
An 1883 lecture (Ѻ) by Rudolf Steiner on Goethe and mathematics.

An 1883 lecture (Ѻ) by Rudolf Steiner on Goethe and mathematics.

In hmolscience, Goethe and mathematics refers to the topic of Goethe’s relationship with mathematics, the subject of which, along with astronomy, he seemed to have peculiar distancing relationship with. [1]

Overview
In 1893, Goethe penned “Mathematics and its Abuse”, some noted quotes of which are as follows: [5]

“Considering my inclinations and conditions I had to appropriate to myself very early the right to investigate, and to conceive nature in her simplest, most conspicuous creations also without the aid of mathematics. I was accused of being an opponent, and enemy of mathematics in general, although nobody can appreciate it more highly than I, as it accomplishes exactly those things which I was prevented from realizing.”
— Johann Goethe (1893), “Mathematics and its Abuse” (pg. 78)

“It is a wrong conception to think that a phenomenon could be explained by calculus or words. Mathematicians are like Frenchman; if one speaks to them they translate it into their own language, and then it will be very soon something entirely different.”
— Johann Goethe (1893), “Mathematics and its Abuse” (pg. 98)

Here, to note, we are reminded of Gibbs and his c.1895 statement that: “a mathematician may say anything he pleases—but a physicist must be a least partially sane”. In the next quote, Goethe seems to praise Lagrange:

“The mathematician is perfect only in so far as he is a perfect man, as he feels the beauty of truth; only then does he become thorough, penetrating, pure, clear, graceful and even elegant. All this is necessary to become like Lagrange.”
— Johann Goethe (1893), “Mathematics and its Abuse” (pg. 138)

In 1826, Goethe, in his "On Mathematics and its Misuse", a discussion of his objection to the work on light and color by Newton, commented: [2]

“I receive mathematics as the most sublime and useful science, so long as they are applied in their proper place; but I cannot commend the misuse of them in matters which do not belong to their sphere, and in which noble science as they are, they seem to be mere nonsense. As if things only exist when they can be mathematically demonstrated [see: da Vinci on real science]. It would be foolish for a man not to believe in a woman’s love for him because she could not prove it to him mathematically [compare: The Mathematician in Love]. She can mathematically prove her dowry, but not her love. The mathematicians did not find out the metamorphosis of plants. I have achieved this discovery without mathematics, and the mathematicians were forced to put up with it. To understand the phenomena of color nothing is required but unbiased observation and a sound head, but these are scarcer than folks imagine.”

Ironically, Goethe did prove that love exists mathematically, seventeen-years prior, in his 1809 Elective Affinities, when he used the chemical mathematics of Swedish chemist Torbern Bergman's 1775 affinity tables, to present a treatise on the additions and subtractions of human chemical reactants when brought together, to participate in human chemical affinity reactions. The point expressed by Goethe, above, is exemplified by ridiculous incorrectness of the conclusions reached in the 1962 stable marriage problem, using pure mathematics, versus conclusions reached using the more realistic circa 1975 Gottman stability ratio (measurement + psychology + mathematics), versus even more realistic modern synthesis of circa 2005 human chemical bonding theory (measurement + chemistry + thermodynamics + physics + evolutionary psychology + mathematics).

In commentary on individuals such as d’Alembert and Lagrange, Goethe states: [4]

“It pleased me not to find my intentions were falsely interpreted. I have heard accusations against me as though I were an opponent, an enemy of mathematics altogether; yet there is none who holds it in greater esteem than I, for it is able to do the very thing which to perform has totally denied me.”

On the topic of mathematical physics, he said “number and proportion, in their nakedness, destroy all form, and banish the spirit that informs real perception.” Goethe seemed to use mathematics in his own unique way.

Other
In 1914, Emch Arnold penned “Goethe and Schopenhauer on Mathematics”, comparing Goethe and Arthur Schopenhauer (see: Goethe and Schopenhauer) and their similar relation to mathematics. [6]

In 1958, Ernst Lehrs penned “Goethe, Faraday, and Mathematics”, a comparison of Goethe with Michael Faraday, wherein he summed up the view of Goethe’s style of mathematics as follows: [3]

“In recent centuries there have been two great men who have shown, in their approach to scientific research, that man is capable of proceeding like a true mathematician even though he is not using mathematics in the accepted sense. These two men were Goethe and Faraday.”

Considered mathematics “the most sublime and useful science”, but was guarded against its misuse or misapplication, where it can become reduced to nonsense. Curiously, Goethe seemed to have been attacked by fellow scientists for his non-direct use of mathematics.

Quotes | On
The following are related quotes:

“Goethe’s theory of colors was most criticized for the non-use of mathematics therein, and therefore, one presumed to categorize this epoch-making work of physics among the productions of the fine arts. What a miscalculation!”
— Johann Werneburg (1817) [7]

Quotes | By
The following are quotes by Goethe in respect to mathematics:

“Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identities fades out of sight.”
— Johann Goethe (c.1820); compare: feigned IQ (Ѻ)

“Mathematics can remove no prejudices and soften no obduracy. It has no influence in sweetening the bitter strife of parties, and in the moral world generally its action is perfectly null.”
— Johann Goethe (c.1820) (Ѻ); compare "friction of rubbing together of human molecules" (Carey, 1858); see also: moral symbols (and Otto Weininger 1903 quotes)

References
1. (a) Steiner, Rudolf, Goethe, Johann, and Barnes, John. (2000). Nature’s Open Secret: Introduction to Goethe’s Scientific Writings (ch. 12: Goethe and Mathematics, pgs. 151-53). SteinerBooks.
(b) Steiner, Rudolf. (1950). Goethe the Scientist (ch. XII: Goethe and Mathematics, pgs. 189-92). Anthroposophic Press.
(c) Wells, George A. (1979). Goethe and the Development of Science, 1750-1900 (section: Goethe’s Criticism of Mathematical Physics, pgs. 100-). Publisher.
2. Goethe, Johann, Eckermann, Johann E., Soret, Frederic J., and Oxenford, John. (1883). Conversations of Goethe with Eckermann and Soret (pg. 181). G. Bell & Sons.
3. Lehrs, Ernst. (1958). “Goethe, Faraday, and Mathematics” (Ѻ), in: Man or Matter (editors: Nick Thomas and Peter Bortoft) (Appendix II, pgs. 495-514) (pdf). Publisher, 1985.
4. Goethe, Johann. (1826). “On Mathematics and its Misuse” (Über Mathematik und deren Missbrauch), in: his collection of essays: Zur Naturwissenshaft im Allgemeinen (On Science in General).
5. (a) Goethe, Johann. (1893). “Mathematics and its Abuse”, Naturwissenschaftliche Schriften, 2d part, Vol. II (pgs. 78, 98). Weimar.
(b) Emch, Arnold. (1914). “Goethe and Schopenhauer on Mathematics” (pdf), The Open Court, 9(2):521-28.
6. Emch, Arnold. (1914). “Goethe and Schopenhauer on Mathematics” (pdf), The Open Court, 9(2):521-28.
7. Werneburg, Johann Friedrich Christian. (1817). "Bizarre Phenomena at and through Different Prisms: To Properly Honor Newton’s and Goethe’s Theories of Colors" (“Merkwürdige Phänomene an und durch verschiedene Prismen: Zur richtigen Würdigung der Newton’schen und der von Göthe’schen Farbenlehre”) (Translator: Name) (Ѻ) (preface, pg. #). Publisher.

Threads
● Goethe, Math & Universal Genius (2010) – Hmolpedia.