### Primary Contributors:
Andreas Kleinert and Martin Mattmüller (Bernoulli-Euler-Zentrum, Basel)

Andreas Kleinert and Martin Mattmüller (Bernoulli-Euler-Zentrum, Basel)

### Leonhard Euler (1701–1783)

Leonhard Euler was born in Basel on 15 April 1707. His father, Paul Euler, was a Reformed minister, the first university graduate from a family of craftsmen; his mother, Margarethe Brucker, counted among her ancestors several scholars from the city’s humanist tradition. Their eldest son Leonhard grew up at the vicarage of Riehen, attended the local Gymnasium, and then, at the age of thirteen, the University of Basel.

With the help of the famous mathematician Johann (I) Bernoulli, he progressed so rapidly in mathematics and physics that in 1727 he was appointed to the newly founded Imperial Russian Academy of Sciences at St Petersburg, obtaining the chair of mathematics just six years later. In 1741 he moved to the Berlin Academy, which had been revived by Frederick II of Prussia, and in 1766 he was recalled to St Petersburg. Despite almost total loss of his eyesight, he continued to work, surrounded by his numerous family members and a team of assistants, until his death on 18 September 1783.

Euler was a tremendously productive scientist: the index of his works compiled by Gustaf Eneström in 1911 comprises more than 650 research papers, published mainly in the journals of the most prestigious scientific academies throughout Europe. Although he never had regular teaching obligations, Euler authored influential textbooks on a great variety of subjects including differential and integral calculus, mechanics, ballistics and acoustics, astronomy, the theory of music, and ship-building, as well as the Letters to a German Princess, a three-volume compendium of his century’s views on all of natural science.

There is no doubt that Leonhard Euler numbers among the great scientists of all time. His work exhibits a unique combination of broad interests and brilliant insights, it displays original ways of tackling challenges and great persistence in the pursuit of his ideas, and it shows a profound yet sympathetic appreciation of his predecessors’ and colleagues’ achievements. Euler is chiefly remembered as the leading mathematician of his time, but his works also comprise ground-breaking contributions to physics, astronomy, and engineering. Moreover, his vast correspondence yields fascinating insights into the development of his ideas and the entire scientific community of the eighteenth century.

#### Partners and Additional Contributors

After several failed attempts to set up an edition of Euler’s collected works, in 1907 Ferdinand Rudio, a professor of mathematics at the Zürich Polytechnic, spurred the *Schweizerische Naturforschende Gesellschaft* (now the Swiss Academy of Science [SCNAT]) into appointing a committee (*Euler-Kommission*) charged with planning, funding, and realizing such a project: *Leonhardi Euleri Opera Omnia* (LEOO) was under way. In 1911, the first volume was printed; at present, of the seventy-two volumes in three series devoted to Euler’s published works (I. Mathematics, II. Mechanics, Astronomy, III. Physics, Miscellanea), all but two are available.

In the *Opera Omnia* project of 1910, it had already been envisaged to include Euler’s scientific correspondence; however, this was postponed indefinitely, and the first twentieth-century publications of Euler letters all occurred independently, mainly due to the activities of the Soviet Academy of Science and its cooperation with the Academy of the German Democratic Republic (see below). Only in 1967 did the Swiss Euler Committee finally decide to start an additional series of LEOO, which was to contain Euler’s correspondence (IVA) and his manuscript heritage (IVB). Since most of the original papers were preserved in the Leningrad Archive of the Soviet Academy of Science and there was a considerable number of Euler experts living in Russia, the new Series IV was set up as a joint project of the Swiss and Soviet Academies.

The first volume of series IVA was published in 1975: it is an inventory of all of Euler’s correspondence known at that time. For each letter, it gives a short summary and some (unfortunately, not always reliable) metadata: extant versions, date, language, location of manuscripts, publications. Since 1980, six correspondence volumes have appeared, and two more are under way (for details, see below). With the publication of vol. IVA/9 in 2020, the centenary project of the print publication of LEOO will come to an end, comprising by then almost all of Euler’s printed works, but only about 40% of the 3,200 extant letters — though presumably the scientifically most interesting ones — and almost none of his other unpublished manuscripts.

