*“Mathematics is written for mathematicians.”*

In his preface to *De revolutionibus orbium coelestium* (*On the revolutions of the heavenly spheres*), Nicolaus Copernicus described his reasons for hesitating to publish his work. He admitted to fearing the ridicule of others, but finally decided that those mostly likely to heap scorn upon his work were those who are least qualified to judge it. It is at this point in the preface that the phrase “*Mathemata mathematicis scribuntur*” [Copernicus 1543, p. vii] appears.

Painting of Copernicus, 1580. Public domain, *Convergence* Portrait Gallery.

Unfortunately, the Latin here is potentially ambiguous, with the same words sometimes used to refer to astronomy or even astrology, rather than mathematics. Historian Dorothy Stimson translated the preface as part of her 1917 doctoral dissertation at Columbia University, *The Gradual Acceptance of the Copernican Theory of the Universe*. In her text, the words were consistently translated as references to mathematics:

If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgement as rash. For it is not unknown that Lactantius, the writer celebrated in other ways but very little in mathematics, spoke somewhat childishly of the shape of the earth when he derided those who declared the earth had the shape of a ball. So it ought not to surprise students if such should laugh at us also. Mathematics is written for mathematicians [Stimson 1917, p. 115].

Photograph of Dean Dorothy Stimson, 1926. Donnybrook Fair Yearbook Collection,

Goucher College Digital Library, Goucher College Archives, Towson, MD*.*

On the other hand, a more recent translation by historian Edward Rosen consistently interpreted the Latin in terms of astronomy instead:

Perhaps there will be babblers who claim to be judges of astronomy although completely ignorant of the subject and, badly distorting some passage of Scripture to their purpose, will dare to find fault with my undertaking and censure it. I disregard them even to the extent of despising their criticism as unfounded. For it is not unknown that Lactantius, otherwise an illustrious writer but hardly an astronomer, speaks quite childishly about the earth’s shape, when he mocks those who declared that the earth has the form of a globe. Hence scholars need not be surprised if any such persons will likewise ridicule me. Astronomy is written for astronomers [Copernicus 1978, p. 5].

Which of these translations interprets “*Mathemata mathematicis scribuntur*” correctly? Interestingly, that very issue seemed to be addressed by Copernicus in the introduction of Book I. Copernicus began by arguing that, of all things that can be studied, nothing is more important than the study of the heavens and the movements of the stars. Copernicus explicitly recognized the ambiguity of how this study has been named:

If then the value of the arts is judged by the subject matter which they treat, that art will be by far the foremost which is labeled astronomy by some, astrology by others, but by many of the ancients, the consummation of mathematics. Unquestionably the summit of the liberal arts and most worthy of a free man, it is supported by almost all the branches of mathematics. Arithmetic, geometry, optics, surveying, mechanics and whatever others there are all contribute to it [Copernicus 1978, p. 7].

If the study of the stars is truly to be viewed as the “consummation of mathematics,” arguing about the distinction between “Mathematics is written for mathematicians” and “Astronomy is written for astronomers” appears somewhat unimportant.

##### References

Copernicus, Nicholas. 1543. *De revolutionibus orbium coelestium*. Nuremberg: Johann Petreius.

Copernicus, Nicholas. 1978. *On the Revolutions*. Translation and commentary by Edward Rosen. Edited by Jerzy Dobrzycki. Vol. 2. London: Palgrave Macmillan.

Stimson, Dorothy. 1917. *The Gradual Acceptance of the Copernican Theory of the Universe*. New York: Baker & Taylor.

“Quotations in Context” is a regular column written by Michael Molinsky that has appeared in the *CSHPM/SCHPM Bulletin* of the Canadian Society for History and Philosophy of Mathematics since 2006 (this installment was first published in May 2008). In the modern world, quotations by mathematicians or about mathematics frequently appear in works written for a general audience, but often these quotations are provided without listing a primary source or providing any information about the surrounding context in which the quotation appeared. These columns provide interesting information on selected statements related to mathematics, but more importantly, the columns highlight the fact that students today can do the same legwork, using online databases of original sources to track down and examine quotations in their original context.