Skip to main content
32 votes
Accepted

Euler: “A baby on his lap, a cat on his back — that’s how he wrote his immortal works” (origin?)

The origin is undoubtedly Dieudonné Thiébault, as the anecdote is reported in his personal recollections of his stay in Berlin, published in Mes souvenirs de vingt ans de séjour à Berlin, vol. 5, (...
user6530's user avatar
  • 3,950
13 votes
Accepted

Did Euler produce any Russian text?

Yes, Euler wrote letters in Russian: (Euler's letter to Nartov, June 18, 1743) Interestingly, he signed papers as "Леонгардъ Эулеръ", a direct transliteration of his name, not how he is ...
Anixx's user avatar
  • 662
12 votes
Accepted

Have all of Euler's works been translated?

No, not all. I don't think that they are even all published in the original language. There is an ongoing project of translating Euler's mathematical work (only mathematical) Euler archive and you can ...
Alexandre Eremenko's user avatar
12 votes
Accepted

What's that on Euler's head? Does the head covering shown in Emanuel Handmann 1753 painting signify scholarship?

He wears the head wrap in combination with a silk banyan. In the 18th century... It was fashionable for men of an intellectual or philosophical bent to have their portraits painted while wearing ...
jkien's user avatar
  • 1,921
11 votes

Did Sophie Germain find a flaw in Euler's equations for elastic vibrations?

There were two episodes with Germain and Euler's mistake in elasticity, but neither one of them is of Germain discovering Euler's mistake. The first one is from 1811 when she was starting to work on ...
Conifold's user avatar
  • 77.6k
10 votes
Accepted

Exact source that Descartes had observed that $V-E+F=2$ for planar graphs

The reconstruction of the story is dealt with in the volume Descartes on Polyhedra: A Study of the "De solidorum elementis". Long story short: while in Paris in 1675-1676, Leibniz copied a ...
user6530's user avatar
  • 3,950
8 votes

Who first called $\mathrm e$ "Euler's number"?

Google Ngram does not show any use of "Euler's number" before 1880s, and early sources typically call "Euler's number" what is now called the Euler–Mascheroni constant $0.57721...$...
Conifold's user avatar
  • 77.6k
8 votes
Accepted

Who was Fleury? And what was his first name?

A Google scan of Fleury's article "Deux problèmes de géométrie de situation" can be found here, and identifies the author as "M. Fleury, chef d'institution", where "M." ...
njuffa's user avatar
  • 6,704
6 votes
Accepted

When did the word "Real number" begin to be used as an official terminology to refer to both rational and irrational numbers?

It is hard to say what "official" means exactly, it is not like there was a bureau of terminological standards. But "real numbers", "real values" and "real ...
Conifold's user avatar
  • 77.6k
6 votes
Accepted

Euler's proof of infinite primes first since Euclid?

There is a proof by Goldbach, which appears in a letter he wrote to Euler in 1730 (a few years before Euler published his product formula for the zeta function). It is as follows: if $F_n=2^{2^n}+1$ (...
José Carlos Santos's user avatar
6 votes
Accepted

Euler's Derivation of Euler's Method for ODEs

What motivated Euler was not any problem in particular, but rather the general need to solve differential equations approximately when an analytic solution could not be found. He explains the method ...
Conifold's user avatar
  • 77.6k
6 votes
Accepted

Did Euler ever write $f(x)$, with parentheses?

I’m guessing no. But how does one make sure? (Maybe with 85+ volumes of clean pdfs...) Cajori, who started that $f(\frac xa+c)$ example, points out a $\varphi(z)$ in D’Alembert (1754, p. 50). For “...
Francois Ziegler's user avatar
6 votes
Accepted

Clairaut's proposed correction (reported as "D'Alembert's, Clairaut's and Euler's corrections") to the Newtonian inverse-square law of gravity

This answers (with some explanation and references) the two questions, (a) Were any concrete corrections proposed (in the 1740s, to the law of gravitation)? and (b) Where can one read about it? (a) ...
terry-s's user avatar
  • 4,600
6 votes

Did Euler know Ancient Greek?

From Euler's Autobiography, p. 2: Nachdem musste ich mich auf Gutbefinden meiner famille beÿ der Theologischen Fakultaet einschreiben lassen, da ich mich denn ausser der Theologie besonders auf die ...
Michael E2's user avatar
  • 1,911
5 votes
Accepted

Are there any arithmetic problems studied by Euler still open?

Here are some open problems that go back to Euler or, in the last case, his contemporary Goldbach. The classification of all idoneal (convenient) numbers. They were introduced by Euler and he ...
KCd's user avatar
  • 5,689
5 votes

What are some of Euler's mistakes?

There is Betteridge's law of headlines: "Any headline that ends in a question mark can be answered by the word no." The article you quote (Euler's “Mistake”?) is not an exception. $\sqrt{ab}=...
Alexei Kopylov's user avatar
4 votes

Reference for Euler's Introductio in Analysin Infinitorum

Yes, the reference is to Euler's Introductio in Analysin Infinitorum (Introduction to Analysis of the Infinite) in which Euler investigates infinite series. The reference seems to point to Volume 1, ...
Hal's user avatar
  • 41
4 votes
Accepted

Where did Euler prove 'his' theorem on homogeneous functions?

Lucky you! (or me :-) ). This question was answered a while back on Math.SE I found his original thoughts in the translated version of "Institutiones calculi differentialis cum eius usu in ...
Carl Witthoft's user avatar
3 votes

Have all of Euler's works been translated?

If you are interested in reading Euler in English translation, you should take a look at Ian Bruce's excellent web site https://www.17centurymaths.com. His project involves the translation of ...
BlakeDavis's user avatar
3 votes

How to derive the power series of $\sin(x)$ and $\cos(x)$ followed the footstep of Euler

Concerning your question "Obviously the first term is $v$, but what about the rest of the terms?". Since he considers $n$ to be infinitely large he probably has $n(n-1)(n-2)\cdots (n-(k-1))=...
Michael Bächtold's user avatar
3 votes
Accepted

Seven bridges of Königsberg - did people know that it was impossible?

It looks like there wasn't really a common belief; see the question What was the origin of the Seven Bridges of Königsberg problem before Euler?. The answer by user @Conifold quotes researcher Teo ...
Glorfindel's user avatar
2 votes

What is the basis of the claim that $F_5$ was fully factored in 1732?

Once you know that factors of $F_5$ must be of the form $64k+1$, then it is very easy to try all of the possible factors of 6700417. You need try $64k+1$ for $k\le 40$. You can easily use Sieve of ...
Alexei Kopylov's user avatar
2 votes

Did Euler know Ancient Greek?

Since Leonard Euler went to a Gymnasium in Basel, he surely learnt greek, every student had to learn it, he graduated in theologie, which one could not do without greek as a language, "womit es ...
trula's user avatar
  • 141
2 votes

Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?

These are assorted comments too long for a comment. Boyer is unreliable and should not be used as a source. Bernoulli's "proof" of the existence of infinitesimals was rejected by Leibniz, ...
Mikhail Katz's user avatar
  • 6,131
1 vote

Have all of Euler's works been translated?

Some new translations (mostly into German but also into English) can be found on the website of the Euler Kreis Mainz.
Michael Bächtold's user avatar
1 vote

Have all of Euler's works been translated?

There are now 128 volumes in Euler's opera in the German central catalog of libraries here. There is no hope to get the formula digitized in the current state of mathematical OCR. There is some hope ...
Roland F's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible