Historical and Biographical Resources

The Opera Omnia
Euler's work
Euler's books and publications
Euler's correspondence
Biographies of Euler
Background on 18th century science

Euler Opera Omnia

Published by Birkhäuser and the Euler Commission of Switzerland, the Opera Omnia is the definitive print source for Euler's works. Publication began in 1911, growing to scores of volumes comprising nearly all of Euler's works.

Put simply, the Opera Omnia is the authoritative source of Euler's works. Not only do his writings appear in neatly typeset, edited form, but each volume also includes commentaries—some of them very lengthy and very scholarly—on those works. The Opera Omnia can be found in many large research libraries, and is well worth the time spent with it.

Most recently, Springer has been publishing volumes of Euler's correspondence, and has several more volumes in preparation.

Euler's work

  • Eneström, Gustaf.   "Die Schriften Eulers chronologische nach den Jahren geordnet, in denen sie verfasst worden sind," Jahresbericht der Deutschen Mathematiker-Vereinigung (1910-1913).

    Eneström's index remains the definitive reference guide for Euler's work. Greta Perl has translated Part 1 of the index into English. Both the original German, and English translations, are available on the Euler Archive. See our Eneström index page for details.

  • Bradley, Robert, and Sandifer, Edward. (Editors.)  Leonhard Euler: Life, Work and Legacy. (Studies in the History and Philosophy of Mathematics, Volume 5)  Elsevier Science, 2007.
    Description from Amazon.com:

    The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work.

    Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Eulers innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.

  • Sandifer, C. Edward.  The Early Math of Leonhard Euler. (Volume 1: The MAA Tercentary Euler Celebration.)  Mathematical Association of America, 2007.
    Description from MAA Online:

    The Early Mathematics of Leonhard Euler describes Euler's early mathematical works: the 50 mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These works contain some of Euler's greatest mathematics: the Konigsburg bridge problem, his solution to the Basel problem, his first proof of the Euler-Fermat theorem. It also presents important results that we seldom realize are due to Euler: that mixed partial derivatives are equal, our f(x) notation, and the integrating factor in differential equations. The book provides some of the way mathematics is actually done. For example, Euler found partial results towards the Euler-Fermat theorem well before he discovered a proof of the Fermat theorem itself, and the Euler-Fermat version came 30 years later, beyond the scope of this book.

    The book shows how results in diverse fields are related, how number theory relates to series, which, in turn relate to elliptic integrals and then to differential equations, There are dozens of such strands in this beautiful web of mathematics. At the same time, we see Euler grow in power and sophistication, from his first work on differential equations as an 18-year old student, a paper with a serious flaw in it, to the most celebrated mathematician and scientist of his times, when, at the age of 34, he was lured away like a superstar athlete might be traded today. The book is a portrait of the world's most exciting mathematics between 1725 and 1741, rich in technical detail. Woven with connections within Euler's work and with the work of other mathematicians in other times and places, laced with historical context.

  • Dunham, William. (Editor.)  The Genius of Euler: Reflections on his Life and work. (Volume 2: The MAA Tercentary Euler Celebration.)  Mathematical Association of America, 2007.
    Description from MAA Online:

    This book celebrates the 300th birthday of Leonhard Euler (1707-1783), one of the brightest stars in the mathematical firmament. The book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity—one who has been rightly called "the master of us all." The collected articles, aimed at a mathematically literate audience, address aspects of Euler's life and work, from the biographical to the historical to the mathematical. The oldest of these was written in 1872, and the most recent dates to 2006.

    Some of the papers focus on Euler and his world, others describe a specific Eulerian achievement, and still others survey a branch of mathematics to which Euler contributed significantly. Along the way, the reader will encounter the Königsberg bridges, the 36-officers, Euler's constant, and the zeta function. There are papers on Euler's number theory, his calculus of variations, and his polyhedral formula. Of special note are the number and quality of authors represented here. Among the 34 contributors are some of the most illustrious mathematicians and mathematics historians of the past century, e.g., Florian Cajori, Carl Boyer, George Pólya, Andre Weil, and Paul Erdös. And there are a few poems and a mnemonic just for fun.

  • Dunham, William.  Euler: The Master of Us All.  Mathematical Association of America, 1999.
    Reknowned mathematics author William Dunham's book is the most complete examination in English of Euler's mathematical work. Written for the mathematically literate (The reader should be familiar with calculus), Dunham examines selected mathematics of Euler, and places his work in a historical context. Over eight chapters, Dunham looks separately at some of Euler's contributions to Number Theory, Logarithms, Infinite Series, Analytic Number Theory, Complex Variables, Algebra, Geometry, and Combinatorics. Dunham's book also contains a brief biography of Euler.
  • Youskevich.  The Dictionary of Scientific Biography, "Euler."
    Perhaps the longest full discussion in English of Euler's science and mathematics, the Euler entry in The Dictionary of Scientific Biography runs 17 pages, and is an excellent resource.
  • Truesdell, Clifford.  An Idiot's Fugitive Essays on Science Methods – Methods, Criticism, Training, Circumstances.  New York: Springer-Verlag, 1984.
    Description from a review by Ed Sandifer:

