[Ads-l] Antedating of "Number Theory"

Chris Waigl chris at LASCRIBE.NET
Sat Nov 19 03:11:15 UTC 2022

(Given that so much of the academic disciplinary jargon of the 19th century
was developed in various European / European culture countries
simultaneously ...)

I took a look in DWDS for "Zahlentheorie". One of their corpus links is
down, but for the others the two oldest hits are"

- 1850, Alexander von Humboldt ("Kosmos"): "Die Pythagoreer, denen Zahl die
Quelle der Erkenntniß, die Wesenheit der Dinge war, wandten ihre
Zahlentheorie, die alles verschmelzende Lehre der Zahlverhältnisse auf die
geometrische Betrachtung der früh erkannten 5 regelmäßigen Körper, auf die
musikalischen Intervalle der Töne, welche die Accorde bestimmen und
verschiedene Klanggeschlechter bilden, ja auf den Weltenbau selbst an:
ahndend, daß die bewegten, gleichsam schwingenden, Klangwellen erregenden
Planeten nach den harmonischen Verhältnissen ihrer räumlichen Intervalle
eine Sphärenmusik hervorrufen müßten." ["The Pythagoreans, for whom number
was the source of knowledge, the essence of being, applied their number
theory, the all-encompassing learning of the ratios of numbers to the
geometric examination of the five regular bodies, which were known in early
times, to the musical intervals of tones, which determine chords and the
diverse genres of sound, and even to world building: ...." - my
quick-and-rough translation]
- 1861, a handbook of symbols of freemasonry: "Der Mensch besitzt als das
einzige und zugleich höchste Winkelmass, als den prüfenden Massstab, seines
Fühlens, Denkens und Handelns die Vernunft; die Pythagoräer, zumal
Telauges, der Sohn des Pythagoras, und Philolaos, sowie Archytas, Plato und
Speusippos, hatten zu diesem oder die Zahl und Zahlen erheben wollen, bis
diese pythagoreische Zahlenlehre, Zahlentheorie von Aristoteles, dem
grösseren und glücklichen Nachfolger und Erben der Pythagoräer, beseitigt
und durch eine streng wissenschaftliche Denklehre oder Logik und
Erkenntnisstheorie oder Metaphysik ersetzt wurde." ["Man possesses reason
as the only and simultaneously highest compass, as the probing measuring
stick of his feeeling, thinking and action; the Pythagoreans, as well as
Telauges, Pythagoras's son, and Philotas, and also Archytas, Plato and
Speusippos, [etc] wanted to elevate number or numbers to this rank, until
this pythagorean number concept, number theory, was done away with by
Aristoteles, who was the greatest and most favoured of the successors and
heirs of the Pythagoreans, and replaced it with a strictly scientific
theory of thought or logic and epistemology, or metaphysics" (I think ther
ewas an OCR error, but the sentence is opaque enough that it doesn't

Funny that it came up as a Pythagorean and post-Pythagorean concept.


On Sun, Nov 13, 2022 at 7:05 AM Shapiro, Fred <fred.shapiro at yale.edu> wrote:

> number theory (OED 1899)
> Jeff Miller's "Earliest Known Uses of Some of the Words of Mathematics"
> webpage states the following:
> Number theory appears in 1853 in Manual of Greek literature from the
> earliest authentic periods to the close of the Byzantine era by Charles
> Anthon: "The ethics of the Pythagoreans consisted more in ascetic practice
> and in maxims for the restraint of the passions, especially of anger, and
> the cultivation of the power of endurance, than in scientific theory. What
> of the latter they had was, as might be expected, intimately connected with
> their number-theory" [University of Michigan Digital Library].
> Number theory appears in 1864 in A history of philosophy in epitome by Dr.
> Albert Schwegler, translated from the original German by Julius H. Seelye:
> "Not only the old Pythagoreans, who have spoken of him, delighted in the
> mysterious and esoteric, but even his new-Platonistic biographers, Porphyry
> and Jamblichus, have treated his life as a historico-philosophical romance.
> We have the same uncertainty in reference to his doctrines, i. e. in
> reference to his share in the number-theory. Aristotle, e. g. does not
> ascribe this to Pythagoras himself, but only to the Pythagoreans generally,
> i. e. to their school" [University of Michigan Digital Library].
> Fred Shapiro
> ------------------------------------------------------------
> The American Dialect Society - http://www.americandialect.org

Chris Waigl . chris.waigl at gmail.com . chris at lascribe.net
http://eggcorns.lascribe.net . http://chryss.eu

The American Dialect Society - http://www.americandialect.org

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