3.8. Implementación de estrategias
3.8.2. Matriz de estrategias versus objetivos a largo plazo (MEOLP)
As mentioned above, Bützberger was an avid Steiner scholar. His scientific estate in the ETH Library Archive contains a host of letters and notes connected to his research. The correspondence indicates that Bützberger’s research lasted for several decades. Furthermore, it also shows that he was in touch with a number of his colleagues on the organising committee – Geiser in particular – as well as fellow mathematicians in Switzerland and abroad. Correspondence with Johann Heinrich Graf, Julius Gysel, and Sidler deserves a special mention here, but the list also includes Moritz Cantor, Arnold Emch, Wilhelm Fiedler, and Theodor Reye.
Whilst I am not able to do all the material in the estate justice within the scope of this thesis, I will give a brief overview.
As one would expect, there are sheets and slips of paper with notes54
on the topic of his Steiner research, some of them in French or English (e.g. [7m]). There are also a number of manuscripts and drafts of papers relating to Steiner. Among these, a handwritten, 125-page biography of Steiner [7a] and a draft of a book on Steiner’s mathematical manuscripts 1823-1826 [7b; 7c] stand out. It seems that this book, Jakob Steiners Nachlass aus den Jahren 1823–1826, was never published. As Burckhardt notes in [18], the manuscript is held in the ETH Library (Burckhardt refers to the copy in Hs 92 in the ETH Library
54
Among these is an undated invoice for a student, one A Spaerry, in which Bützberger charges him 55 Franks for 10.5 hours of private mathematics lessons plus ‘2 notebooks [and] 1 sheet of plotting paper’ [7r]. Presumably the only reason why it was kept are a few notes on Steiner that Bützberger scribbled on the back, but it gives a small insight into Bützberger’s life as a teacher.
Archive, which contains papers relating to Steiner’s works). However, Bützberger did publish two papers on Steiner’s life: Jakob Steiner bei Pestalozzi in Yverdon55
(1896), and Zum 100. Geburtstage Jakob Steiners56
(1896), in which he focuses on Steiner’s notebooks as a student at Pestalozzi’s school and at university. Letters from Geiser suggest that it may have been the same paper: In November 1895 he arranges for Bützberger’s paper to be published in Schweizerische Pädagogische Zeitschrift and puts him in touch with its editor, Friedrich Fritschi57 [7u; 7v]. Furthermore, he proposes a re-publication in Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht. Indeed, in February 1896 he recommends the paper to the journal’s editor Immanuel Carl Volkmar Hoffmann58, as Geiser himself ‘could not provide [Hoffmann] with
the desired article [on Steiner]’ [7w]. These short letters nicely illustrate Geiser’s remarkable networking skills, which are also apparent in his letters to Gysel (section 5.2.2). Translations of the full letters are in appendix E.2.2. There are several postcards in Bützberger’s estate in which colleagues congratulate him on his paper – “paper” in the singular, without any specification as to which one is being referred to. Nevertheless, a card by Cantor from 1896 [7s] represents the sentiment echoed in these cards:
Dear Colleague!
Thank you very much indeed for your exceptionally intriguing paper on Steiner’s background. Like all our peers, I dare say, I eagerly anticipate the continuation of your publications.
Yours respectfully M. Cantor
55 “
Jakob Steiner at Pestalozzi’s in Yverdon” [22]
56
“On the Occasion of Jakob Steiner’s 100th Birthday”
57Friedrich Fritschi (1851-1921), Swiss teacher, politician, and editor of Schweizer Lehrerzeitung. Cf. biography by M Bürgi in Historisches Lexikon der Schweiz: http://www.hls-dhs-dss.ch/textes/d/D3636.php, accessed 13/05/2014.
58
Volkmar Hoffmann (1825-1905), a German teacher, founded and edited Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht. Cf. http://personen- wiki.slub-dresden.de/index.php/Hoffmann,_Immanuel_Carl_Volkmar, accessed 13/05/2014.
In fact, it was Geiser who suggested that Bützberger send his paper to Cantor [7u; italics by the author]:
Should you have reservations about entrusting your fine work to a non-mathem[atical] journal, do contact Prof. Cantor in Heidelberg, so that the Zeitschrift für Mathematik & Physik includes the article. Do not hesitate to say that I asked you to send the paper if you think that this would have an impact.
However, for some reason unknown to us the paper was not published in Cantor’s journal. Perhaps Bützberger did not send it to Cantor after all, and Cantor commented on an already published version of it.
