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In his paper "The geometry of Finsler spaces" (available at https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-56/issue-1.P1/The-geometry-of-Finsler-spaces/bams/1183514449.full) Busemann quotes Poincaré (p. 8):

Poincaré said somewhere$^5$ on the subject of generalizations: On ne fait pas un grand voyage pour ne trouver que ce qu'on a chez soi.

with the footnote being

$^5$ The author forgot where he saw this remark and was unable to locate it, but would be grateful for a reference.

A naive search online points to Busemann's paper. I have also done naive searches on digital copies of the standard Poincaré "philosophy" books to no avail. I second Busemann.

The quote roughly translates to: "One does not make a big trip to find only what one has at home." Certainly this is in character, as far as I can see.

Thank you for your time.


As a disclaimer, I've asked this question on M.SE about six months ago (https://math.stackexchange.com/q/4204323/169085), but the question did not get much traction.

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  • $\begingroup$ Sounds like a quote from an old Chinese book. $\endgroup$
    – markvs
    Jan 27 at 17:43

1 Answer 1

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I think this is a paraphrase of a passage found in the seminal paper "Analysis Situs" (Journal de l'École polytechnique, t.1, p. 1-121, 1895; you can find it in Oeuvres d'Henri Poicaré, t. VI, the quote is at pages 193-194, i.e. 13-14 of the scan) where he says

Aussi y a-t-il des parties de l’Hypergéométrie auxquelles il n’y a pas lieu de beaucoup s’intéresser : telles sont, par exemple, les recherches sur la courbure des surfaces dans l’espace à n dimensions. On est sûr d’avance d’obtenir les mêmes résultats qu’en Géométrie ordinaire et l’on n’entreprend pas un long voyage pour retrouver des spectacles tout pareils à ceux que l’on rencontre chez soi.

i.e.

There are also parts of the Hypergeometry in which there is no need to be very interested: for example, research on the curvature of a surface in a n-dimensional space. One is sure in advance to obtain the same results as in ordinary Geometry and one does not undertake a long journey to find spectacles quite similar to those which one meets at home.

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