Preserving documents of Hermite and Picard III: Picard’s youth

[You are currently viewing a post that is part of a series : the story ; Hermite’s 1892 jubilee ; Picard’s youth ; Other items.]

In a nutshell, Émile Picard has been one of the main french mathematicians of the 1880-1920 era. He’s been precocious (earning his doctorate in 1877 aged 20), prolific (from the full list of his notes to Comptes-Rendu de l’Académie des Sciences, one sees he had 8-10 per year at the beginning, not to mention his longer papers in other journals), and very versatile (he touched on most subjects of those times, including relations with physics).  He thus obtained lots of honors, including Pleanary Speaker (1908) and President (1920) of an ICM, and Grand-Croix de la Légion d’Honneur (the highest, very select, grade). In 1917 he became permanent secretary of the Académie des Sciences, and controlled most of what was being published in France, sometimes to ill-effects.

But in this post we’ll focus on his early career, since that’s what the documents obtained shed some light on (see the story). They can be broken into three parts : (a) a stack of letters that Picard’s mother had kept, (b) Picard’s own copy of his 1886-87 Cours d’Analyse, (c) reprints of many papers, and books written by him.


About that last item (c) I shall say no more, since they are just what appeared in print at the time with no handwritten additions (so the content available in libraries or online –see numdam for many papers, and for some papers and his books— is identical).

Next we turn to (b) :


According to the Académie des Sciences, in 1885, after junior positions in Paris and Toulouse, Picard became the tenured professor of the Chaire de Calcul Différentiel et Intégral at Faculté des Sciences de Paris (until 1897 when he took up another position). In 1887, his course was edited (here is the GDZ digitized copy) by l’Association Amicale des élèves et anciens élèves.  This served as a precursor to Picard’s highly regarded Traité d’Analyse (vol. 1, vol. 2, vol. 3) a few years later.

The copy obtained was Picard’s, and contains lots of handwritten additions. I’ve put pictures of all of them on this online album on flickr (and if you want to see in larger size you must remove the final part of the URL and add instead /sizes/h/  e.g. like on this picture). To help locate them in the book I’ve usually taken first a picture of the page number next to (or behind) which they have been made.

These additions must then date from between 1887 and 1890 (when the new Traité appeared).  I’m no history specialist, but I did try to see if among them one could find the first occurence of one of Picard’s ideas. Net result: probably not, or not entirely at least. Historians will tell in due course, hopefully.

For example, as mentioned in his footnote on page 531 of vol.3 of his Traité, Picard first extended the ideas of Galois theory to linear ODEs in 1883 (in this CRAS note) and later came back to it in 1887 (the year of our copy, then).  We do find some pages (starting here) where he discusses what became later known as the Picard-Vessiot group of an ODE. He uses different inks, so it looks like he wrote that in stages as ideas came to him, but was that just material for his students, or stuff for his own understanding ? Tom Archibald wrote on that topic a paper that probably settles the issue (but it’s behind a paywall and I haven’t read it yet).


There are also two pages (one, two) that mention birational transformations and cycles in relation to a theorem of Max Noether, when it is known that Picard’s involment in then nascent algebraic geometry ranges from 1884 to 1905, according to Houzel’s chapter in Gispert’s book (see also Lefschetz’s 1968 autobiographical sketch in Bull. AMS, as well as the introduction to Kleiman’s paper The Picard Scheme).


The parts on more traditional topics like uniform continuity probably don’t contain anything new, since according to Hairer and Wanner’s excellent Analysis by its History these concepts date back from much earlier.  But perhaps the parts on existence of solutions of ODEs do (the chapter starts here) : after all, Picard’s method of successive approximations dates precisely from about 1888 (the method itself dating back to Liouville but not applied to existence results, see Archibald’s very interesting paper, in particular page 86 onwards).

That’s it for the mathematical part of the documents. We now turn to the more biographical part (a), which helps correct some inaccuracies in online biographies, and adds new material.

When I obtained the stack of letters that Picard’s mother had kept, they were all mixed (probably by the seller). After reading them, it appears they can be organised into the following twelve substacks :

(a) Letters adressed to Élisa Picard (née Plocq) on the occasion of her mariage in 1852 (nothing about Émile there then).

(b) Letters to Élisa from her husband, and a letter of Élisa to a cousin.

(c) Letters to Élisa on the occasion of her husband’s death in 1872, after a long illness.

(d) Letters from Alexandre Plocq and his wife. He was a cousin of Élisa and had been entrusted as the one to provide guidance to Émile and his younger brother Édouard.  Indeed it seems to have been a good choice : in those letters this Alexandre appears as a very righteous man, with high regard for studies and hard work. He himself enjoyed a high social status as Ingénieur en Chef des Ponts et Chaussées at the harbor of Dunkerque, which he obtained as a former top student of l’X (École Polytechnique). In particular, he appears to have been instrumental in both children obtaining a full bursary to study.

(e) Letters of congratulations adressed to Élisa on the occasion of academic successes of her sons.

(f) Letters to Élisa from a cousin living in New-York (an uncle of Émile then).

(g) Letters adressed to Émile during his youth, including one (probably) from Classicist Charles Graux when Émile obtained his doctorate, as well as some earlier ones from the american uncle, and from Alexandre Plocq suggesting to wait for the results of l’X before choosing École Normale Supérieure (so preaching a little bit for his chapel here, but he then wrote to Élisa that she should accept Émile’s choice)

(h) Letters to Élisa from Émile. There are several ones from 1887, including some not very sympathetic remarks about his father-in-law Hermite (who, apparently, was a bit of a grumpy old man by then), and the occasional odd XIXth century idea (“le passage du col du géant n’est vraiment pas à recommander pour la coqueluche“). There’s also an earlier touching one from october 29th, 1880 where Émile (aged 24) finds Hermite’s daughter “de mieux en mieux et elle me plait infiniement” but wonders how to know whether M & Mme Hermite have any plans for himself, and asks his mother what she makes of this.

(i) Letters to Élisa by the Hermite family. It includes a letter from Monsieur Hermite dated november 13th, 1880, in which he accepts to give the hand of his daughter to Émile (so the latter must have proposed in early november, perhaps after a letter from his mother). The tone of the letter is both solemn and humorous, Hermite adding “Venez donc, chère Madame, prendre la grande part qui est due dans notre bonheur, venez traiter et résoudre des problèmes dont la solution demande notre réunion” (Quick translation: “Come thus, dear Madam, to take the great part that is due in our joy, come adress and solve problems whose solution requires our union“.)

(j) Letters to Élisa on the occasion of Émile’s marriage.

(k) Letters to Émile from his younger brother Édouard. This brother was also very talented, he entered l’X and became a top student there (and became Ingénieur des Ponts et Chaussées, just like his mentor Alexandre Plocq). Although they also met in Paris, Édouard tells Émile how he is doing academically (note: in France marks are out of 20, e.g. 17 is quite good, especially for oral exams such as colles).

(l) Letters to Élisa from the brother Édouard, including many from Algeria where he later worked (I must say I haven’t read most of those).

Next post : Other items.

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