There are important and interesting parts of Euler’s heritage that will not be edited within the *Opera Omnia*. However, digital online publishing now provides new possibilities of reaching the principal goal set by Ferdinand Rudio and his successors of making all of Euler’s writings available to the scientific community. Currently the Euler Committee is working on a project to present all of the printed and manuscript material in a web-based virtual research environment, Bernoulli-Euler Online [BEOL]: so it is hoped that the task which the mathematical community undertook at the beginning of the twentieth century will be completed for the benefit of twenty-first century-mathematicians and historians of science as a monument to the lasting glory of Leonhard Euler.

The publication of the remaining volumes of LEOO and the implementation of BEOL are coordinated by an international team of editors centred at the Bernoulli-Euler-Zentrum, which has been established at the Basel University Library in 2012.

#### Key Bibliographic Source(s)

*Leonhardi Euleri Opera Omnia* (Basel: Birkhäuser; Springer, 1911–).

Series Quarta A: ‘Commercium epistolicum’ (General Editor: Andreas Kleinert).

LEOO IVA/1: ‘Descriptio Commercii epistolici / Beschreibung, Zusammenfassungen der Briefe und Verzeichnisse’, ed. Adolf P. Juškevič, Vladimir I. Smirnov and Walter Habicht (Basel, 1975).

LEOO IVA/2: ‘Commercium cum Johanne (I) Bernoulli et Nicolao (I) Bernoulli / Briefwechsel mit Johann (I) Bernoulli und Niklaus (I) Bernoulli’, ed. Emil A. Fellmann and Gleb K. Mikhajlov (1998).

LEOO IVA/3: ‘Commercium cum Daniele, Johanne II, Johanne III Bernoulli. Commercium Johannis Alberti Euleri cum Daniele Bernoulli. Commercium Danielis Bernoulli cum officialibus Academiae Scientiarum Petropolitanae (epistolae selectae) et cum Nicolao Fuss / Briefwechsel mit Daniel, Johann II und Johann III Bernoulli. Briefwechsel Johann Albrecht Eulers mit Daniel Bernoulli. Briefwechsel Daniel Bernoullis mit Amtsträgern der Petersburger Akademie der Wissenschaften (Auswahl) und mit Niklaus Fuss’ (2 parts), ed. Emil A. Fellmann † and Gleb K. Mikhajlov (2016).

LEOO IVA/4: ‘Commercium cum Christiano Goldbach / Correspondence with Christian Goldbach’ (2 parts), ed. Franz Lemmermeyer and Martin Mattmüller (2015) [available for download now at: http://edoc.unibas.ch/58842 and on the Bernoulli-Euler OnLine platform at: beol.dasch.swiss].

LEOO IVA/5: ‘Commercium cum A. C. Clairaut, J. d’Alembert et J. L. Lagrange / Correspondance avec A. C. Clairaut, J. d’Alembert et J. L. Lagrange’, ed. Adolf P. Juškevič and René Taton (1980).

LEOO IVA/6: ‘Commercium cum P.-L. M. de Maupertuis et Frédéric II / Correspondance avec P.-L. M. de Maupertuis et Frédéric II’, ed. Pierre Costabel, Eduard Winter †; Ašot T. Grigorijan and Adolf P. Juškevič (1986).

LEOO IVA/7: ‘Commercium cum L. Bertrand, Ch. Bonnet, M. M. Bousquet, J. de Castillon, G. Cramer, Ph. Cramer, G. Cuenz, A. von Haller, G.L. Lesage, J. M. von Loen, J. C. Wettstein / Correspondance avec L. Bertrand, Ch. Bonnet, M. M. Bousquet, J. de Castillon, G. Cramer, Ph. Cramer, G. Cuenz, A. von Haller, G. L. Lesage, J. M. von Loen et J. C. Wettstein [avec un supplément à la correspondance avec J. d’Alembert]’, ed. Siegfried Bodenmann, Vanja Hug, Mirjana Ilic, and Andreas Kleinert (2017).

