Leonhard Euler: Mathematical Genius in the Enlightenment

by Ronald S. Calinger

This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory.

The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous "Introductio in analysin infinitorum," devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling "Letters to a German Princess"--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.

Some images inside the book are unavailable due to digital copyright restrictions.

Genres: Biography, Mathematics, History, Science, Nonfiction, History Of Science, Memoir

696 pages, Kindle Edition

First published September 8, 2015

About the author

Ronald Callinger is Professor of History at the Catholic University of America. He earned his doctorate from the University of Chicago in 1971.

Reviews

[Oren · Rating 4 out of 5]

Interesting read but definitely not a page-turner. Euler was a genius on par with Leibniz, Newton, Descartes, etc. Few if anyone equaled his mathematical prowess during his lifetime and maybe for another 200 years, except for a few random geniuses here and there like the Bernoullis and D'alembert, etc. To give an idea of how prolific and advanced he was, he would be remembered today for Euler's number and work on logarithms alone. For five of his breakthroughs, logarithms and calculus of variations and a few others cumulatively, he'd be remembered as a giant of math. But he probably had 120 or so such discoveries. And he was totally blind for the last 20 years of his life.

Euler was alive when the war over who invented calculus was raging across Europe, Newton vs Leibniz. Back then scientists were natural philosophers by name, and they were carving out paths in mostly physics, math, biology, anatomy, etc. They were inventing entire fields left and right. Hydraulics, electrical engineering... countless fields and niches. Their skills were highly valued by royalty bc of the constant need to improve ballistics, engineering huge building projects or those using new technology, and harness nature's power for industry. Also, all the most powerful emperors and kings were personally very involved in building up universities and natural philosophy societies, and of course, were important patrons. So there is an interesting historical element to the book. Euler became very involved in administration in Berlin and a typical scene in the book would be Euler needing money or some sort of resource or even just an answer from the emperor, who at the moment was in some field tent fighting a war.

The best parts of the book are those discussing his work. Euler developed many notations we still use today, pi, i for imaginary numbers and "Euler's Number" e, which = 2.7818 but is irrational. Euler was in constant disputes with various philosophers, but at any given time maybe 1 to 3 people on the planet were able to fully understand his work. He was breaking new ground every time he moved his pencil. Solving Fermat theorems and ancient unsolved problems left and right. He took many of Newton and Leibniz's discoveries and developed new math to carry them further. For example, many mathematicians and Euler spent considerable time solving the vibrating string problem. This is remarkable considering how prolific and advanced wave mechanics are today. He was the master of differential equations, derivatives, integrals and various other types of calculus. He married physics to differential equations. And every now and then a young genius like the polish LaGrange and French D'alembert would pop up and the two would collaborate to push math theory, etc even further. 150 years before Einstein, Leibniz suggested that time and space were relative. And during Euler's time there was a heated debate over Monads, which was their idea of what we'd probably call an atom today. What was it, etc? They were developing early physics, both theory and thru experimentation. All these fields were so new that very respected individuals had very serious differences of opinion of fundamental ideas that would be the basis of various fields. They wanted to develop standards for their fields, find constant values and fundamental laws, etc but also for science itself. The scientific method is a good example.

[Peter Flom · Rating 3 out of 5]

This is the definitive biography of Leonhard Euler (1707-1783) who is generally regarded as one of the four greatest mathematicians of all time (the others being Archimedes, Newton and Gauss). It's prodigiously researched and reasonably well-written (although the author has a proclivity for some odd word orders). Unfortunately, it has some problems:

First, Euler's life doesn't seem to have been that interesting
Second: There is less on the enlightenment than the subtitle led me to believe.
Third (and I don't know how this one could be solved) Euler's volume of work was so large, and so much of it so important and deep, that it is impossible for one book to cover even a small fraction of it in any depth.

[William Easton · Rating 4 out of 5]

For what it is, it is excellent. It's extremely thorough book, documenting each year of his life, the topics he pursued, the many auxiliary characters, and the larger historical and scientific background. However, because of that thoroughness, it's not exactly a light, fun read. It can be quite dense and sometimes goes on what feel like irrelevant tangents. Overall though, it is the authoritative text on the man. It perhaps needs to be this dense in order to do justice to the sheer quantity of Euler's incredible achievements.

[Morgan Lang]

Excellent detailed biography of Euler: Calinger walks steadily through Euler's life and gives a thorough picture of what it looked like to be a genius in the Enlightenment. Calinger is a diligent historian and I definitely recommend this for anyone interested in Euler!

[Jd · Rating 5 out of 5]

One of the best scientist biographies and definitely the best biography of Euler

[Bob Gustafson · Rating 2 out of 5]

This book is thorough, authoritative and dry as dust. Read a different biography.

[Stefan Gluszek · Rating 4 out of 5]

It's very thorough work, lots of fact, wouldn't call it a pleasant read.

[Misrab · Rating 2 out of 5]

Euler's life and work were fascinating, but the writing here is jumbled. It seems the author was overwhelmed with primary sources and details. The outcome is a lack of coherence and depth.

[University of Chicago Magazine]

Ronald S. Calinger, PhD’71
Author

From Dialogo Spring/Summer 2016: "Leonhard Euler chronicles the life of one of the greatest mathematicians and theoretical physicists of all time. In this first full-scale biography of Euler (1707–83), Calinger highlights his life and achievements in mathematics and in areas including shipbuilding, cartography, and music theory. Calinger is professor emeritus of history at the Catholic University of America in Washington, DC, and the founding chancellor of the Euler Society."

[Mills College Library]

Biog E88c 2016