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Duplicate of this question ... http://jameslogancourier.org/?itemid=2996
Since I do not want to do discussions about which questions are appropriate for MO and which are not every other day, I thought I won't try to answer the question at hand but only the underlying one (sorry for going off-topic):
There is something close to what J.S.H. asks for in writings of Kronecker, but to say it is due to Kronecker might be a stretch. [To exclude that he (Kronecker) said this elsewhere is of course hard to exclude, still it seems that Kronecker is not the one who invented that metaphor.]
The paper 'Ueber den Zahlbegriff' [On the notion 'number'; my ad-hoc translation] by Kronecker (Journal für die reine und angewandte Mathematik [Crelle], volume 101 (1887), 337-355)
[see http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN243919689 for all the old volumes of that journal]
it is written (on the first page):
Quoting Kronecker (verbatim except for typos I might have introduced and a reformatting of the footnote):
So soll dies hier in Beziehung auf den Zahlbegriff geschehen, den einfachsten jener drei Begriffe, dessen dominierende Stellung Jacobi in einem seiner Briefe an Alexander v. Humboldt sehr schön hervorgehoben hat(2). "Ein Alter" -- so beginnt einer dieser Briefe -- "vergleicht die Mathematiker mit den Lotophagen. Wer einmal, sagt er, die Süssigkeit der mathematischen Ideen gekostet, kann nicht mehr davon ablassen. [...]"
(2) Die Briefe haben sich in G. Lejeune Dirichlets Nachlass gefunden.
End Quote.
My ad-hoc translation (it is certainly not as elegant as the original but I am confident the basic content is preserved):
Here we thus shall do so for the notion 'number', the simplest of those three notions, whose dominating role Jacobi emphazised very nicely in one of his letters to Alexander v. Humboldt (2). "An Old One" -- thus commences one of these letters -- "compares the mathematicians to lotus-eaters. Who once, he says, tasted the sweetness of mathematical ideas, can never again abandon. [...]"
(2) The letters have been found in G. Lejeune Dirchlet's Nachlass.
End translation.
Some comments and notes:
The text starts with some remarks on the three notions number, space, time. And then focuses on number (the simplest one).
The word 'Mathematiker' meaning 'mathematicians' not 'number theorists' (which would be typically 'Zahlentheoretiker' in German) is used.
The letter by Jacobi should have been written in 1846/47. In the quote later on there is mention of 'the preceeding letter' that is date Dec 26, 1846, so somewhat after that date seems a good guess.
While this almost got me confused it is really the case that the letter is attributed to Jacobi but was found in the Nachlass of Dirichlet (not sure if Nachlass can be actually used in English some sources claim so; in case not, this roughly means the collected informal writings of somebody that 'remains' after his/her death, letters, notes, unpublished manuscripts and so on).
Conclusion: In a published article of Kronecker something close to the claimed quote (though not identical cf. mathematician vs number theorist) can be found. However, Kronecker only quotes Jacobi, and expresses approval of Jacobi's statement. Thus, to attribute this quote to Kronecker seems problemeatic; even if he said this later on, the originator of this metaphor seems to be Jacobi (or still somebody else before, but not Kronecker). [I did not try to find Jacobi's letters and so take the attribution of Kronecker to Jacobi on faith.]
In an informative comment, an_mo_user wrote parenthetically
My impression is that it's fairly commonly used and understood in English-speaking academic circles.
As another data point: I'll admit that Nachlass is not a word I recognize (even though I know enough German to basically figure out it means), and I would not feel confident about it being understood by an English speaker.
Thank you for the friendly responses!
Andreas Blass, I am not certain what he wants to say. My best guess is it is intended purely as a figure of speech, and not as referring to somebody specific (including himself); he was (only) slightly above 40 at the time of writing the letter and more importantly A. v. Humboldt, the recipient, was much (about 35 years) older then he. The context in which he says this is not completely clear to me. But what I know is, after a standard opening, the letter starts with this passage, and then continues using this fact as some sort-of apology/justification for what he wrote in an earlier letter. To put it informally, the continuation suggests he wanted to express something like: 'We mathematicians are all a bit crazy [about mathematics], please keep this in mind when judging what I said.' And thus looked for a formulation to transmit something as a general sentiment, something like 'It is/somebody said that math are like lotus-eaters...'
Yet, now that I searched for it, it seems this correspondence (with comments) is fairly easily accessible (though not online); it is in Google-books but one gets only bits and pieces. In one of the pieces I saw a footnote metioning that Moebius in 1907 attributed this quote to Jacobi. I believe that tomorrow I'll have access to the entire correspondence, and will have a closer look.
Nachlass ... dictionary.reverso.net has these translations:
den Nachlass eröffnen to read the will / den Nachlass verwalten to administer the estate / literarischer Nachlass literary estate / Gedichte aus dem Nachlass unpublished poems / aus dem Nachlass des Dichters from the poet's estate /
For J.H.S. and whoever else might be interested some more information on the subject. Sorry for the delay; on the one hand I got distracted by the off-line world, on the other hand out of sheer stupidity on my side I completely lost a final first version of this.
As mentioned above the quote in question, or to be precise, something extremely close to it was mentioned in a letter of Jacobi (to von Humboldt) several decades before Kronecker quoted (with precise attribution) it in a paper.
Now, due to the precise phrasing in Jacobi's letter it was not completely clear whether or not Jacobi is also only quoting still somebody else. I already said that I believe that he was not, but now present some more, and I believe convincing, evidence that the sentence is due to Jacobi (and not Jacobi quoting somebody else).
