In the pantheon of great mathematicians, Leonhard Euler (1707-1783) is one of the supreme deities. It is not possible even to outline his accomplishments within the word limit of this review. Euler was the founding father of the calculus of variations and of graph theory. He did pioneering work in calculus, differential equations, complex number theory, number theory, and differential geometry, and also in celestial mechanics, continuum mechanics, and optics. He invented the constant e. There is Euler’s formula ei θ = cos(θ) + i sin(θ) and the other Euler’s formula V+F-E = 2. There is Euler’s totient function φ(n), Euler’s constant γ, Eulerian angles, Eulerian paths, and the Eulerian formulation of continuum mechanics. There are the Euler numbers, not to be confused with the Eulerian numbers. Euler was one of the leading figures in the victory of Newton’s physics over Descartes’ physics, and in establishing that all of the behaviors of the solar system then known could be explained in terms of Newton’s law of gravity. And on and on. His collected works fill 80 volumes; their translation into English is an ongoing project.
Euler was also central in establishing the scientific institutions of his time. In particular, he was one of the leading figures in the creation of the Berlin (Royal Prussian) Academy of Sciences under Frederick II.
However, in the popular mythology of mathematics that celebrates the pantheon, Euler cuts a rather gray figure. Few interesting stories are told about Euler, and few interesting sayings are quoted. There are no anecdotes that show how, though an amazing mathematician, he was also a regular guy, and very few that show how he was an unusual guy. One collection of mathematical quotations  contains one apocryphal story of how Euler flummoxed Diderot with a bogus algebraic proof of the existence of God, one rather pedestrian quote about maxima and minima, and a second quote about the distribution of primes. The single striking personal anecdote in Calinger’s 699-page book is about how boring he could be:
Her [the queen mother of Prussia] efforts to draw Euler into the spirited conversation failed. He responded only to queries in monosyllables. The exasperated queen chided him asking, “Why do you not wish to speak to me?” Euler
who remembered the brutality of the Bironovschina period in Russia responded, “Madame, it is because I have just come from a country where a man’s words can get him hanged.”
As the subtitle indicates, Ronald Calinger’s new biography of Euler places him in the context of the Enlightenment. He recounts in detail Euler’s close interactions with fellow mathematicians and scientists, such as the Bernoullis, Maupertuis, and d’Alembert, and his more superficial interactions with Enlightenment figures such as Diderot and Voltaire. The biography is very thorough and deeply researched; it includes a 50-page bibliography and a glossary/index of about 500 names, practically a “who’s who” of the 18th-century Enlightenment, particularly its scientific side.
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