# Euler and Diderot

From Dirk J. Struick’s A Concise History of Mathematics (1967), quoted by Shallit:

There exists a widely quoted story about Diderot and Euler according to which Euler, in a public debate in St. Petersburg, succeeded in embarrassing the freethinking Diderot by claiming to possess an algebraic demonstration of the existence of God: “Sir, (a+b^n)/n = x; hence God exists, answer please!” This is a good example of a bad historical anecdote, since the value of an anecdote about an historical person lies in its faculty to illustrate certain aspects of his character; this particular anecdote serves to obscure both the character of Diderot and of Euler, Diderot knew his mathematics and had written on involutes and probability, and no reason exists to think that the thoughtful Euler would have behaved in the asinine way indicated. The story seems to have been made up by the English mathematician De Morgan (1806-1871). See L. G. Krakeur and R. L. Krueger, Isis, Vol. 31 (1940), pp. 431-32; also Vol. 33 (1941), pp. 219-31. It is true that there was in the eighteenth century occasional talk about the probability of an algebraic demonstration of the existence of God; Maupertuis indulged in one, see Voltaire’s Diatribe, Oeuvres, Vol. 41 (1821 ed.), pp. 19, 30. See also B. Brown, Amer. Math. Monthly, Vol. 49 (1944).

Krakeur and Krueger state that his investigations into mathematics “dominated Diderot’s youthful activities and represent an important phase of his universal interests.” They speculate that a lack of mathematical background among scholars who studied the man impaired those scholars’ ability to address this part of Diderot’s life.

## 5 thoughts on “Euler and Diderot”

1. I thought Euler’s “proof” was supposed to be e^(i*pi)=-1. Not that it matters, though it seems a little more interesting than Struick’s version (which is true for a very wide range of a, b and n).

2. I’ve definitely heard it quoted this way, or at least with the letters specified by Struick: it’s hard to recall a particular nonsense formula out of all the possible nonsense formulae, but a grapheme-color synaesthete like me can remember arbitrary symbols pretty well, sometimes. Wherever I read the anecdote (Isaac Asimov’s Treasury of Humor, perhaps?) is a splotch of color in my memory.

3. Lucky bastard. I wish I was a synaesthete…

4. Escuerd says:

I also specifically remember it containing an a, b and x, and (a+b^n)/n=x looks consistent with the form I remember. This was from a book called “The Art of Mathematics”. It kind of disgusted me to see that the author seemed to take no issue with the use of mathematics as a tool of obscurantism when much of math’s beauty depends on its clarity.

If it had been e^(pi*i)+1=0 it could at least have been an honest (though still thoroughly unimpressive and unworthy of Euler) rehashing of the argument that beauty necessitates God. That might make that version of the story marginally more palatable, though no less dubious.

[Tangentially, I’ve always associated the graphemes I grew up with with specific colors, some more strongly than others. It never occurred to me until about a year ago that many people did not do so. At least one of my sisters does, though the associations we have are different. I wonder how common this particular set of associations actually is.]

5. Escuerd says:

Interesting. I had never heard of grapheme-color synesthesia by name before, but a quick google/wiki check seems to indicate that it’s not so uncommon. I wasn’t sure if this was a standard name or an ad hoc description you were using. Now I’ll have to waste some time looking up real studies related to it, haha.