“The laws of nature are but the mathematical thoughts of God.”

—  Johannes Kepler

Attributed to Kepler in some sources (though more recent sources often attribute it to Euclid), such as Mathematically Speaking: A Dictionary of Quotations edited by Carl C. Gaither and Alma E. Cavazos-Gaither (1998), p. 214 http://books.google.com/books?id=4abygoxLdwQC&lpg=PP1&pg=PA214#v=onepage&q&f=false. The earliest publication located that attributes the quote to Kepler is the piece "The Mathematics of Elementary Chemistry" by Principal J. McIntosh of Fowler Union High School in California, which appeared in School Science and Mathematics, Volume VII ( 1907 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PR3#v=onepage&q&f=false), p. 383 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PA383#v=onepage&q&f=false. Neither this nor any other source located gives a source in Kepler's writings, however, and in an earlier source, the 1888 Notes and Queries, Vol V., it is attributed on p. 165 http://books.google.com/books?id=0qYXAQAAMAAJ&pg=PA165#v=onepage&q&f=false to Plato. Expressions that relate geometry to the divine "mind of God" include comments in the Harmonices Mundi, e.g., "Geometry is one and eternal shining in the mind of God", and "Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world".
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Johannes Kepler photo
Johannes Kepler 51
German mathematician, astronomer and astrologer 1571–1630

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“The laws of nature are but the mathematical thoughts of God.”

Euclid (-323–-285 BC) Greek mathematician, inventor of axiomatic geometry

The earliest published source found on google books that attributes this to Euclid is A Mathematical Journey by Stanley Gudder (1994), p. xv http://books.google.com/books?id=UiOxd2-lfGsC&q=%22mathematical+thoughts%22+euclid#search_anchor. However, many earlier works attribute it to Johannes Kepler, the earliest located being in the piece "The Mathematics of Elementary Chemistry" by Principal J. McIntosh of Fowler Union High School in California, which appeared in School Science and Mathematics, Volume VII ( 1907 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PR3#v=onepage&q&f=false), p. 383 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PA383#v=onepage&q&f=false. Neither this nor any other source located gives a source in Kepler's writings, however, and in an earlier source, the 1888 Notes and Queries, Vol V., it is attributed on p. 165 http://books.google.com/books?id=0qYXAQAAMAAJ&pg=PA165#v=onepage&q&f=false to Plato. It could possibly be a paraphrase of either or both of the following to comments in Kepler's 1618 book Harmonices Mundi (The Harmony of the World)': "Geometry is one and eternal shining in the mind of God" and "Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world".
Misattributed

“This is not what I thought physics was about when I started out: I learned that the idea is to explain nature in terms of clearly understood mathematical laws; but perhaps comparisons are the best we can hope for.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 22, Quantum Computing, Putting qubits to work, p. 203

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“All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty.”

Georg Christoph Lichtenberg (1742–1799) German scientist, satirist

As quoted in Lichtenberg : A Doctrine of Scattered Occasions (1959) by Joseph Peter Stern, p. 84
Context: All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true.

Paul Dirac photo

“It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power”

Paul Dirac (1902–1984) theoretical physicist

The Evolution of the Physicist's Picture of Nature (1963)
Context: It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

“It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws. Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members.
On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the 113 student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy. But it is exactly in this respect that our view of nature is so far above that of the ancients; that we no longer look on nature as a quiescent complete whole, which compels admiration by its sublimity and wealth of forms, but that we conceive of her as a vigorous growing organism, unfolding according to definite, as delicate as far-reaching, laws; that we are able to lay hold of the permanent amidst the transitory, of law amidst fleeting phenomena, and to be able to give these their simplest and truest expression through the mathematical formulas”

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Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 37.

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[Léon Brillouin, Science and Information Theory, second edition, Academic Press, New York, 1962, 0-48643-918-6, 314]

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There are no authorities which are not overseen, within nonlinear structures. Constitutional language is formally constructed to eliminate all ambiguity and to be processed algorithmically. Democratic elements, along with official discretion, and legal judgment, is incorporated reluctantly, minimized in principle, and gradually eliminated through incremental formal improvement. Argument defers to mathematical expertise. Politics is a disease that the constitution is designed to cure.
"A Republic, If You Can Keep It" https://web.archive.org/web/20140327090001/http://www.thatsmags.com/shanghai/articles/12321 (2013) (original emphasis)

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