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La correspondance d’Henri Poincaré avec des mathématiciens de A à H. (Henri Poincaré’s correspondence with mathematicians from A to H). (French) Zbl 0582.01014

Cah. Sémin. Hist. Math. 7, 59-219 (1986).
As is well-known the correspondence of Henri Poincaré was voluminous, with mathematicians, with physicists, and with many others. While some of this was published long ago, e.g. the Klein-Poincaré correspondence by Nørlund, much of it remains unknown. The present publication represents a start on publication of Poincaré’s correspondence with mathematicians.
Many of the letters are given in full and unedited, though others exist only in editorially excerpted form, with ample editorial comment as to their content. As it is, this procedure has produced 161 pages of letters between Poincaré and ”Mathematicians from A to H” together with commentary. All letters in languages other than French are provided with a French translation as well, though commentary by foreign commentators consulted is left in its original language. According to the preface, there are plans for a future edition of all of Poincaré’s correspondence.
While this publication contains letters from, among others, Appell, Brouwer, Georg Cantor, Darboux, Fredholm, Fuchs, Halphen, and Hermite; unfortunately there are very few letters from Poincaré himself. This is not because the editors have not attempted to locate these letters, but simply because they do not seem to be available. For example the correspondence of Hermite occupies fully 1/4 of this publication, yet there are no letters from Poincaré and an editorial remark (p. 196) informs us that the correspondence of Hermite, which had apparently come into the possession of Émile Picard, was burned in a fire several months after his death.
The letters that exist here, however, are well worth their publication. In addition to the mathematical content of many, there is other material of interest to historians. Some examples follow. One of the correspondents was Georges Brunel, who at the time of the Poincaré- Klein ”competition” was a student in Leipzig taking a course with Klein. A letter from Cayley reveals his belief (in January 1892) in the absolute truth of Euclidean geometry (contrary to Poincaré’s conventionalism). The Darboux correspondence discusses the attempt to obtain for Poincaré the post of Secrétaire perpetuel for the physical sciences in the Académie des Sciences (apparently in part because some of his friends thought it might help make him elligible for a Nobel prize), and Poincaré’s subsequent withdrawal of his name - Darboux was at the time Secrétaire perpetuel for mathematics. It also contains letters about Poincaré’s thesis on which Darboux was one of the ”rapporteurs”, and, as editorial comment, Darboux’s actual final report on June 6, 1879.
We get another glimpse of academic politics when Hermite discusses with Poincaré which foreigners should be elected ”Correspondants de l’Académie des Sciences”. Another letter from Hermite remarks that Weierstrass and Kronecker have no affection for Klein’s character and judge his papers with some severity. A letter from Cantor shows he considered over a period of years Weierstrass and all the ”Berlin powerful” as much as his enemies as Kronecker even after the latter’s death. Other letters from Cantor indicate his role in founding the first international congresses of mathematicians. A brief exchange between Hilbert and Poincaré reveals the world before preprints and xerography. Hilbert asks Poincaré for a copy of his ”Théorie des quanta” in the Journal de Physique, and Poincaré replies that alas he had received no reprints, only four copies of the journal, already given away. There is much else as well.
Not only are the letters themselves of interest, but, as already indicated, they have been provided with excellent and valuable scholarly commentaries placing them in various relevant contexts, and providing discursive glosses on the texts. These are sometimes somewhat pungently expressed (for example, in the case of Dieudonné), but nonetheless valuable.
All in all the editors are to be commended on this production which will be of undoubted use to all interested in the history of mathematics during Poincaré’s life or related to Poincaré’s work. One looks forward with anticipation to the correspondence with ”mathématiciens de J à Z” as well as the other correspondence.
Reviewer: S.Segal

MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Poincaré, H.
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