Letters to a German Princess: Euler’s blockbuster lives on

That’s Maths: The collection of letters shows Euler was not only a ‘master’ mathematician but also a master teacher

The great Swiss mathematician Leonhard Euler produced profound and abundant mathematical works. Publication of his Opera Omnia began in 1911 and, with close to 100 volumes in print, it is nearing completion. Although he published several successful mathematical textbooks, the book that attracted the widest readership was not a mathematical work but a collection of letters.

For several years, starting in 1760, Euler wrote a series of letters to Friederike Charlotte, princess of Brandenburg-Schwedt, a niece of Frederick the Great of Prussia. The collection of 234 letters was first published in French, the language of the nobility, as Lettres à une Princesse d'Allemagne.

This remarkably successful popularisation of science appeared in many editions, in several languages, and was widely read. Subtitled “On various subjects in physics and philosophy”, the first two of three volumes were published in 1768 by the Imperial Academy of Sciences in St Petersburg, with the support of the empress Catherine II.

The lettres are a veritable encyclopaedia of science. Euler began at an elementary level since the princess had little knowledge of science or mathematics. In the first letter Euler examined the concept of “size”. Starting with the familiar length of a foot, he explained how to define a mile and to calculate the diameter of the earth in miles. He then calculated the distance of the planets in units of earth diameters.


The next two letters were on velocity and on sound. Euler calculated the speed of sound to be 1,142 feet per second, very close to the actual value. He advanced gradually to more difficult topics, always maintaining great clarity of exposition. The lettres contained no mathematics other than simple calculations.

Optics and light

There were letters on music, on the air and the atmosphere, on optics and on light. Since the time of Galileo it was thought that light travelled at a finite but enormous speed. By rational arguments Euler calculated that it travelled 12 million miles per minute, close to the true value of about 11 million miles per minute.

Euler continued with letters on mechanical, optical, magnetic, and electrical phenomena as well as on gravity, the tides and cosmology. In Letter 60 he discussed the probability of intelligent life on other planets of the solar system and on planets around other stars. He reasoned that extra-terrestrial life was a virtual certainty.

In a letter dealing with logic Euler introduced the popular diagrams now known as Venn diagrams.

Many of the letters in the second volume deal with philosophy, theology and logic. However, when Euler visited the princess in 1761 she said she found these indigestible and difficult to understand, and asked him to confine his writing to physical questions. In the third volume Euler concentrated again on the physical sciences.

European languages

From Euler's time to the present day the collection has continued to be remarkably successful. By 1800 it had been translated into eight European languages. The first English translation appeared in 1795. The letters attracted the notice of leading German savants, including Immanuel Kant, Johann Wolfgang Goethe and Arthur Schopenhauer, who praised them.

Letters to a German Princess is still in print after 250 years. The collection shows Euler, described in mathematics as “the master of us all”, was also a master teacher. The book was the most comprehensive and authoritative popularisation of natural science written during the Enlightenment.

Peter Lynch is emeritus professor at UCD school of mathematics & statistics, – he blogs at thatsmaths.com