”). The following pertinent excerpt occurred in the letter:3
Wenn aber aus einer berechtigten Abneigung gegen solches illegitime A. U. sich in breiten Schichten der Wissenschaft, unter dem Einflüsse der modernen epikureisch-materialistischen Zeitrichtung, ein gewisser Horror Infiniti ausgebildet hat, der in dem erwähnten Schreiben von Gauß seinen klassischen Ausdruck und Rückhalt gefunden, so scheint mir die damit verbundene unkritische Ablehnung des legitimen A. U. kein geringeres Vergehen wider die Natur der Dinge zu sein, die man zu nehmen hat, wie sie sind, und es läßt sich dieses Verhalten auch als eine Art Kurzsichtigkeit auffassen, welche die Möglichkeit raubt, das A. U. zu sehen, obwohl es in seinem höchsten, absoluten Träger uns geschaffen hat und erhält und in seinen sekundären, transfiniten Formen uns allüberall umgibt und sogar unserm Geiste selbst innewohnt.
Here is one possible translation:
But if, out of a justified aversion to such illegitimate “actual infinite”, a certain “Horror of the Infinite” has developed in broad sections of science under the influence of the modern Epicurean-materialist movement, which found its classic expression and support in the aforementioned writing by Gauss, then the associated uncritical rejection of legitimate “actual infinite” seems to me to be no less of an offense against the nature of things, which one has to accept as they are.
This behavior can also be understood as a kind of short-sightedness which robs us of the possibility of seeing the “actual infinite”, although in its highest form it created and sustains us, and in its secondary, transfinite forms it surrounds us everywhere and even inhabits our spirit itself.
In 1982 Rudy Rucker published “Infinity and the Mind” which included the quotation in English as mentioned previously.
In 1984 Rucker published “The Fourth Dimension: Toward a Geometry of Higher Reality”, and he printed the translated statement from Georg Cantor again:4
A somewhat similar passage can be found in an 1886 essay, “On the Various Standpoints with Respect to Actual Infinity,” by the German mathematician Georg Cantor:
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
In 2003 U.S. literary figure David Foster Wallace published “Everything and More: A Compact History of Infinity” which included the following footnote:5
It’s only fair to point out that Cantor made his share of wacky-sounding pronouncements in the controversy over infinite sets, many with an ominously grandiose religious flavor, as in “I entertain no doubts as to the truth of the transfinites, which I have recognized with God’s help,” or “The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us.”
In conclusion, Georg Cantor deserves credit for the German version of this quotation which he appeared in a letter in 1885. Rudy Rucker published a somewhat compressed translation into English in 1982. Rucker’s version is the most popular English version.
Image Notes: Symbol of the infinite number aleph zero
Acknowledgement: Great thanks to Lee Edwards whose inquiry led QI to formulate this question and perform this exploration.
- Website: Goodreads, Article title: Galileo Galilei > Quotes > Quotable Quote, Timestamp on first ‘Like’: Apr 11, 2017 09:07AM, Website description: Goodreads is a large community for readers that provides book recommendations; Amazon owns the site. (Accessed goodreads.com on May 10, 2025) link ↩︎
- 1982 Copyright, Infinity and the Mind: The Science and Philosophy of the Infinite by Rudy Rucker, Chapter 1: Infinity, Quote Page 43, Birkhäuser, Basel, Switzerland. (Verified with scans) ↩︎
- 1932 (1962 Reprint), Georg Cantor: Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind (Collected Treatises on Mathematical and Philosophical Content With explanatory notes and additions from the Cantor-Dedekind correspondence), Herausgegeben von Ernst Zermelo (Edited by Ernst Zermelo), Nebst einem Lebenslauf Cantors von Adolf Fraenkel (Including a biography of Cantor by Adolf Fraenkel), Article: Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche (On the different points of view regarding the actual infinite), Note: Letter excerpt from Georg Cantor to Mr. G. Eneström in Stockholm dated 4 November 1885, Start Page 370, Quote Page 374 and 375, Georg Olms Verlagsbuchhandlung (Georg Olms Publishing House), Hildesheim, Germany. (Verified with scans) ↩︎
- 1984, The Fourth Dimension: Toward a Geometry of Higher Reality by Rudy Rucker, Chapter 11: What Is Reality?, Quote Page 201, Houghton Mifflin Company, Boston, Massachusetts. (Verified with scans) ↩︎
- 2003, Everything and More: A Compact History of Infinity by David Foster Wallace, Section: Small But Necessary Foreword, Quote Page 41, Footnote 27, W. W. Norton & Company, New York. (Verified with scans) ↩︎