I listened to the second episode of A Brief History of Mathematics on Euler yesterday. I was quite taken with a quote from Euler which, to me, says something of the potential dangers of the application of mathematics to the real world. The relevant section of the programme is:
“In the year that Issac Newton died, Euler, then aged just 19, was awarded the most prestigious mathematical prize of the day, the first of many, many achievements and accolades he would receive during his lifetime. The annual mathematical challenge issued by the Paris Academy of Science in 1727 was this: “What is the best way to arrange masts on a ship?” At first sight it’s a very practical problem, but the young Swiss mathematician Leonhard Euler attacked it as a purely mathematical puzzle. Despite having never set foot on a ship, he felt perfectly well qualified to calculate the optimal arrangement of masts. For him, it was a problem that could be solved by mathematics alone.
“‘I did not find it necessary to confirm this theory of mine by experiment because it is derived from the surest and most secure principles of mathematics, so that no doubt whatsoever can be raised on whether or not it be true and takes place in practice.’
“Leonhard Euler had absolute faith in mathematics….”
Having copied this out and investigated a little, I have a couple of small factual problems with this passage.
Newton died in 1727 (on 20 or 31 March, depending on your calendar) and Euler was born 15 April 1707, so I’m happy Euler was 19 in the year Newton died. And Euler’s report was submitted to the 1727 Grand Prize of the Paris Academy on the arrangement of masts on a ship. (Whether the Prize was awarded pre- or post-15 April I cannot find, but this seems almost irrelevant really; that, according to the Euler Archive, Euler wrote the paper in 1726 isn’t really relevant since the claim made is of the award of the prize.) Euler didn’t, however, win the prize. He came second. The first prize was shared between Pierre Bouguer and Charles-Étienne Camus. This is regarded as a substantial achievement in any case given Euler’s age and the fact that Bouguer was an established expert on ships. The programme doesn’t quite say he came first, but the wording “was awarded the most prestigious mathematical prize of the day” is strange when Euler was second to Bouguer and Camus.
My second factual issue is that I can’t find the quote as quoted anywhere. I can only find it quoted online as:
“I did not find it necessary to confirm this theory of mine by experiment because it is derived from the surest and most secure principles of mechanics, so that no doubt whatsoever can be raised on whether or not it be true and takes place in practice.” (emphasis added)
The quote is from Euler’s submission to the Grand Prize, which was not written in English, so there are translation issues here. The Euler Archive at Dartmouth provides a scan of the original printed in Recueil des pièces qui ont remporté lex prix de l’académie royale des sciences (1732):
“Haud opus esse existimavi istam meam theoriam experientia confirmare, cum integra et ex certissimis et irrepugnabilibus principiis Mechanicis deducta, atque adeo de illa dubitari, an vera sit ac an in praxi locum habere queat, minime possit.”
Ian Bruce provides an original translation where the relevant passage is given as:
I do not think that it is necessary to confirm my theory by experiment, since the whole has been deduced from both the surest and the most irrefutable principles of mechanics, and thus concerning that there cannot be the least doubt or the truth can be put to the test in practice.
In any case the latin “Mechanicis” or the Ian Bruce translation “mechanics” suggests “mechanics”, not “mathematics”.
This puts me in mind of another recent programme, The Beauty of Diagrams, in an episode on Newton and optics Marcus says “and, as Newton took up residence again at Trinity, over in Italy Galileo was busy working out the speed at which light reaches us from the Sun”. The problem here is that Galileo died almost a year before Newton was born.
My feeling is that the Prize issue may have been a quick shorthand as this is a side point and the programme is very short overall. The essential point is “Euler made fantastic achievements from an early age and here’s something of his view on the application of mathematics”. Then the mathematics/mechanics mixup seems likely to me to have been a change to avoid having to explain the term mechanics.
I have a lot of sympathy with getting obscure facts wrong with this sort of thing, which I feel is an ever-present danger in everything I do and I’m sure I will sometimes land on the wrong side of correct. I also have a lot of sympathy with trying to get the core message across without getting distracted by details in a limited timeframe. This is something I haven’t had a lot of experience with in my self-published podcast endeavours, in which if you need an extra 30 seconds to explain something you can just take it (although you perhaps shouldn’t).
In any case, I would recommend any applied mathematicians hang a sign somewhere with the following wording, as a warning against arrogance:
“I do not think that it is necessary to confirm my theory by experiment, since the whole has been deduced from both the surest and the most irrefutable principles of mechanics.”
Leonhard Euler, c.1727.
Also, consider including the wording in your next grant application.
would you say that the moral of the passage;
“I do not think that it is necessary to confirm my theory by experiment, since the whole has been deduced from both the surest and the most irrefutable principles of mechanics.”
is that no matter what we as individuals seem to understand and have a strong grasp of, there are subtleties and different angles of inspection that will further ones understanding?
I also read somewhere that Euler was a devout christian and would have bible study in his home with his children and all other in which everyone was encouraged and most likely i feel were obligated to participate.
can you point me in any direction to any philosophical writings That Euler wrote later in life?
– Nico
Perhaps, BBC Radio 4 is presenting this as more of historical fiction, although fiction doesn’t quite catch what I mean. They are telling a story, and doing a superb job as far as I can see (or hear.) I found the podcast engaging, just what is needed to draw in a younger audience of future mathematicians. When you are travelling back to the 18th century, its not always possible to tell a complete story. To tell a story, you need to create an umbrella for some of the facts, and sometimes you need to make a best guess to complete the picture. This approach has enabled the creation of a wonderful, engaging, and mostly accurate (i.e. of the most important facts) vignette of his life. I felt entirely pulled into Euler’s time and place and the conundrums he faced, something that is very difficult for a historical narrator to accomplish. Free yourself just a tad from the literal, and see the joy in this piece instead of tearing it down.