LEOO IVA/8: ‘Commercium cum T. Abbt, B. Brauser, J. P. Eberhard, F. C. Jetze, W. J. G. Karsten, C. A. Körber, C. G. Kratzenstein, J. G. Krüger, J. J. Lange, J. A. Osiander, J. E. Philippi, J. H. Schulze, J. A. von Segner, J. W. von Segner / Briefwechsel mit T. Abbt, B. Brauser, J. P. Eberhard, F. C. Jetze, W. J. G. Karsten, C. A. Körber, C. G. Kratzenstein, J. G. Krüger, J. J. Lange, J. A. Osiander, J. E. Philippi, J. H. Schulze, J. A. von Segner und J. W. von Segner’, ed. Andreas Kleinert and Thomas Steiner (forthcoming).

LEOO IVA/9: ‘Commercium cum F. J. Buck, I. Kant, M. Knutzen, L.G. Kessler, J.C.Langenheim / Carteggio con F. J. Buck, I. Kant e M. Knutzen, L.G. Kessler, J.C.Langenheim’, ed. Antonio Moretto, et al. (forthcoming).

#### Contents

Leonhard Euler led a vast correspondence all over Europe; more than 3,200 letters exchanged with nearly 300 correspondents have been preserved, most of them from the period that Euler spent in Berlin (1741–1766). Among Euler’s most frequent correspondents may be found almost all prominent scientists of his time: Johann I, Nicolaus I and Daniel Bernoulli, Christian Wolff, Jacob Hermann, Poleni, Marinoni, J.-N. Delisle, Lalande, Clairaut, Bouguer, d’Alembert, the marquise du Châtelet, Maupertuis, Charles Bonnet, Gabriel Cramer, Tobias Mayer, Haller, Segner, Lambert, Lagrange and Aepinus. Patrons and officials connected to the Petersburg and Berlin Academies such as Frederick II of Prussia, Christian Goldbach, Gerhard Friedrich Müller, Johann Daniel Schumacher, and K. G. Razumovsky also figure prominently. A third group is formed by (mostly junior) academics such as Heinrich Kühn, M. V. Lomonosov, W. J. G. Karsten, A. G. Kästner, or Martin Knutzen, who apply to Euler for patronage, for expert opinions on their work, as well as for help with appointments.

The basic language of a majority of the letters by and to Euler (approximately 61%) is German; however, when mathematical and scientific topics are discussed, the professional terminology often fails, and the correspondents switch to Latin in mid-sentence (with the implied shift to another script style). Letters written entirely in Latin account for about 12% of the correspondence; those in French make up 26%; and a few letters are in English, Russian, or Italian.

### Provenance

Euler was aware of the potential value of his correspondence and carefully preserved almost all the letters that were addressed to him in a professional context; in some cases he also archived drafts or copies of his own letters. Along with his scientific notebooks and manuscripts, this vast heritage, which by itself accounts for almost 75% of the extant Euler correspondence, ended up at the St Petersburg Branch of the Archive of the Russian Academy of Sciences. Not all of Euler’s correspondents were equally careful: thus, for example, only a fraction of the letters he sent to Daniel Bernoulli, d’Alembert, or Clairaut and almost none to Bouguer, Segner, or Knutzen has survived. In consequence, fewer letters by Euler than to him are known (approximately 1,200 *versus *2,000). The largest collections of Euler letters outside Russia are to be found at the Berlin and Paris Academies’ archives, in Tartu (Estonia), in Basel, and in Geneva.

Only few of Euler’s letters were written with a view to publication or were printed in his lifetime. The edition of his large manuscript heritage started in earnest around the middle of the nineteeth century with several publications by Euler’s great-grandson Paul Heinrich Fuss; in particular, the two volumes of *Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle* published in 1843 comprised a substantial part of Euler’s correspondence with the Bernoullis and with Goldbach.

In the following decades, several of Euler’s smaller scientific correspondences were published rather haphazardly: in the journals of regional learned societies, in the collected works of notable correspondents such as Frederick II, Wolff and Lagrange, in two volumes of *Opera Postuma* published by Fuss and his brother, in institutional histories of the Petersburg Academy and other scientific corporations across Europe. A resurgence of interest was triggered early in the twentieth century by Euler’s imminent bicentenary: besides the launch of the *Opera Omnia* edition and the definitive inventory of his works established by Eneström, this also led to expanded editions of the Euler–Bernoulli correspondences and the first publications from the important exchanges with Lambert and Delisle.