Bützberger must have spent much of his time trying to track down any remaining relatives and friends of Steiner, as well as pictures of and documents relating to him. Over the years he built up quite an extensive network of contacts that could provide him with information. Among them was his own father-in-law Johann Kohler, who lived about 20 km from Steiner’s hometown59. Letters in Bützberger’s estate suggest that Kohler did a
lot of research in the region [7h]. Friends of Bützberger, such as Johann Petri, and relatives of Steiner, e.g. one J Werner-Mathys60, helped as well. Gysel tried
to track down a certain Conrad Maurer for him, who seems to have been Steiner’s mathematics teacher at Pestalozzi’s school [7z].
Bützberger showed a particular interest in Steiner’s family tree, especially how Steiner and Geiser were related. His findings are mentioned in Geiser’s biography (section 2.2).
Another very profitable source of information was Sidler, who inherited some of Steiner’s manuscripts [cf. 38, p. 48-51] and for whom Steiner had been
59Johann Kohler (1843-1908), a member of the cantonal parliament, lived in Forst, a
hamlet outside of Bützberg in canton Bern. Bützberg is part of the municipality Thunstetten.
60
There is not much information about him in any of the letters, except that he lived in Fribourg and owned three of Steiner’s books [7F]. As Sidler explains, a Jakob Mathys, one of Steiner’s nephews, inherited most of Steiner’s money [7E]; Werner- Mathys was probably one of his descendants.
a fatherly friend. Indeed, Bützberger reports in his Sidler biography that ‘Sidler visited [Steiner] almost daily during [Steiner’s] bitter time of suffering. His dear widowed mother […], who had lived with him since 1861, ministered to the terminally ill geometer as well, for which he was very grateful’ [23, p. 70]. In fact, in 1906 Bützberger asks Sidler’s permission to include this anecdote in his ‘soon to be completed work’61 [7k]. In his reply
[7E], Sidler suggests changes to the manuscript and gives background information on some points, such as Steiner’s character traits and his heirs. Moreover, he recounts some anecdotes that explain Steiner’s difficulties with writing and the end of his friendships with Carl Jacobi, Lejeune Dirichlet, and his doctor Johann Schneider. Sidler also comments on the rumour about Steiner’s illegitimate daughter. Apparently Bützberger planned to ask Geiser for comments on the manuscript as well [7F].
Furthermore, Sidler responds to Bützberger’s accusations against Graf and tries to calm him down: According to Bützberger, Graf included some of Bützberger’s results regarding Steiner’s years in Yverdon in his own papers but failed to reference them. In his Steiner biography, Graf remarks that the Yverdon section is based on Bützberger’s paper. Comparing the two papers today, some passages are almost identical and would require better referencing [cf. 38, p. 2-6; 22, p. 20-26]. However, Bützberger seems most outraged about Graf’s 1905 paper, in which he is not referred to at all. The matter of dispute is the year of Steiner’s arrival in Yverdon: Bützberger, believing that he settled the issue, cannot understand why Graf revived the debate. This is explained in letters to one Dr Israel, in which Bützberger complains about Graf [7C], and to Graf himself, in which he expresses his displeasure [7f]. In his reply, Graf insists that this must have been a misunderstanding and encloses a postcard with Steiner’s birthplace, ‘to prove
61
Bützberger probably referred to Über bizentrische Polygone… here, his only Steiner- related publication in the 20th century. As he explains to Sidler why he included a
‘biographic preamble’, we can assume that this work was not purely a biography. Sadly, Sidler did not live to read the finished book.
As Kiefer writes in [48, p. 423], Bützberger also worked on an extensive Steiner biography, and he expresses the hope that it might be published posthumously. However, it seems that the biography remained unpublished.
[that he] is not cross with [Bützberger]’ [7e] – a rather curious reaction! Whilst Bützberger had a point, his reaction was rather dramatic given the scale of this academic dispute. In his letter, Sidler urges Bützberger to remain professional:
Your work should become a classic in memory of the great geometer & it should go without saying that the preface should be nobly written. As an example, look at the second part of Poncelet’s Propriétés des figures projectives. Surely everybody laments that Poncelet got too carried away with polemics there; this tarnishes Poncelet’s memory. [7E; italics by the author]
The other letters that Bützberger and Graf exchanged suggest that their relationship was generally professional [7g; 7x; 7y].
