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Pitfalls and Potential Solutions to Your Primary Source Problems: Does anyone in the department read Greek . . . or crack uncrackable codes?

Adam E. Parker (Wittenberg University)


What happens when you can't read the language that the source is written in?


Danny Otero explained this particular challenge well:

The problem of getting these readings into the hands of my students has been most formidable. I have been able to make do with standard source books in the history of mathematics, but no single source for all of these readings currently exists. I have used Calinger’s Classics of Mathematics as a textbook with some success; it has the added benefit of including some well-written summaries of the history of mathematics that make for fine supplemental reading. By my count, 10 of the 21 readings that form the core of the course can be found in some form in Calinger’s book. One or two other texts can be found in Struik’s Source Book and Fauvel & Gray’s Reader. Still, some of the readings cannot be found in any of these and must be hunted down through the literature and made available to the students through the reserve desk of the university library. Even worse, four of the readings (by Fibonacci, St. Vincent, Briggs, and Cauchy) do not exist in print in English at all. . . . I have been forced to prepare my own translations of these texts for distribution to the students [Otero 1999, p. 68]. 

Anything other than English is problematic for me. I can get the gist of French because I’m old enough that I passed a language exam for my PhD, and I chose French. I can sometimes recall my high school Spanish. I can guess at Latin. But I’m practically fluent in these compared to my understanding of things written with Greek, Cyrillic, Asian or Indian alphabets. How is it that my most popular projects are from Carl Runge (1856–1927) and Martin Kutta (1867–1944) in German and Giuseppe Peano (1858–1932) in Italian? Here are some strategies.

It may help to know that . . .

  • While not common, sometimes mathematicians were deliberately vague about their discoveries in order to prevent plagiarism and maintain priority. So don’t be discouraged if sometimes you hit a dead end—that might have been the intent of the author. This occurred in many ways, but perhaps the most interesting was the use of anagrams to encode discoveries.[12]

The history of anagrammatism is a part of the history of superstition, but it sometimes concerns the historian of science. Not only in a general way, as truth is not always sharply separated from error, nor reason from unreason, but also because anagrams were occasionally used by men of science who desired to announce a discovery and establish their priority without running the risk of being plagiarized by unscrupulous rivals.

. . .

Another famous scientific anagram was introduced twenty years later than Huygens’ by no less a person than Newton.[13] In the latter’s very long letter of Oct. 24, 1676 to the Secretary of the Royal Society, Henry Oldenburg, he concealed anagrammatically his discovery of the infinitesimal calculus [Sarton 1936, pp. 136, 138]. 

George Sarton, Notes on the History of Anagrammatism, Isis 26, no. 1(1936):132–138.
Figure 5. The first page of [Sarton 1936].

The referenced letter by Newton was intended for Leibniz and came to be known as the “Epistola Posterior.” It actually contains two different anagrams:

The foundation of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6a cc d æ 13e ff 7i 3l 9n 4o 4q rr 4s 8t 12v x.[14]


At present I have thought fit to register them both by transposed letters, lest, through others obtaining the same result, I should be compelled to change the plan in some respects. 5accdæ 10effh 12i 4l 3m 10n 6oqqr 7s 11t 10v 3x: 11ab 3cdd 10eaeg 10ill 4m 7n 6o 3p 3q 6r 5s 11t 7vx 3acæ 4egh 6i 4l 4m 5n 8oq 4r 3s 6t 4v, aaddaeeeeeeeiiimmnnooprrrssssttuu.[15]

You could hardly be blamed for not seeing this as a very early statement of calculus.

  • Much mathematical symbolism in undergraduate mathematics has been relatively unchanged over the past 200 years. So even if you can’t read the language, you may be able to understand things from mathematical context. Otero points out limits to this, though: “Mathematicians who lived before Euler used mathematical notation only idiosyncratically, and before Descartes’ day rarely, if at all. The mathematical manuscripts of the late Renaissance (for example, Cavalieri’s work on computing areas, the source of his famous Principle) are largely opaque to the modern reader, and require considerable exegesis to extract their meaning, even in English translation” [Otero 1999, p. 60].
  • Google Translate, Babelfish, and other online translation sites can give you an idea of what your text is about. If you have a document with Optical Character Recognition (OCR), it can simply be copied into some of the translation websites. You may want to remove the mathematical symbolism and any LaTeX commands.
  • You might be more literate than you think. In general, mathematicians wanted their work to be seen by others[16] and that could be done in two ways. First, they would write in their native language but use simple structure so non-native speakers could understand. Or, they would use a more popular language (such as Latin) that the author wasn’t native in, which would necessitate simple structure. In either case, the texts tended to be easier to read than standard writings in that language. As Barnett noted above, primary sources rarely use “specialized vocabulary” [Barnett et al. 2015].
  • While a source may not be translated into English, it may be translated into another language (often French or German) which would be easier for you to read or translate.
  • Your colleagues in language departments can be assets. Just remember that their expertise extends well beyond simple translation, so asking them to read long passages for you can be interpreted as insulting. But I’ve found them very collegial for specific questions.
  • Your students can also be assets since some will have majors, minors, or interests in foreign languages and can help you out. This has by far been my most productive path. I have had students translate and analyze passages in French, German, and Latin, and that work became beneficial for all involved.[17]

[12] I’m really just including the following quote because I’d never heard, but very much like, the word “anagrammatism”.

[13] Huygens’ anagram, aaaaaaaacccccdeeeeeghiiiiiiiillllmmmnnnnnnnnnnoooopppqrrstttttuuuuu, was to guarantee priority in the discovery of Saturn’s rings. It was published in [Huygens 1656] and later unscrambled in [Huygens 1659, p. 47] (obviously in Latin) as “surrounded by a ring, thin, flat, nowhere touching, inclined to the ecliptic.”

[14] Ten years later Newton deciphered this passage in his Principia as “Given an equation containing any number of fluent quantities, to find fluxions, and inversely.” Because this passage was originally written in Latin, don’t try to count letters to double check.

[15] Newton deciphered this as “One method consists in extracting a fluent quantity from an equation at the same time involving its fluxion; but another by assuming a series for any unknown quantity whatever, from which the rest could conveniently be derived, and in collecting homologous terms of the resulting equation in order to elicit the terms of the assumed series” [Fauvel & Gray 1987, p. 407]. It is even more difficult to crack the code on this message, as it was not sent correctly. Fauvel and Gray continue, “On counting the letters, one finds that there are two i’s or j’s too few and one s too many. The anagram was inaccurately transcribed in the copy which Leibniz received.”

[16] I realize that I’ve given multiple examples of mathematicians whose actions have contradicted this, but the practice of concealing one's work became less common over time.

Adam E. Parker (Wittenberg University), "Pitfalls and Potential Solutions to Your Primary Source Problems: Does anyone in the department read Greek . . . or crack uncrackable codes?," Convergence (December 2023)