Images of Italian Mathematics in France by Frédéric Brechenmacher Guillaume Jouve Laurent Mazliak & Rossana Tazzioli

Author:Frédéric Brechenmacher, Guillaume Jouve, Laurent Mazliak & Rossana Tazzioli
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

What ensued was a tense discussion between the two mathematicians and an exchange of letters that show how each wished to make his point of view known. The publications that Fréchet mentioned in the previous letter (Fréchet 1911a, b) are both entitled ‘Sur la notion de differentielle’. They certainly do not make any reference to Volterra’s work on functional calculus; they are two very brief papers that do not go into detail, but which set forth a general way of conceiving the differential. Paper Fréchet (1912) is more detailed and focuses over fourteen pages on elements that might bring Volterra to mind. Volterra’s works are cited in passing, and this probably caused a change of humour in the Italian mathematician.To arrive at a generalisation of the theorems of differential calculus, one must first of all generalise the notion of derivative where differential. One might base oneself, to carry out this extension, on the method used in the calculus of variations, which is but a chapter of functional calculus.

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