    In an era when most Euler scholarship was done in the Soviet Union and in the DDR, Truesdell kept the candle lit in the West, though his work and his personality were both controversial... This volume contains 42 "Fugitive essays", about a third of which directly concern Euler, and more than half of the rest involving Euler indirectly.... the Fugitive Essays ought to be required reading for anyone trying to understand Euler. They are entertaining, opinionated, well informed and at times controversial.
  • Havil, Julian.  Gamma: Exploring Euler's Constant.  Princeton Universiry Press, 2003.
    While not explicitly about Euler's mathematics, his work does come up often in this interesting, though technical, book on the constant gamma (γ).
  • Hakfoort, Casper. Optics in the Age of Euler.  Cambridge University Press, 1995
    An English translation of Optica in de eeuw can Euler (published in Dutch, 1986), Hakfoort's book is a careful look at the role played by Euler's Nova theoria lucis et colorum (see E88) in the development of 18th Century Optics. Those interested in closely examining Euler's impact on 18th Century Science should consider this required reading.
  • Fellmann, Emil (ed).  Leonhard Euler 1707-1783 : beitrage zu leben und werk.  Basel: Birkhäuser-Verlag, 1983.
    Published for the 200th anniversary of Euler's death, this multi-lingual volume (English, French, and German) contains thirty essays on Euler's life and work.
  • Festakt und Wissenschaftliche Konferenz aus Anlass des 200. Todestages von Leonhard Euler.  Berlin: Akademie-Verlag, 1983.
    Proceedings of a conference on the 200th anniversary of Euler's death, this festakt contains 16 essays on Euler's life and work. One of these is written in English; the rest are in German.
  • Schroeder, Kurt.  Sammelband der zu Ehren des 250. Geburtstages Leonhard Eulers.  Berlin (DDR): Akademie-Verlag, 1959.
    Another collection of essays (in German), this one published for the 250th anniversary of Euler's birth.

Euler's Books

  • Introduction to Analysis of the Infinite : Book I, and
  • Introduction to Analysis of the Infinite : Book II , John D. Blanton (Translator) (Springer, 1989)
    John Blanton's impressive translation of Euler's Introductio in analysin infinitorum (E101).
  • Foundations of Differential Calculus, John D. Blanton (Translator)
    John Blanton's translation of the first nine (of 27) chapters of Euler's Institutiones calculi differentialis (E212).
  • Letters of Euler on different subjects in natural philosophy
    Also known as "Letters to a German Princess," several volumes of this work have been published over the last half century. The most recent edition is a 1997 reprint by Thoemmes Continuum, featuring an English translation by Henry Hunter, and a new introduction by Andrew Pyle. This edition can be puchased at the Thoemmes Website.

Euler's Correspondence

  • The Opera Omnia
    Once again, the Euler scholar should turn first to the Opera Omnia. Series IV A is a comprehensive list of Euler's letters, describing every letter known and kept at the University of Basel. Volumes in this series are organized as follows:
    • Volume 2 (pub. 1998), correspondence with Johann and Nicolaus Bernoulli
    • Volume 3 (pub. 2017), correspondence with Daniel Bernoulli
    • Volume 4 (pub. 2015), correspondence with Christian Goldbach
    • Volume 5 (pub. 1980), correspondence with Clairaut, d'Alembert, and Lagrange
    • Volume 6 (pub. 1986), correspondence with Maupertuis and Frederick II
    • Volume 7 (pub. 2017), correspondence with Bertrand, Bonnet, Castillon, Cramer, and others
  • Die Berliner und die Petersburger Akademie der Wissenschaften im Briefwechsel Leonhard Eulers.
    This is a three-volume collection of Euler's correspondence sent between the Berlin and St. Petersburg Academies. Akademie-Verlag in Berlin, 1959, 1961, and 1976.
    • Volume 1 contains correspondence sent when Euler lived in Berlin, between Euler and Gerhard Friedrich Muller, the secretary of the Saint Petersburg Academy, from 1734-1767.
    • Volume 2 contains the correspondence of Euler with Nartov, Razumovskij, Schumacher, Teplov, and the Petersburg Academy, from 1730-1763.
    • Volume 3 contains correspondence between Euler and about 30 others, spanning his professional life.
  • Fuss, P H.  Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle.  New York, 1968.
    This work by Fuss contains extensive correspondence between Euler, Goldbach, and Bernoulli, among others.
  • Leonhard Euler und Christian Goldbach: briefwechsel 1729-1764.  Berlin: Akademie-Verlag, 1965.
    Published for the 250th anniversary of Euler's birth (two years early), this work contains the complete correspondence between Euler and Goldbach.
  • The Euler-Mayer Correspondence (1751-1755): A New Perspective on eighteenth-century advances in the lunar theory.  American Elsevier, 1971.
    In this book, Eric Forbes presents the 31 known letters in the correspondence between Euler and Tobias Mayer, all translated into English, with commentary and notes.
  • Tweedle, Ian.  James Stirling: This about Series and Such Things.  Scottish Academic Press, 1988.
    Some of Euler's correspondence with Stirling is published, in English translation, in this book on Stirling.
  • Engelsman, Steven B.  Families of Curves and the Origins of Partial Differentiation.  Amsterdam: North Holland Mathematical Studies #93, 1984.
    Engelsman's book contains a manuscript of Euler's published in English and Latin.

