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Who really said it

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 created and sustains us

Not Galileo — Georg Cantor, in a letter of 1885 Georg Cantor 1845–1918 · German mathematician, founder of set theory
Disputed In copyright

Quote Investigator settled this in May 2025 ↗: Cantor deserves the credit, the source is a letter he wrote to the Swedish mathematician G. Eneström on 4 November 1885, and QI “has found no substantive support for the attribution to Galileo Galilei who died in 1642.” We read the German for ourselves in a printing QI does not cite — Cantor’s own Zur Lehre vom Transfiniten (Halle a. S.: C. E. M. Pfeffer, 1890), p. 7 ↗, where the piece is headed “Über die verschiedenen Standpunkte in Bezug auf das actuale Unendliche … Aus einem Schreiben des Verf. an Herrn G. Eneström in Stockholm vom 4. Nov. 1885” and the sentence runs “es läßt sich dieses Verhalten auch als eine Art Kurzsichtigkeit auffassen…” The English everyone quotes is Rudy Rucker’s, from Infinity and the Mind (1982).

Last verified 22 Aug 2026 · how we verify · spot an error?

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Disputed credit — copy with the correction

“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 created and sustains us” Not Galileo. Georg Cantor, from a letter to G. Eneström in Stockholm dated 4 November 1885, printed in Zur Lehre vom Transfiniten, Erste Abtheilung (Halle a. S.: C. E. M. Pfeffer, 1890), p. 7: "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." English translation by Rudy Rucker, Infinity and the Mind (1982), p. 43. Traced by Quotle.info. · Verbatim: “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”

The slide-ready mistake: crediting this to Galileo Galilei. Use the credit shown above instead.

Can you use it?

Still under copyright (rights held by Rudy Rucker and Birkhäuser (the 1982 English translation)). A short, credited quote is generally fine for talks, teaching, and internal decks; for commercial, published, or large-scale reuse, get permission.

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In context

Evoking the world of Georg Cantor — German mathematician, founder of set theory. Theme: "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 created and sustains us". Atmospheric and restrained, cinematic directional light, a muted period-appropriate palette, fine grain and texture. Compose with generous empty space for the quote and a small credit line. No lettering in the image itself.

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Minimalist editorial slide for the quote "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 created and sustains us". Clean background, a single muted accent color, generous negative space, subtle paper or linen texture, no literal illustration — let the words carry it. Reserve clear space for a serif quote and a small credit line. No lettering in the image itself.

Provenance

A mathematician defending his own numbers

Work
Über die verschiedenen Standpunkte in Bezug auf das actuale Unendliche
Author
Georg Cantor (1845–1918), professor at Halle
Written
In a letter to G. Eneström in Stockholm, 4 November 1885
Read here in
Zur Lehre vom Transfiniten, Erste Abtheilung (Halle a. S.: C. E. M. Pfeffer, 1890), p. 7
English
Rudy Rucker, Infinity and the Mind (1982), p. 43 — per Quote Investigator

… 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 secundären, transfiniten Formen uns allüberall umgiebt und sogar unserm Geiste selbst innewohnt.

Transcribed from the Fraktur of the 1890 printing, which spells umgiebt and secundären; the 1932 collected edition modernises both, on the evidence of Quote Investigator’s transcription of it, which is the only text of that edition we could reach. “A. U.” is Cantor’s own abbreviation, used throughout the letter, for Actual-Unendliches — the actual infinite. The English in circulation also drifts by a word: Rucker’s rendering reads “even though it in its highest form has created and sustains us.”

Cantor, Zur Lehre vom Transfiniten (1890), p. 7, at the Internet Archive

How we verified this

In copyright

Two different answers here. Cantor’s German is public domain — he died in 1918 and the printing we read is from 1890 ↗. The English sentence at the top of this page is not: it is Rudy Rucker’s translation, published in Infinity and the Mind (Birkhäuser, 1982) ↗, which remains in copyright. Quote it as a quotation, with the credit, and not as free text.

Rights status is our research, not legal advice — and copyright varies by country and edition. For commercial or published use, confirm with the rightsholder. See terms.

Fact-check

Often misattributed

Two men who thought hard about the actual infinite, 243 years apart, and only one of them wrote this sentence.

Galileo Galilei Misattributed

Quote Investigator states plainly that it has “found no substantive support for the attribution to Galileo Galilei who died in 1642” ↗. The sentence also appears in none of the sourced, attributed or misattributed quotations on his Wikiquote page ↗.

Georg Cantor, 4 November 1885

QI traces it to Cantor’s letter to G. Eneström ↗ and we read the German on p. 7 of Cantor’s own 1890 collection ↗, where the piece carries the letter’s date in its heading. Cantor was defending transfinite numbers against mathematicians who would not entertain them; the myopia is theirs.

Rudy Rucker, Infinity and the Mind (1982) Translation, not the original

QI identifies the familiar wording as Rucker’s translation, on p. 43 of his book ↗. “Myopia” for Kurzsichtigkeit and “in its highest form” for in seinem höchsten, absoluten Träger are his choices, and they are why the sentence reads like an epigram rather than a clause in a mathematical argument.

Galileo’s paradox, 1638 Context

Galileo really did get there first in one respect: Wikiquote quotes E. T. Bell noting that in 1638 Galileo observed there are precisely as many squares as positive integers ↗, the property that defines an infinite set — and Bell dates Cantor’s own observation of the denumerable / non-denumerable distinction to 1878. Galileo saw the paradox. Cantor wrote the sentence.

