Pierre Duhem on fashion in mathematics

Pierre Duhem begins his article 'Émile Mathieu, His Life and Works', Bulletin of the New York Mathematical Society 1 (1891-1892), 156-168, with his thoughts on fashion in mathematics. Of course, this is being used as a lead-in to Émile Mathieu's life but we present it here as simply on his thought on fashion:

Pierre Duhem's thoughts on fashion in mathematics

If it were asked what tyranny in this world has least foundation in reason and is at the same time most overbearing and capricious, none could be found to answer better to this description than fashion; that fashion which makes us admire today what but yesterday would have excited astonishment, and which may provoke ridicule tomorrow. We all know that this sovereign whose iron rule is so much more keenly felt on account of its injustice governs the thousand and one details of everyday life; that it is supreme in literature and in the arts. But those who have not watched closely the life of the scientific world may perhaps be surprised to hear that even there if you would please you must bend the knee to fashion. "What?", might exclaim the stranger to the world of science, "can it be true that the mathematician knows other laws than the inflexible rules of logic? Does he care to obey other orders than the invariable commands of reason?" - Well, yes. Of course, to have a mathematical production accepted as correct, it is sufficient that it conform to the precepts of logic; but to have it admired as beautiful, as interesting, as of importance, to gain honor and success by it, more is required: it must then satisfy the manifold and varying exactions imposed by the prevailing taste of the day, by the preferences of prominent men, by the preoccupations of the public. Thus it comes to pass that, in mathematics as elsewhere, fashion will sometimes award the laurels to those who have not deserved the triumph and make victims of men whose lack of success is an injustice. In every country there are such victors and such victims; but nowhere perhaps are they more numerous than in France. In this country where centralization is carried to an extreme, nothing is accepted unless it receive the sanction of Paris, or rather of certain constituted bodies, of certain official persons residing in Paris. Those who have been so fortunate as to have their work noticed by these persons and approved by these bodies, who have been granted admission to the chairs of the capital, form in the opinion of the French public the only men of science worthy of honor. The others, relegated to the provinces, are left to oblivion, almost like those seigneurs in the age of Louis XIV whom a caprice of the monarch relegated to their country estates.

JOC/EFR May 2017

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