Another, much more comprehensive wave of editions from Euler’s manuscript heritage was started in the 1930s by a group of historians of science based at the Soviet Academy of Science in Leningrad. Various inventories and collections were published in the following decades by S. Ya. Lur’e, I. I. Lyubimenko, S. I. Vavilov, I. G. Bashmakova, A. P. Yushkevich, V. I. Smirnov, T. N. Klado, Yu. Kh. Kopelevich, and several others, presenting to the public for the first time Euler’s correspondence with such eminent scientists as Lomonosov, Tobias Mayer, Charles Bonnet, and Giovanni Poleni (or at least parts of it). Their most ambitious project was planned in the context of Euler’s two-hundred-and-fiftieth anniversary as a joint venture of the Academies at Leningrad and Berlin (i.e. its Eastern part, then the capital of the German Democratic Republic). A bi-national team led by Yushkevich and Eduard Winter established a collection documenting the cultural ties that had linked their countries and their academies in the eighteenth century. Besides several smaller publications and a new edition of the Euler–Goldbach correspondence, they edited three volumes of Euler’s letters exchanged during his Berlin period with his former colleagues at Petersburg (here the replies are only summarized).

Taking into account the eight correspondence volumes of *Opera Omnia* IVA, some printed text is (or soon will be) available for a vast majority of the Euler correspondence (at present, our estimate is 84% of all the letters, including 87% of those written by Euler). The only larger collections for which this is not the case are about 275 notes exchanged among the staff of the Berlin Academy and fifty letters sent to or received from Basel civil servants on official business. However, some of the smaller correspondences that have not attracted the attention of researchers hitherto can be of considerable interest, by way of example for contributions to philosophical debates of the eighteenth century, for the history of attempts to square the circle, for institutional history, or for the transmission of document heritages.

#### Scope of Catalogue

For the identification of authors and recipients, places, dates, and manuscript repositories, the conventions used by EMLO have been applied. In particular, for letters originally dated according to the Julian calendar (as most but not all of those written in Russia during the 18th century are), the date has been converted to the Gregorian ‘new style’.

With respect to the vast collection of Euler letters preserved at the St Petersburg Branch of the Archive of the Russian Academy of Sciences, a ‘shorthand’ notation has been adopted: thus ‘136/2/5, 23–24’ stands for the shelfmark ‘f[ond] (collection) 136, op[is’] (part) 2, no. 5, pp. (or fols) 23–24′. A caution needs to be added here: most of the Petersburg shelfmarks, and some of those referring to other libraries and archives as well, have not been verified for several decades and may have been changed since the publication of earlier catalogues.

Each letter from the Euler correspondence has, as an additional identifier, a number of the form R xxxx, which refers to the *Repertorium* published in 1970 as vol. IVA/1 of LEOO; these numbers have been used for reference to individual letters in later volumes of *Opera Omnia* and in various other publications. Letters discovered or reclassified after the publication of vol. IVA/1 are indicated by an R number inserted into the ordering of the original list by adding a lower-case letter or a ‘fractional part’.

#### Further resources

**Bibliography**

On Leonhard Euler’s life and works

*Leonhard Euler 1707–1783. Beiträge zu Leben und Werk: Gedenkband des Kantons Basel Stadt*, ed. J. J. Burckhardt, *et al*. (Basel, 1983).

Fellmann, Emil A., *Leonhard Euler*, rororo monographien, 387 (Reinbek bei Hamburg, 1995; Japanese translation: Tokyo, 2002; English translation: Basel, 2007).

‘300 Jahre Leonhard Euler’, Uni Nova Wissenschaftsmagazin der Universität Basel, 105 (March, 2007), pp. 5–27.

Calinger, Ronald S., *Leonhard Euler: Mathematical Genius in the Enlightenment* (Princeton, 2015).

Inventories of Euler’s works, manuscripts and correspondence [see also LEOO IVA/1]

Eneström, Gustaf, ‘Verzeichnis der Schriften Leonhard Eulers’, in *Jahresbericht der Deutschen Mathematiker Vereinigung, Ergänzungsband, *IV (Leipzig 1910–13).

Eneström, Gustaf, ‘Bericht an die Eulerkommission der Schweizerischen naturforschenden Gesellschaft über die Eulerschen Manuskripte der Petersburger Akademie’, in *Jahresbericht der Deutschen Mathematiker Vereinigung*, 22 (1913), ‘Angelegenheiten der Deutschen Mathematiker Vereinigung’, pp. 191–205.