In fact, both were members of the Steiner-Schläfli Committee, as was Geiser, along with Sidler and five more mathematicians62. In a circular of
October 1895 the committee explains that its main objective was to raise money for tombs for Steiner and Schläfli63. As Graf writes in [36, p. 19],
Bützberger and a colleague, Christian Moser, found Steiner’s lost grave, and Sidler donated a small tombstone. However, as the graveyard was closed down, the committee successfully applied for permission to exhume Steiner. The committee organised Steiner’s re-interment and the erection of a grand tombstone on Schläfli’s grave in 1896 to celebrate Steiner’s centenary and the anniversary of Schläfli’s death (who had died in 1895) [cf. 3664
; 6G]. It seems that the committee disbanded afterwards.
62
These mathematicians were: Hermann Kinkelin from Basel, Hugo Schiff from Florence, and Gottlieb Huber, Christian Moser, and Eduard Ott, all from Bern. Graf was president.
63
As Neuenschwander writes in [61, p. 34; p. 77-78; p. 83], the Swiss Mathematical Society founded a Steiner Committee and Steiner Archive in 1930, with the objective of safeguarding and publishing Steiner’s manuscripts. In 1937, it was renamed Steiner-Schläfli Committee – there do not seem to be any links to the committee referred to in the text here. It disbanded in 1956, after having published Schläfli’s complete works (Gesammelte Abhandlungen, three volumes: 1950, 1953, 1956). It seems that they only published one of Steiner’s works, Allgemeine Theorie über das Berühren und Schneiden der Kreise und der Kugeln, edited by R Fueter, F Gonseth (1931).
64
Graf includes the most important correspondence between the committee and authorities, the commemorative speeches by Geiser and himself, and congratulatory letters from a number of mathematicians. Among them we find Schwarz, Cremona,
Letters from Reye [7D] and Emch [7t] to Bützberger suggest that he might have planned to publish Steiner’s posthumous works. As Hollcroft writes, Bützberger ‘died before he had completed the work of editing the Steiner manuscripts’ [45, p. 794]. However, he did publish Über bizentrische Polygone, Steinersche Kreis- und Kugelreihen und die Erfindung der Inversion in 191365,
dedicating a separate section for each of the three topics. The ‘carefully and clearly written’ [30, p. 415] book was reviewed favourably, with particular praise for the historical background: ‘The numerous historical and biographical facts add particular value to this book’ [7p]. Furthermore, reviewers note that Bützberger used elementary geometric methods (instead of analytical methods), such as reciprocal radii. In the second section in particular, he treats ‘Steiner series of circles and of spheres; here [he] follows Geiser’s view: “Einleitung in die synthetische Geometrie”, last chapter “Das Prinzip der reziproken Radien”’ [54]. An analysis of Geiser’s book is given in section 5.1.
All the reviews available to me also agree that the third section is the most intriguing one. Danzer for example writes [7o]:
I think that Bützberger’s book is very interesting; the first and second sections, in which hardly any new material is included, less so, but certainly the third section, which provides an insight into “Master Steiner’s” workshop.
Specifically, Bützberger cites a document that he found among Steiner’s manuscripts, which proves that Steiner did invent the inversion, as had been suspected previously [cf. 7q; 30, p. 414]. Presumably in preparation for the book Bützberger copied down a dozen relevant papers in a scrapbook, from 1896 onwards. Among the papers are excerpts from J Plücker (Crelle’s Journal
11, 1831), papers on Steiner’s solution of the Malfatti problem (by H Schröter,
Brioschi, Beltrami, and Rudio. Schläfli’s friend Gysel and Cantor both apologise for their absence – in Cantor’s case, floods made rail travel impossible [cf. 36, p.21-22]. Curiously, Graf also describes the exhumation itself, concentrating on the shape and measurements of Steiner’s skull. Photographs of the skull are included, as ‘surely people would like to own a picture of it’ [36, p. 13].
65
“On Bicentric Polygons, Steiner Series of Circles and of Spheres, and the Invention of Inversion”
1873; W Goit, 1877; and J Petersen, 1879), and Geiser’s 1896 paper Das räumliche Sechseck und die Kummersche Fläche [7l].
As an aside, a couple of letters that Bützberger exchanged with Sidler have mathematical content as well. Sidler lent his friend mathematical books from his extensive library and pointed out further reading on the subject of the geometry of triangles, Sidler’s particular interest [7i]. In 1898 Sidler sent Bützberger a copy of a proof by Droz-Farny66 concerning a property of
triangles67
, ‘as I presume that you will take as much pleasure in it as I have’ [7j].