Biographies of Euler

  • Calinger, Ronald S.   Leonhard Euler: Mathematical Genius in the Enlightenment.  Princeton University Press, 2016.
    This is the first biography of Euler available in the English language. Calinger's work is very comprehensive, providing a full narrative of Euler's life and career, with ample citation and a generous bibliography.
  • Fellmann, Emil A.  Leonhard Euler.  Hamburg, 1995.
    A chronological recounting of Euler's life, Fellmann's work is a very accessible biography of Euler, and avoids technical details by being "entirely formula free". This book contains much interesting information, though it is rather short (156 pages). This biography was originally written in German, but an English translation by Erika and Walter Gautschi was published by Birkhäuser in 2007.
  • Thiele, Rüdiger.  Leonhard Euler.  Leipzig, 1982.
    The first modern biography of Euler. Thiele's work is a concise (110 pages) but interesting read. Thiele's work is a much more balanced biography than those from the early 20th century (cf. du Pasquier, below). This biography is written in German, and has not been translated into English.
  • Fueter, Rudolf.  Leonhard Euler.  Basel, 1948
    This is a very short (24 pages) and little known (we've never seen it referenced) biography of Euler, written as part of Birkhäuser-Verlag's Kurze Mathematiker-Biographien series.
  • du Pasquier, G.  Euler et Ses Amis.  Paris, 1927
    A complete, but slightly eulogistic, biography of Euler published in French, this book also contains some good information about Euler's contemporaries. This book has long been out of print, but it is being reprinted, along with a translation (Euler and his Friends) by John Glaus of The Euler Society in 2008.
  • Rudio, Ferdinand.  Leonhard Euler.  Zürich: Zürcher & Furrer, 1909.
    Paperback, bound with staples, approximately 6" x 9". A short 15-page biography of Euler in German. This booklet is a reprint of the text of an address that Rudio gave in 1883 at a celebration of the 100th anniversary of Euler's death. Rudio was a founding member of the editorial committee of the Opera Omnia and edited several of the early volumes, including some on number theory.

18th Century Science

The Eighteenth Century is the height of the Enlightenment, and is an important and fascinating period of time in the History of Science. It's a slightly confusing time, however, with academies, societies, and monarchs controlling almost all science and scientists of the day. If you're looking for a good starting place to learn more about this time, and to put Euler's work in a good historical context, The Euler Archive suggests the following books:

  • Bertrand, Joseph.  L'Académie des Sciences et les Académiciens de 1666 à 1793. (French)  Amsterdam: B. M. Israël, 1969.

  • Boss, Valentin.  Newton & Russia: The Early Influence, 1698-1796.  Cambridge, MA: Harvard University Press, 1972.

  • Hahn, Roger.  The Anatomy of a Scientific Institution: The Paris Academy of Sciences, 1666-1803.  Los Angeles: University of California Press, 1971.

  • Hartley, Harold, Sir.  The Royal Society, its Origins and Founders.  London: The Royal Society, 1960.

  • Lyons, H. G., Sir.  The Royal Society, 1660-1940; a History of its Administration Under its Charters.  Cambridge, UK: The University Press, 1944.

  • McClellan, James E.  Science Reorganized: Scientific Societies in the Eighteenth Century.  New York: Columbia University Press, 1985.
    A fantastic resource! Includes a detailed accounting of the development of Academy-based science in the 18th century, as well as a list of all major private, public, and semi-public academic institutions in Europe for the same time period.
  • Porter, Roy, ed.  The Cambridge History of Science, vol. 4. "Eighteenth-Century Science."  Cambridge, UK: Cambridge University Press, 2003.

  • Purver, Margery.  The Royal Society, Concept and Creation.  Cambridge, MA: M.I.T. Press, 1967.

  • Terrall, Mary.  The Man Who Flattened the Earth: Maupertuis and the Sciences in the Enlightenment.  Chicago: University of Chicago Press, 2002.
    A readable biography of Pierre-Louis Moreau de Maupertuis; also includes a good deal of information regarding the development of the Berlin Academy, and some information on Euler's experiences in Berlin.
  • Vucinich, Alexander.  Science in Russian Culture.  Stanford, CA: Stanford University Press, 1963.
    A comprehensive resource on the history of the St. Petersburg Academy as well as on general cultural, social and political developments in the Russian Empire, up to 1917.