*Рукописные материалы Л. Ейлера в Архиве Академии наук СССР.* Том I. Научное описание [*Rukopisnye materialy L. Eǐlera v Arkhive Akademii nauk SSSR*. Tom I. Nauchnoe opisanie / *Manuscripta Euleriana Archivi Academiae Scientiarum URSS*. Tomus I. Descriptio scientifica] in *Труды Архива Академии наук СССР* [*Trudy Arkhiva Akademii nauk SSSR*], 17, ed. Yu. Kh. Kopelevich, *et al.* (Moskva, Leningrad, 1962).

*Л. Ейлер. Переписка. Аннотированный указатель* [*L. Eǐler. Perepiska. Annotirovannyǐ ukazatel’* / *Leonhard Eulers Briefwechsel. Beschreibung und Resümees*], ed. A. P. Yushkevich, *et al*. (Leningrad, 1967).

On the *Opera Omnia* edition of Euler’s works

Speiser, Andreas, ‘Einteilung der sämtlichen Werke Leonhard Eulers’, in Commentarii Mathematici Helvetici, 20 (1947), pp. 288–318.

Burckhardt, Johann Jakob, ‘Die Eulerkommission der Schweizerischen Naturforschenden Gesellschaft – ein Beitrag zur Editionsgeschichte’, in *Gedenkband des Kantons Basel Stadt *(1983), pp. 501–09.

Fellmann, Emil A., Im Hof, Hans Christoph, ‘Die Euler-Ausgabe. Ein Bericht zu ihrer Geschichte und ihrem aktuellen Stand’, in *Jahrbuch Überblicke Mathematik*, ed. S.D.Chatterji, *et al*. (Braunschweig, 1993), pp. 185–98.

Kleinert, Andreas, Mattmüller, Martin, ‘Leonhardi Euleri Opera Omnia: a centenary project’, in *Newsletter of the European Mathematical Society*, 65 (September 2007), pp. 25–31.

Kleinert, Andreas, ‘Leonhardi Euleri Opera Omnia: Editing the works and correspondence of Leonhard Euler’, in *Prace Komisji Historii Nauki PAU*, XIV (2015), pp. 13–35.

Selected editions from Euler’s correspondence [see also LEOO IVA/2–9]

*Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, précédée d’une notice sur les travaux de Léonard Euler, tant imprimés qu’inédits*, ed. P.-H. Fuss, 2 vols (Saint Petersburg, 1843).

*Die Berliner und die Petersburger Akademie der Wissenschaften im Briefwechsel Leonhard Eulers, Quellen und Studien zur Geschichte Osteuropas*, ed. A.P. Juškevič, *et al*. Teil 1:* Der Briefwechsel L. Eulers mit G.F. Müller, 1735–1767* (Berlin, 1959); Teil 2: *Der Briefwechsel L. Eulers mit Nartov, Razumovskij, Schumacher, Teplov und der Petersburger Akademie, 1730–1763*‘ (Berlin, 1961); Teil 3: *Wissenschaftliche und wissenschaftsorganisatorische Korrespondenzen, 1726–1776* (Berlin, 1976).

*Леонард Ейлер. Письма к ученым* [*Leonard Eǐler. Pis’ma k učenym* / *Leonhard Euler. Letters to scholars*], ed. T. N. Klado, *et al*. (Moskva, Leningrad, 1963).

‘Leonhard Euler und Christian Goldbach. Briefwechsel 1729*–*1764′ in *Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin, *Jg. 1965, No. 1 (Berlin, 1965).

‘Л. Ейлер и Ж.-Н. Делиль в их переписке, 1735–1765′ [‘L. Eǐler i Ž.-N. Delil’ v ikh perepiske, 1735–1765’ / ‘L. Euler et J. N. Delisle dans leur correspondance, 1735–1765′], ed. A. P. Yushkevich, *et al*., in *Русско-французские научные связи* [*Russko-francuzskie nauchnye svyazi* / *Relations scientifiques russo-françaises*] (Leningrad, 1968).

*The Euler–Mayer correspondence, 1751–1755: a new perspective on eighteenth-century advances in the lunar theory*, ed. E.G. Forbes (New York, 1971).