Archive for the ‘history’ Category

Some february 2017 newslets

February 18, 2017

[Posted on february 18, 2017.]

Firstly, some recent items:


Also to be noted, two upcoming auctions:

  • on march 14 (estimated at €20,000/30,000) in Paris, arare copy of the 1637 first edition of Descartes’ Discours de la Méthode (containing the famous appendix La Géométrie)
  • on february 22 (estimated at €200/300) in Lyon, a 326 pages manuscript c.1810 on dynamics and other topics (author unknown) [edit: won by the floor at €280]

Finally, it appears this blog was started 10 years ago, in what was definitely another era: before Polymaths, MO, arxiv overlay journals…and all the new official youtube channels in math and beyond.

Who was Joseph Ser ?

August 25, 2016

In an interesting paper, Iaroslav Blagouchine has presented, among other things, the equivalence of the explicit analytic continuation of \zeta due to Hasse  (in this 1930 paper) \zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+1}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{1-s}  with one derived 4 years earlier by a Joseph Ser (in this paper) \zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+2}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{-s}.

It may be that these could help improve the situation regarding the location of the non-trivial zeros of \zeta, although of course the classical Mertens approach with logs and the trigonometric identity cannot be mimicked here due to the ever growing number of terms added for each new n.

But who was Joseph Ser then ? There’s a short wikipedia bio saying that nothing much is known about him. There seems to be a genealogical entry for him here, with little more details beyond dates.  I couldn’t find his name among Normaliens nor Polytechniciens. He also doesn’t appear in the list of pre-1901 professeurs agrégés, and neither in the list of PhDs compiled by Hélène Gispert in her book.

As for published material, Numdam has 3 papers from him, where only the earliest one has a tiny indication: Nantes.  One can also find that a book of Ser, Les Calculs Formels des Séries de Factorielles, got a quite unfavorable review  in Bull AMS, while the same book got a more positive review in L’Enseignement Mathématique. And finally, he seems to have authored several articles in Mathesis, at least until 1953 when he was well into his seventies.

Feel free to comment if you know more about his work and career.

20160824_170956Caniculaire. (Metz, late august 2016, Public Domain.)

Quick observations concerning the Séminaire Bourbaki

June 21, 2015

Since the next Séminaire Bourbaki is due to take place next saturday, it is a good opportunity to make some quick observations.

Started in 1948, its goal as an expository seminar was clear from the start: the very first exposé was by H. Cartan on the work of Koszul rather than on his own results, and many recent advances were presented at the seminar (e.g. the same year Pisot reviewed the elementary proof of the PNT by Selberg and by Erdős).

The first issues regroup several years, and in 1968 things settled on the current format : 4 sessions during the academic year, held in november, january, march, and june. The year 2014-2015 is its 67th year, and will end with the 1103th exposé. One can notice the following :


Most of Grothendieck’s manuscripts to be digitized

June 18, 2015

According to an article by Stéphane Foucart in Le Monde, it has been announced at the Grothendieck conference in Montpellier that :

  • about 15,000 pages of manuscripts held by the university were now in the process of being digitized (that’s the archive that was given to Jean Malgoire in the 1990’s, which in turn he donated to the university)
  • about 50,000 pages found in Grothendieck’s Lasserre home will be digited by the Bibliothèque Nationale de France (of Gallica fame), once legal hurdles are cleared, and which contain a mix of mathematical and non-mathematical texts

Let’s see : assuming 50% of mathematical content, that’s (15,000+50,000)/2=32,500 pages.  Chopping that into bunches of 200 pages, that’s about 162 books. In comparison, Euler’s Collected Works are said to fill 60 to 80 books…

The Tombstone of Madame du Châtelet (1706-1749)

April 5, 2015

In 2006, to mark the tricentenary of the birth of first ever frenchwoman scientist, Émilie Du Châtelet, an exhibition was organized in Paris by Elizabeth Badinter (booklet here).

Then, a few years ago, several newly found mathematics and physics manuscripts written by la Marquise du Châtelet were sold at an important Christie’s sale.

What about the final resting place of such a fine woman? Well, it is a very sober black tombstone in Saint-Jacques church, in Lunéville. Elisabeth Badinter, and Annie Jourdain, tried to have something done so that it is not walked over by the faithfull, but there were no protective barriers when I visited a few days ago.

