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Pitfalls and Potential Solutions to Your Primary Source Problems: X doesn’t mark the spot.

Adam E. Parker (Wittenberg University)


You have identified the primary source with the seed of the topic,
but when you go to find it . . . it isn’t there.


I was working with Janet Heine Barnett on polishing my PSP on higher order linear differential equations with constant coefficients [Parker 2021a], when she noticed that I had cited a certain letter between Leonhard Euler (1707–1783) and Johann Bernoulli as:[10]

Der Briefwechsel zwischen Leonhard Euler und Johann I. Bernoulli – III. 1739–1746, Bibl. Math. (3) 63 (1905) 16–87.

while in an earlier paper [Parker 2016], I had cited the same article as:

Der Briefwechsel zwischen Leonhard Euler und Johann I Bernoulli [Teil] III, 1739–1746 (Seventeen Letters from Euler to Johann I Bernoulli Part III, 1739–1746). Biblioth. Mathem., 53: 16–87, 1905.

She understandably wondered which volume was correct. The Euler Archive lists the citation of E863 as:

Originally published by G. Eneström in the three articles: Der Briefwechsel zwischen Leonhard Euler und Johann I. Bernoulli. I – III; Bibl. math. 43, 1903, p. 344–388; 53, 1904, p. 248–291; 63, 1905, p. 16–87 [Eneström 2018].

It also links to scans of the three articles, from which I used three letters contained in the third of the three articles. Unfortunately, the scans don’t include the front-page information and so, to answer Janet's question, I decided to go directly to Bibliotheca Mathematica to see which volume number was correct. But when I looked, I couldn’t find any Volume 43, 53, or 63! They just weren’t there. So, the short answer to the question is that neither citation is correct!

Now, should I have realized this earlier? Absolutely. But I didn’t. It still needed to be fixed.

It may help to know that . . .

  • Lots of journals have very similar names, even if they have nothing to do with each other. Do you know the difference between the currently published journals The Mathematica Journal, Mathematica, and Mathematika? I don’t.
  • The converse is also true, as the same publication may have many different names. Journals aren’t static. They start and end. They take breaks and reappear. They split and combine with other journals. The Euler Archive notes that the flagship publication of the Academy of Sciences in St. Petersburg (in which Euler published much of his work) has gone through several name changes.
    • 1726–1746 Commentarii Academiae Scientiarum Imperialis Petropolitanae
    • 1750–1776 Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae
    • 1777–1782 Acta Academiae Scientiarum Imperialis Petropolitanae
    • 1783–1802 Nova Acta Academiae Scientiarum Imperialis Petropolitanae
    • 1803–1916? Mémoires de l’Académie Impériale des Sciences de St. Pétersbourg, avec l’Histoire de l’Académie
      • Series V: 1803–1830?
      • Series VI: 1830?–1859?
      • Series VII: 1859?–1897?
      • Series VIII: 1897?–1916?

All of these St. Petersburg publications should not be confused with the St. Petersburg Mathematical Journal, which is an AMS publication and is the English translation of the Russian journal Algebra i Analiz.

  • The format of information contained in citations is not consistent. As you can see above, the same article was cited in three different formats in Mathematics Magazine, the PSP, and the Euler Archive. Citations were even less standardized in the past.
  • Abbreviations for journal titles only recently became standardized in the USA by Mathematical Reviews. Prior to this, sources were named in many different ways and formats. For example, a citation of “Acta” would require context to determine which of the dozens of Acta journals in the classification it is referring to, or perhaps one of the older non-cataloged journals such as the Acta Eruditorum.
  • Many authors have published articles or books with extremely similar, or identical, names. While researching classroom materials on Wronskians, I found that Giusippe Peano (1858–1932) wrote two short articles, “Sur le Déterminant Wronskien” and “Sur les Wronskiens.” The similar titles became more confusing when I learned that the articles appeared in the same issue of the same journal, [Peano 1889a] and [Peano 1889b]!
  • The organization of texts was sometimes more elaborate than it is now, which can lead to misleading citations. One that often confuses me is Euler’s “Institutionum calculi integralis.” The first Volume consists of an Introduction with 39 Problems, Solutions, Theorems, Demonstrations, Corollaries, Applications, or Examples [Euler 1768]. (For simplicity lets call these PSTDCAEs.) The Introduction is followed by three Sections (with 356 PSTDCAEs spread over 9 chapters, 270 PSTDCAEs spread over 7 chapters, and 37 PSTDCAEs spread over 0 chapters, respectively). After all that, Euler published two additional Volumes, all in the same work.
  • References sometimes don’t refer to the original article, but to a republication in the collected works of the mathematician. For example, the above letters to and from Bernoulli to Euler do appear in three different volumes of Bibliotheca Mathematica. However, the Euler Archive notes that they can also be found in the collected works of Euler (called the Opera Omnia) in Series 1, Volume 23, pp. 450–455.[11]

Because of all of this, things get mixed up. In an attempt to clear up confusion for my PSP, I researched the journal in question: Bibliotheca Mathematica. Joe Dauben wrote that Gustav Eneström (1852–1923) started it as an addendum to Gösta Mittag-Leffler’s (1846–1927) Acta Mathematica in order to catalog mathematical literature. Today, this is considered the first series of the journal. In 1887 Eneström split it from the Acta and focused it on math history, which began its second series of 13 volumes. The third series consisted of 14 volumes between 1900 and 1914 [Dauben 1999]. Hence, the volumes in question can’t possibly be 43, 53, and 63. So, what should they be?

I went back to the first page of the first article and there Eneström cited earlier work in Biblio. Math. but included no volume numbers. However, on the first pages of the second and third articles, the references to previous work now included volume numbers—just in an odd format. See Figure 4.

References for Euler's second article.

References for Euler's third article.
Figure 4. Citations from the first and third of Eneström's articles. Screenshots provided by author.

Putting this all together, I learned I wasn't referring to volumes \(43\), \(53\), and \(63\), but rather \(4_3\), \(5_3\) and \(6_3\). Somewhere along the line, the subscripts got lost and everything became hard to follow. In today's notation, the citations probably should have read “Series 3, Volume 6” instead of “63”.

[10] Pay special attention to the boxed volume numbers .

[11] Actually, as I type this, it seems unlikely that this citation could be correct, given that it is only 5 pages long. Hmmmm. . . .


Adam E. Parker (Wittenberg University), "Pitfalls and Potential Solutions to Your Primary Source Problems: X doesn’t mark the spot.," Convergence (December 2023)