Quote Investigator credits Cantor and rules out Galileo ↗; the German is on p. 7 of Cantor’s 1890 collection ↗, under the date 4 November 1885.

Context

Why it mattered

Cantor was not writing about the sublime. He was losing an argument with his profession. By 1885 he had shown that infinities come in different sizes, and much of mathematical opinion — Kronecker most damagingly — treated the actual infinite as a confusion to be legislated out of existence. This sentence is what a man writes when the objection he keeps meeting is not a counter-argument but a refusal to look.

That is also why the word he chose was Kurzsichtigkeit, short-sightedness. He writes of a certain “horror infiniti” that, he says, found its classic expression and its support in a letter of Gauss’s he had mentioned earlier, and his complaint is that it is a habit of the eye rather than a result: an unwillingness to focus, not a proof of anything. The clause after the famous one ↗ says the infinite is not remote at all — that in its secondary, transfinite forms it surrounds us everywhere and is present in our own minds.

A. U. — Cantor’s shorthand, all through the letter, for the actual infinite.

Read the full story

The letter had a specific addressee and a specific provocation. Gustaf Eneström ↗, the Swedish historian of mathematics, had written to Cantor asking whether he had read the Abbé Moigno’s pamphlet arguing that an actually infinite number is impossible and drawing theological conclusions from it. Cantor’s reply traces the position back through Cauchy to P. Gerdil (1718–1802) — whom he describes as a highly placed and respected figure and an esteemed philosopher, for a time a professor at Turin, later tutor to the future Charles Emmanuel IV of Piedmont and called to Rome by Pius VI in 1776 — disposes of it, and only then reaches the sentence people quote — which is a diagnosis of his opponents, delivered mid-argument.

The religious note in it is not decoration either. Cantor was a devout Lutheran who corresponded with Catholic theologians about the transfinite ↗, and the German says the actual infinite “in its highest, absolute bearer has created and sustains us.” Rucker’s “in its highest form” smooths that into something a poster can carry. It is a good translation of a sentence that was never meant to be quoted alone — and once it was quoted alone, it needed a famous name, and the nearest famous name in the history of infinity was Galileo.

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Filed under

More provenance-checked quotes on the same theme, each with its reuse status.

Knowledge Courage Doubt

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Dig deeper

Trusted places to keep pulling the thread — primary archives, fact-checks, and scholarship. We show how we used each one before you leave.

Quote Investigator: The Fear of Infinity Is a Form of Myopiaquoteinvestigator.com

The investigation this page defers to: Cantor credited, the 1885 Eneström letter identified, Rucker’s 1982 translation named, and no substantive support found for Galileo.
Cantor, Zur Lehre vom Transfiniten (Halle, 1890)archive.org

Cantor’s own collection of his philosophical papers. The first piece is the Eneström letter of 4 November 1885; the sentence is on p. 7.
Wikipedia: Georg Cantoren.wikipedia.org

The author: 3 March 1845 to 6 January 1918, founder of set theory, who proved that the real numbers outnumber the naturals and that there is an infinity of infinities; a devout Lutheran whose beliefs shaped his philosophy of science.
Wikipedia: Gustaf Eneströmen.wikipedia.org

The man Cantor was writing to: Swedish mathematician, statistician and historian of mathematics (1852–1923), of Eneström-index fame.
Wikiquote: Galileo Galileien.wikiquote.org

His sourced, attributed and misattributed quotations — none of which is this — plus E. T. Bell on Galileo’s 1638 anticipation of Cantor.
Rucker, Infinity and the Mind (1982)archive.org

The book whose English rendering became the quotation. The scan is lending-restricted, so we did not read p. 43 ourselves; the citation is Quote Investigator’s.

The author

About Georg Cantor

Georg Cantor

1845–1918 · German mathematician, founder of set theory

Georg Ferdinand Ludwig Philipp Cantor was born in 1845 and spent his career at Halle, where he created set theory almost single-handedly. He established the one-to-one correspondence as the test of sameness of size, proved that the real numbers are more numerous than the natural numbers, and showed that this implies an endless hierarchy of infinities — results that a substantial part of the profession, led by Kronecker, refused to accept in his lifetime. He was a devout Lutheran who took the theological stakes of the actual infinite seriously, corresponded about them with Catholic scholars, and whose recurring bouts of depression, from 1884 to the end of his life, have been blamed on the hostility of his contemporaries. He died in 1918.

For writers & researchers

Cite this

The primary source (Chicago)

Georg Cantor, “Über die verschiedenen Standpunkte in Bezug auf das actuale Unendliche” (from a letter to G. Eneström in Stockholm, 4 November 1885), in Zur Lehre vom Transfiniten: Gesammelte Abhandlungen aus der Zeitschrift für Philosophie und philosophische Kritik, Erste Abtheilung (Halle a. S.: C. E. M. Pfeffer, 1890), 7. English wording from Rudy Rucker, Infinity and the Mind (Birkhäuser, 1982), 43, per Quote Investigator.

This verification page

Quotle.info. “Who really said ‘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 created and sustains us’?” Last verified 22 Aug 2026. https://quotle.info/who-said/the-fear-of-infinity-is-a-form-of-myopia-that-destroys-the/

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