For me some unclarity remains what precisely Jacobi wished to express with his construction, but either interpretation I can think of clearly suggests he is not truly quoting somebody else.
The remainder of the answer is structured as follows: First, I give a bit of context for the letter in question. Then, I give the relevant part of the letter itself (in the original form, and ad-hoc translation due to me). Finally, I add some commentary.
The letter itself as well as most of the information below is taken from the book "Briefwechsel zwischen Alexander von Humboldt und C.G. Jacob Jacobi" edited by Herbert Pieper; Akademie-Verlag Berlin, 1987. (A 300 pages book containing the correspondence Jacobi--von Humboldt and lots of commentary.) As said, translations are by me; I go for simplicity and clarity rather than for a really good translation (as I would fail anyway, and then an approximation might be worse than something clear and simple).
Context: Jacobi and von Humboldt are engaged in a discussion on the relevance of pure mathematics. The reason is mainly twofold. On the one hand, the necessity to 'fight' for proper employment for Dirichlet to prevent his departure from Berlin (to Heidelberg). [Including a letter from Jacobi to Friedrich Wilhelm IV., King of Prussia, quite interesting to read but tangential here.] On the other hand, precisely at that time there was considerable excitement over the prediction, which was also immediately confirmed, by Leverrier of a then new planet (Neptun). [There is also some priority dispute related to this, but this is also tangential.] Jacobi apparently found that excitement a bit excessive, though he also made more charitable statements on Leverrier then those in these letters.
The relevant letter: Jacobi to von Humboldt, after 27.12.1846 and before 29.1.1847
Original:
Hochgeehrtester Herr Geheimer Rath
Ein Alter vergleicht die Mathematiker mit den Lotophagen. Wer einmal, sagt er, Sie Süssigkeit der mathematischen Ideen gekostet, kann nicht mehr davon ablassen.(2) Schreiben Sie daher meinen vorherigen Brief der Raserei zu, in welche jene Lotosfreeser versinken, wenn sie den Cultus jener Ideen vernachlässigt, oder sie nur wegen ihrer zufälligen Anwendungen wegen geschätzt glauben. Und sagt nicht schon Schiller in den Xenien in seinem kleinen Gedicht
Archimedes und der Jüngling(3)
[10 line poem, praising the superiority of math over astronomy]; [couple of pages more technical content]
Translation:
Most esteemed Mister Privy Councillor
An old one compares the mathematicians to lotus-eaters. He says: "Who once tasted the sweetness of mathematical Ideas, can not anymore abandon." (2) Attribute my preceding letter to the rage, in which those lotus-eaters fall, when they perceive that the cult of those ideas is neglected, or only appreciated due to its random applications. And does not already Schiller say similar things in the 'Xenien' in his little poem 'Archimedes and the Youngster'(3)
[To be continued]
[Continuation]
Commentary: Footnote (3) points out that while there is a poem of Schiller, one of the most famous German writers, this is only very vaguely similar and does not talk about math at all. So, this is some fake-quote. It is so different that this is certainly not a misquote, when quoting from memory, but a genuine poem due to Jacobi. It seems also clear that Jacobi knew that von Humboldt would recognize that this is not actually Schiller. The point it seems to me, is to draw a parallel of the general line of reasoning (the poem is similar in that it is critical of putting emphasize on practical usefulness over genuine interest), and perhaps as a secondary goal to document ones general level of education.
So, even supposedly precise quote to Schiller is not at all precise, but simply points out a very loose connection. Thus, there is no reason why the much vaguer 'quote' of an unspecified 'an old one' should be anything else.
My first interpretation in an earlier comment, and this is in line with the way Möbius recalls the quote (cf. below) was that this 'an old one' is to be understood abstractly something like 'a wise person.' I do not think it is a direct self-reference as, as said, Jacobi was much younger than his correspondent (almost only half his age) and also by rank certainly not more senior.
However, I now also have a second interpretation. Namely, I could well imagine that 'ein Alter' is supposed to mean 'a classical author' where 'classical' is to mean antiquity. Paying reference to the fact that the the lotus-eaters appear in Homer's Odysee; yet, of course not with any link to math. The usage of 'ein Alter' in this form would not be unusual; well, nowadays it perhaps would be because it is less clear which period is meant but then this should have been different some 150 years ago. It seems very natural to me, but this is about all I can say in its favor; and it contradicts M�bius. So, this is not too much evidence.
So what does Möbius say (this and some information on the classical lotus-eaters is in the second footnote). In a 1907 book Möbius writes, without precisely referencing it: "Nach Jacobis Ausspruche ist der Mathematiker dem Lotosesser gleich: Hat er einmal die süsse der Frucht gekostet, so mag er keine andere mehr. Er lebt in seiner Kunst, und je älter er wird, um so treuer wird er ihr." Which roughly means "According to Jacobi the mathematician is like a lotus-eater: After having once tasted the sweetness of the fruit, he does not like an other any more. He live in his art, and the older he gets, the more fidel he is towards it." Thus, really taking the old in a proper sense.
Anyway, I am not sure what is the precise intention of Jaobi. But what seems clear to me is that the passage is 'original Jacobi' and not Jacobi quoting some unspecified other person in a true way (perhaps in this faked way as he 'quotes' Schiller).
p.s. I did not give the poem, but let me recall the last two lines as I believe it is also somewhat well-known and if not perhaps it should be:
"Was du im Kosmos erblickst, ist nur der Göttlichen Abglanz, \ In der Olympier Schaar thronet die ewige Zahl."
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