# Euler's Master's Thesis

At the age of 16, Leonhard Euler defended his Master's Thesis, where he discussed and compared Descartes' and Newton's approaches to planet motion. I don't know anything else about it. In particular, I don’t know what position the young Euler supported.

Is there any modern account of this dissertation? In English or French?

Edit. The only source I know of is of dubious value, to say the least. On the occasion of a celebration of Euler's tri-centenary, I was offered a comics, authored by Andreas K. & Alice K. Heyne (illustrations by Elena S. Pini). There is a lot of good to say about it. But on page 10, block 3.1, Euler is concluding is defense with the words ... so the planets are dragged along by aether vortices. I wonder whether the authors have any source to support this citation.

By the way, I wish to mention that it took a considerable time for Newton's theory of gravitation to be accepted in France, and more generally in continental Europe. Descartes' reputation was so high that any contradiction to his writings was a priori rejected. The Principia were published in 1687, but they penetrated the French scientific community only once Emilie du Chatelet translated them circa 1745, on Voltaire's request.

• I am no expert, but I was looking at the Euler Archive (eulerarchive.maa.org) and it has a comprehensive list of works published by Euler. The earliest paper in the archive is from 1725, which is 2 years past the date at which he defended his philosophy masters. So at the very least, it seems that there is no publication of this work. But this does not mean that there is no account of the thesis, only that the thesis itself was not published. – Christopher A. Wong Jan 2 at 10:20
• @Christopher: Euler's talk on arithmetic and geometry which he gave when he was 14 is not published, as far as I know, but has survived. I can't wait for the day the Euler archives in St. Petersburg go online. – Franz Lemmermeyer Jan 2 at 11:42
• Detail: You "wonder" whether (not "wander" -- middle paragraph). – Peter - Reinstate Monica Jan 4 at 11:26
• Your English is great, no worries. – Peter - Reinstate Monica Jan 4 at 11:32
• If its any consolation the teaching of foreign languages has always been and probably always will be poor in England. – Hollis Williams Jan 6 at 12:56

## 2 Answers

Martin Mattmüller, in his article Leonhard Euler, seine Heimatstadt und ihre Universität on Euler's hometown Basel, writes that this public talk (not a dissertation or written thesis), which Euler gave in 1724, is lost, and that it is not known which position he supported. Euler had obtained his magister degree already in 1723.

As Franz says, it is impossible to know for definite which view the young Euler supported.

However, Newton had already disposed of the Cartesian vortex theory in the Principia which was published almost $$40$$ years before. I presume that Euler must have supported the view of Newton as Euler had almost certainly read the Principia by that age. I don't know how the history goes though, or how long it took for certain people to accept that the model of Descartes was definitely incorrect.

I suspect that at first there might have been quite a lot of resistance to Newton's views, but if the view of Descartes was still regarded as a tenable one in 1724, that is very interesting to me.

• The situation regarding the recognition of Newton's gravitation theory is not simple. See my edits. – Denis Serre Jan 3 at 9:46
• Thanks for these edits, this is interesting as I never knew the detailed history behind it or the acceptance depending on country. It makes sense that anything contradicting Descartes would be rejected because of the esteem he commanded. Almost sounds like the situation we have today where anything goes if it is said by highly respected physicists... – Hollis Williams Jan 3 at 15:42
• Well, I should not compare with today's highly respected physicists. Descartes displayed a bright side and a dark one. He was definitively a great philosopher and as well an outstanding mathematician. But about natural sciences, including Physics, he made many wrong statements. We are aware of his theory of vortices (!), but he also based the so-called Snell-Descartes law upon wrong premisses, and thought that animals were nothing but mechanisms. Also, he did not believe in the vaccum, against Pascal. – Denis Serre Jan 3 at 18:31
• @DenisSerre To be fair, many philosophers now think that animals are no more than mechanisms, they just think that humans are also no more than mechanisms, and that mechanisms are a lot more than what you might naively think. :) – Yakk Jan 4 at 14:35
• One amusing sidenote which you probably know is that despite Descartes' official view, he did keep a pet dog which he was apparently very fond of and didn't treat it as if were a mechanism. – Hollis Williams Jan 4 at 18:51