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The quote is as follows:

"Nur wenn man nicht auf den Nutzen nach aussen sieht, sondern in der Mathematik selbst auf das Verhältnis der unbenutzten Teile, bemerkt man das andere und eigentliche Gesicht dieser Wissenschaft. Es ist nicht zweckbedacht, sondern unökonomisch und leidenschaftlich. ... Die Mathematik ist Tapferkeitsluxus der reinen Ratio, einer der wenigen die es heute gibt."

Where did Robert Musil publish this in 1913?

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This quote is from Der mathematische Mensch (The mathematical man), which is a short essay by Robert Musil, published in 1913.

In this essay Musil makes some considerations about the role and the nature of mathematics.

See for instance:

https://ucldigitalpress.co.uk/Book/Article/64/88/4827/

An English translation is in Musil, Precision and Soul: Essays and Addresses, ‎ University of Chicago Press; Reprint edition (1995).

I haven't the English translation, nor the German original, I checked the quotation in the Italian traslation of Der mathematische Mensch, L'uomo matematico, in Claudio Bartocci (ed.), Racconti matematici, Einaudi, 2006, where the quotation is on pages 290-291.

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  • $\begingroup$ Many thanks! :) The page reference in the German original would also be greatly appreciated. $\endgroup$
    – Frode Alfson Bjørdal
    Apr 6 at 20:12
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    $\begingroup$ You are welcome. Unfortunately, I haven't the German original, but the essay is very short, five pages in my edition, so it should be very easy to find the quotation. In my translation is on the second and third page of the essay. $\endgroup$
    – BakerStreet
    Apr 6 at 20:15
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    $\begingroup$ See what I found! :) degruyter.com/document/doi/10.1515/dmvm-2012-0020/html?lang=de $\endgroup$
    – Frode Alfson Bjørdal
    Apr 6 at 20:17
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    $\begingroup$ Great! Thanks for the link. $\endgroup$
    – BakerStreet
    Apr 6 at 23:14
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R. Musil, "Der mathematische Mensch." In: Der lose Vogel, Leipzig: K. Wolff 1913, pp. 310-314.

Der lose Vogel was intended to be published in monthly installments as a "Monatsschrift", but it appears the project lost impetus towards the end, and resorted to combining multiple issues into one. Musil's brief essay appeared in combined issues 10, 11, and 12. The quoted text from the question appears on page 312.

It should be noted that for each of the poems and essays in this publication the author is not stated. There is merely a list of all authors in the foreword on page VI which includes R. Musil among the essay writers:

[...] die Gedichte sind von M. Brod, F. Werfel, R. Walser. Die Aufsätze sind von: Alain, H. Beloc, F. Blei, S. Butler, E. v. Gebsattel, G. Hecht, A. Kolb, W. Krug, R. Musil, P. Scheffer, M. Scheler, H. Schott, R. Stadler, A. Suares, Vogelstein, O. Vrieslander.

The identification of Robert Musil as the author of "Der mathematische Mensch" must have been based on a different source. Maybe his writing style was easily recognized by contemporaries. The earliest reference to Musil's authorship that I can find is in Musil's "Gesammelte Werke" (collected works) edited by Adolf Frisé, published in 1952, where the essay appears at page 592.

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  • $\begingroup$ Confer my second comment above to @BakerStreet. $\endgroup$
    – Frode Alfson Bjørdal
    Apr 7 at 20:11
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    $\begingroup$ Of course, nowadays there is no doubt that the author was Musil, all the most important publishers in many countries publish it as an essay by Musil, I think that the answer of @njuffa was about the history of this essay. $\endgroup$
    – BakerStreet
    Apr 7 at 20:23
  • $\begingroup$ @BakerStreet That clarifies, and the following makes sense to me now: Andrea Cantini used the quote in his monograph Logical Framworks for Truth and Abstration, Elsevier, 1996, page 149, and simply attributed it to R. Musil 1913. Cantini probably had no access to the publication I linked to above, i.e. doi.org/10.1515/dmvm-2012-0020. $\endgroup$
    – Frode Alfson Bjørdal
    Apr 7 at 20:41
  • $\begingroup$ My idea is that probably there never was any doubt about the fact that the author of Der mathematische Mensch was Musil. I searched for a while and I didn't find any reference to a problem of attribution of this essay. Musil, in 1912 and 1913, published several anonymous articles on the journal Der loss Vogel , but my hypothesis is that the publisher knew that the author was Musil, there wasn’t a problem of attribution. But this is a hypothesis of mine. $\endgroup$
    – BakerStreet
    Apr 7 at 21:04
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    $\begingroup$ Andrea Cantini is Italian, and it is possible that he derived his quotation from the book by Claudio Bartocci I referred to in my answer, because this is a well-known book in Italy, by an important publisher and a well-known mathematician/editor. $\endgroup$
    – BakerStreet
    Apr 7 at 21:22

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