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Euler Reconsidered: Tercentenary Essays

Roger Baker, editor
Kendrick Press
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Ackerberg-Hastings
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This collection appeared among the spate of publications honoring the 2007 tercentenary of Euler’s birth. To assist with putting it into context, I have added the volume to the helpful list compiled by David P. Roberts, along with other secondary sources focused on Euler’s biography and numerous contributions that have been evaluated in MAA Reviews during the intervening decade. (See below; note that the items numbered [1]–[5] comprised the MAA’s own Tercentenary Euler Celebration. With respect to the massive body of primary sources left by Euler, only the Goldbach correspondence has received a review here, although of course the MAA website also houses the Euler Archive for perusing his mathematical materials directly.) Euler Reconsidered continues to be available on a print-by-demand basis from its small publisher.

What does Euler Reconsidered offer that is not in the other books? Robert Ineichen’s account of Euler’s contributions to actuarial mathematics tackles a topic not covered as often as, for instance, Euler’s textbooks. Its style is more descriptive than technical, so it is accessible as student reading. Patricia Radelet-de Grave brings together Letters to a German Princess with several of Euler’s papers to conclude that his work on magnetism represents a preliminary stage in the long process of mathematizing that subject. She calls for historians of science to pay more attention to this topic, and indeed it appears to remain under-researched. Masahito Takase concentrates on Euler’s many attempts to prove all or part of Fermat’s Last Theorem.

Most of the papers in Euler Reconsidered are internalist in approach, meaning that the focus is on the details of particular mathematical ideas rather than on connecting Euler’s works to broader contexts. The articles thus may be useful in mathematics courses in which these topics from analysis, probability, and mechanics arise, to help students trace the development and proof of the concepts.

Reflecting on the role of the book in 2018, I would say that it fits within the larger “rejuvenation” of Euler scholarship represented by the other volumes below. The authors’ interpretations cohere with the consensus of 21st-century historians rather than “reconsider” it. In fact, contributors such as Rüdiger Thiele have also published in several of the other Euler-themed collections.

Unfortunately, editor Roger Baker does not explain how this set of articles came together. I inferred that he gathered pieces that were unpublished or written in languages other than English from European and Asian historians of mathematics — this book is not, for instance, proceedings from a conference. I did not find any essays published elsewhere, although a few authors, such as Marco Panza, have also uploaded theirs to open-access repositories.

The editorial sloppiness does occasionally reappear in the volume. Two examples: “Euler’s Mechanics, 1736–1765” is listed in the table of contents but is not printed in the book, and the first footnote for Panza’s article is omitted. The page layout resulted in large amounts of white space and several blank pages, while the papers’ citation styles are similar but not uniform. Baker assisted with the translations, but some usages that are non-standard in English remain.

Secondary Sources on Euler in MAA Reviews


Euler: The Master of Us All




Euler Through Time: A New Look at Old Themes




Leonhard Euler




Leonhard Euler: A Man to Be Reckoned With

Heyne, Heyne, Pini



Leonhard Euler: Life, Work and Legacy

Bradley, Sandifer, eds.



The Early Mathematics of Leonhard Euler




The Genius of Leonhard Euler: Reflections on His Life and Work

Dunham, ed.



How Euler Did It




Euler and Modern Science

Bogolyubov, Mikhailov, Yushkevich, eds.



Euler at 300: An Appreciation

Bradley, D’Antonio, Sandifer, eds.



Euler Reconsidered

Baker, ed.



Leonhard Euler and His Friends

du Pasquier (1927), trans. Glaus



The Legacy of Leonhard Euler: A Tricentennial Tribute




How Euler Did Even More




Leonhard Euler: Mathematical Genius in the Enlightenment



Amy Ackerberg-Hastings is an independent scholar who researches the histories of American and European mathematics education, mathematical instruments, and women in science and mathematics, among other topics.

  1. Roger Baker, Introduction
  2. Michael Eckert, Mathematics for the King: Was Euler an Impractical Theorist?
  3. Giovanni Ferraro, Euler’s Treatises on Infinitesimal Analysis: Introductio in analysin infinitorum, Institutiones calculi differentialis, Institutionum calculi integralis
  4. Robert Ineichen, The Contributions of Leonhard Euler to Actuarial Mathematics
  5. Marco Panza, Introductio in analysin infinitorum and the Program of Algebraic Analysis: Quantities, Functions and Numerical Partitions
  6. Patricia Radelet-de Grave, Euler and Magnetism
  7. Francisco A. González Redondo, Constants, Units, Measures, and Dimensions in Leonhard
  8. Angel E. Romero, Physics and Analysis. Euler and the Search for Fundamental Principles of Mechanics
  9. Oscar Sheynin, Euler’s Work in Probability and Statistics
  10. Masahito Takase, Euler’s Theory of Numbers
  11. Rüdiger Thiele, The Rise of the Function Concept in Analysis
  12. Vadim Ivanovich Yakovlev, Leonhard Euler and the Foundations of Mechanics