By the way, the Château de Lunéville, which sadly was ravaged by a fire in 2003, has been nicely restaured over a decade, and is well worth a visit. I went there early enough to catch a nice april cold fog.

(full album on flickr)

Auctions of mathematical texts

February 12, 2015

On saturday in Royan there will be on offer (for about €300/350) a handwritten set of lecture notes of Cauchy’s 1824 course on Calcul différentiel et intégral, taken by Lamoricière.  It may well beat that estimate by some margin.

Indeed, last december, the own annotated copy of Hugens’ Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (1673), went for $965,000 after an estimate of 150,000/200,000.

A month earlier, a 1931 offprint of Gödel’s Über Formal Unentscheidbare Sätze der Principia Mathematica und verwandlter Systeme I, achieved £104,500 after an estimate of £12,000/£16,000.

So, there seems to be a market for the rare and historically important items, that’s not too surprising but the level is pretty high (I guess all it takes is just a couple of mathematically enclined high-ranking google executives, or the likes…). And it’s not only auctions, fixed price items exist too, like these 3 manuscript pages by Gauss available for €65,000.

Update: the aforementioned sale has been broadcast online earlier today, and those handwritten notes indeed attracted interest, with a little fight between the floor and online bids ending at €1,300.

Pangaea Ultima

December 31, 2014

Four years ago I mentionned Ron Blakey’s video of evolving continents on the great SpaceRip channel.   Last september they posted an updated beautiful version with much more detailed maps, converging to Pangaea Ultima:

Preserving documents of Hermite and Picard IV: other items

December 16, 2014

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

Together with the jubilee papers, there were three other documents (pictures) :

1) a letter in german from Hermann Schwarz, from the 2nd of june 1893, concerning the great gold medal for science awarded to Hermite by the Kaiser Wilhelm II. There’s an hilarious letter of Hermite to Stieltjes from the 17th of may 1893, where he complains that a small 5-franc sized gold medal that didn’t bear his name had been delivered to him without previous notice nor explanations, and that he had been treated like a dog by the emperor (!!), and had written to Schwarz about it.  This explains that, then. (The portfolio that I couldn’t buy, mentionned in the first post, apparently contained the french translation of that Schwarz letter).  The medal itself is unaccounted for…

2) a letter from Matthias Lerch from the 29th of december 1892, which discussed some results, and also contains a nasty anti-semitic statement. (I don’t think that Hermite shared that kind of opinion, it’d be truly disappointing if he did!)

3) the draft of a letter by Hermite from the 15th of june 1893 thanking the king of Greece for…yet another gold medal.

Appart from that, a late twist was that in mid-november a fifth (!) seller came-up in the ebay auctions, this time with some genealogical documents and pictures of Picard (you can see them here), in particular one dating from 1889 upon his election to the Académie des Sciences (aged 33, now that is a moustache…)


and another one from 1939, a couple years before his death. One sees a very large library behind him, probably full of interesting items!


From this seller I finally learned that in the summer of 2014 an old house had been advertised for clearing, and the belongings sold to different people locally.

At this point it is unclear if most of what was sold then has been preserved: it is odd that the documents do not contain any of Picard’s reprints from before 1883, yet he had lots of papers before that.  It is also suspicious that only one Hermite manuscript would be there.  I’m fearing that some of the most interesting items have discreetly made it to specialized resellers and wealthy private collectors.

Obviously, I’m not expecting all of Picard’s library to have been available anyway: he had five children, three of which died around WW1 while the two remaining daughters married physicists Louis Dunoyer de Segonzac and Jean Villey-Desmeserets (who had four children, one of whom had preserved those documents). So Picard’s library has thus probably been split between his pupils and the sons-in-law physicists in the 1940s, and then between the children and grand-children of all of them.  It was already known that the Villey branch had some items, since in 1970 Pierre Dugac had documented part of the correspondance between Hermite and Stieltjes (which, it is mentionned, had later been given to the Archives de l’Académie des Sciences), but what else there were is as yet unsettled.

This little detective story ends here, for now at least, but it’s been exciting. I cannot begin to imagine the thrill that it must be to make an important archeological find, like the wonderful Kasta Tomb, or indeed any other major discovery

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

December 16, 2014

[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.

Preserving documents of Hermite and Picard II: Hermite’s 1892 jubilee

December 16, 2014

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

It is an ancient tradition in Germany that upon reaching 50 years after obtaining their doctorate, old scholars would have a party thrown up in their honour called a jubilee (from this book it appears that in the early XIXth century von Goethe had one).

Not many people reached their seventies in those days, and the first mathematician to celebrate his jubilee very probably is Gauss (in 1849), while later occurences include Weierstrass in 1885 (the year he proved that theorem), and von Helmholtz in 1891 (a very big one, with hundreds of guests and several ministers and foreign officials in attendance).

Elsewhere in Europe, I could only find cases in the late XIXth century. In France, it seems probable that the first ever was that of Hermite on december 24th, 1892. In the UK, Lord Kelvin had his in 1896.

Which thus brings us to Hermite. If you don’t know the man and you happen to understand french, there’s an interesting hour-long conference by historian of mathematics Catherine Goldstein from 2013 which is worth watching. Readers of english can consult this paper by Tom Archibald. To sum up, Hermite has been a very creative and influential mathematician (indeed the leading figure in France in the 1860-1880 era), and played also a pivotal role in the diffusion in France of important works by german mathematicians (with whom he corresponded extensively).

Most of the documents obtained from the auctions (see the story) are those which Hermite received that day. He also received this medal, designed by Jules-Clément Chaplain and paid for by an international subscription (an idea of Darboux, who had a very pacifist, internationalist worldview), but unfortunately it wasn’t among the items any of those ebay sellers had. (Chaplain had also sculpted Hermite above a door of the Sorbonne, see this illustrated biography by Alain Nahuel)

As I later discovered, a document (available on Gallica) edited on this occasion does mention these papers. In no particular order, they are :

– two leather-bound-gold-plated portfolios : the green one from Die Königl. Gesellschaft der Wissenschaften zu Göttingen (signed by the director and the secretary) and the brown one from l’Académie Impériale des Sciences de St-Pétersbourg signed by all the then academicians (many famous names there!)

– more than two dozens of similar formal unbound documents from many academies and scientific societies : Belgium, Italy, Germany… — but not the UK, why so ?   The stand-out one is probably from Berlin, signed by von Helmholtz, Weierstrass, Kummer, (?), von Bezold, E. DuBois-Reymond, Kundt, Vogel and Fuschs!


– a document from the Société Mathématique de France, signed by les membres du bureau et du conseil (for further reading on the history of SMF there’s a book by Hélène Gispert, which contains also five related studies by other authors)

– a document signed by many former students of Hermite at École Normale Supérieure

– three personal congratulatory letters : one by Brill in french, one by Dedekind in german, and one by Gyldén in french

– several dozens congratulatory telegrams sent just in time for the ceremony on the 24th (from all over Europe except the UK –again– even one from the US by Newcomb).

To view all the corresponding pictures, please go to 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/l/  e.g. like on this picture).

Overvall, nothing scientific per se here, but that’s a nice set documenting the beginnings of the makings of the international mathematical community : the first ICM was held in Chicago six months later, in august 1893 (Hermite, like most europeans, couldn’t attend, but he did contribute a paper which was read there). On that topic, it must be noted that a very comprehensive book edited by Karen Hunger Parshall and Adrian C. Rice has been published by the AMS in 2002 (I do hope to read it one day).

At this point, one might wonder : but where is the medal ?  I regularly checked ebay and other websites for any “Charles Hermite” items, but nothing more came up.  As it happens, mathematicians’ medals tend to fare badly : a gold medal of Gauss ended up as a baby spoon, while one of Grothendieck’s medals became a nutcracker

And then in mid-november, as I was writing these posts, I did so again, and there was the medal, or so it seemed, from yet another seller!  It had been available for a fortnight at buy-now only, and luckily nobody had snapped it (the price was at the very upper limit of what I could manage). The seller said it wasn’t listed in his specialized catalogues, so there’s a good chance it is actually unique and the original one (if not, at least a very rare copy).  Which allows to finally reconstruct what was given to Hermite on December 14th, 1892 :


For the record, a few days later Louis Pasteur’s jubilee also took place at the Sorbonne (with a much bigger crowd, which is not surprising given his life-saving work and examplary scholarly attitude). And, among the documents given to him, there’s one listed that probably is very similar to Hermite’s (the one from l’Académie Impériale des Sciences de St-Pétersbourg).

Next post : Picard’s youth.