Norbert Schappacher     Publications



2015     [XX]

Ideologie, Wissenschaftspolitik, und die Ehre, Mitglied der Akademie zu sein. Ein Fall aus dem zwanzigsten Jahrhundert.

Submitted for publication on the Document server Res doctae of the Göttingen Academy.

Substantially expanded version of a lecture at the Göttingen Academy of Sciences on 1 November 2013, i.e., shortly before the 75th anniversary of the November pogroms.


2014     [Phil / XX]

Pour une lecture continue de Hugo Dingler.

Philosophia Scientiae 18–2 (2014), 105-117 ; Erratum : Philosophia Scientiae 18–3 (2014), 269-272.

The text posted here reconstitutes my original text without the editorial deformations which occured in the issue 18–2 of Philosophia Scientiae and which are recorded in the Erratum. But the pagination of the file posted here does not match the printed version.


2012b    [Rev]  

Panorama eines Umbruchs. Die Modernisierung der Mathematik im Rückblick. Rezension von J. Gray „Plato’s Ghost“.

NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 20 (2012), 233-238.


2012a    [Conf]  

Tacit versus Explicit Knowledge in Mathematics. Conference organized by Tom Archibald, Jeanne Peiffer, N.Sch.

Oberwolfach Reports, vol. 9, no. 1 (2012), 131-210

Introduction by the organizers.


2011    [Conf]  

Felix Bernstein : a failure in emigration because he was old and difficult ?

Oberwolfach Reports, vol. 8, no. 4 (2011), 2922-2925.


2010d   [XX]  

Leo Corry & N. Sch. :

Zionist Internationalism through Number Theory. Edmund Landau at the Opening of the Hebrew University in 1925.

Science in Context  23 (4) (2010), 427-471.


2010c    [XIX / XX] 

Rewriting Points. [Invited talk, History of Mathematics section]

Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010,

pp. 3258-3291.


2010b    [XX]  

History of Mathematics in Germany, 1920 – 1960. Mini-Workshop Oberwolfach organized by Moritz Epple, Volker Remmert, N.Sch.

Oberwolfach Reports, vol. 7, no. 1 (2010), 109-140.

Introduction by the organizers 109-112; The statistician Siegfried Koller 122-123. 


2010a    [XX]  

Eckhard Wirbelauer & N. Sch. :

Zwei Siegeruniversitäten : Die Straßburger Universitätsgründungen von 1872 und 1919.

Jahrbuch für Universitätsgeschichte 13 (2010); pp. 45-72.


2009    [XVIII]  

Von Klangfarben, Predigtmaschinen und den Grenzen der Analysis bei Leonhard Euler.

In Mathesis und Graphé, Leonhard Euler und die Entfaltung der Wissenssysteme (H. Bredekamp, W. Velminski, Hrsg.), Akademie Verlag (Berlin) 2009; pp. 209-224.

See also 2007d.


2008c    [XX]   

El Congreso Bourbaki en El Escorial y otros (no) acontecimientos matématicos de 1936.

La Gaceta de la RSME 11-4 (2008), 721-735.

This is the Spanish translation by Adolfo Quirós of 2006a.


2008b    [Conf]  

How to describe the transition towards new mathematical practice : the example of Algebraic Geometry 1937 – 1954.

In Oberwolfach Reports, vol. 5, no. 2 (2008), 1301-1304.


2008a    [Phil / XX]  

Bemerkungen zu Wittgensteins Philosophie der Mathematik in ihrer Beziehung zur Mathematikgeschichte.

In M. Kross (Hrsg.): „Ein Netz von Normen“. Wittgenstein und die Mathematik.

Parerga Verlag (Berlin) 2008; pp. 199-234.


2007d     [XVIII]  

Der nahe und der ferne Euler.

Elemente der Mathematik 62 (2007), 134-154.


2007c    [XX]  

Sigrid Oehler-Klein & N. Sch. :

Siegfried Koller und die neuen Herausforderungen der Statistik im Nationalsozialismus.

In S. Oehler-Klein (Hrsg.): Die Medizinische Fakultät der Universität Gießen im National-sozialismus und in der Nachkriegszeit: Personen und Institutionen, Umbrüche und Kontinuitäten.

Franz Steiner Verlag (Stuttgart) 2007; pp. 247-262.


2007b    [XX]  

A Historical Sketch of B.L. van der Waerden’s work on Algebraic Geometry 1926 – 1946.

In J.J. Gray & K.H. Parshall (eds.) : Episodes in the History of Modern Algebra (1800-1950).

History of mathematics series, vol. 32, AMS / LMS 2007; pp. 245-283.


2007a    [XIX]  

Catherine Goldstein, N. Sch., Joachim Schwermer (eds.) :

The Shaping of Arithmetic after C.F. Gauss’s  Disquisitones Arithmeticae.

Berlin, Heidelberg, New York : Springer-Verlag 2007. Xii+578 pp.

Within this book:

2007a1

chap. I.1 

Catherine Goldstein & N. Sch. : A book in search of a discipline (1801-1860); pp. 3-65.

2007a2

chap. I.2 

Catherine Goldstein & N. Sch. : Several disciplines and a book (1860-1901); pp. 67-103.

2007a3

chap. V.2 

Birgit Petri & N. Sch. : On arithmetization; pp. 343-374.


2006c    [Rev]

Sozusagen Weihnachtsromane – Buchbesprechungen, inbesondere von D. Kehlmann Die Vermessung der Welt

Mathematische Semserberichte 53 (2006), 129-136


2006b    [XX]  

Christian Bonah, Anne Danion-Grillat, Josiane Olff-Nathan, N. Schappacher (ed.s) :

Nazisme, science et médecine.

Paris : Glyphe 2006.  366 pp.

Within this book:

2006b1

De Felix Bernstein à Siegfried Koller - des implications politiques des statisticiens  

pp. 15-40 & 291-295.


2006a   [XX]

Seventy years ago : The Bourbaki Congress at El Escorial and other mathematical (non)events of 1936.

The Mathematical Intelligencer, Special issue International Congress of Mathematicians Madrid August 2006, 8-15.

Asked for a contribution by my Spanish friends, I wrote this little piece about the politics and mathematics of 1936 for the special issue of the Mathematical Intelligencer which was distributed to all participants of the Madrid ICM in 2006. I only found out after the event that this special issue never made it to the regular subscribers of Mathematical Intelligencer; this is one more reason to post my article here.


2005d    [Rev]

Statistik – Buchbesprechungen.

Mathematische Semsterberichte 52 (2005), 251-257.


2005c    [XX]   

Felix Bernstein. 

International Statistical Review 73/1 (2005), 3-7.


2005b    [XIX-XX]

N. Sch. & Klaus Volkert:

Heinrich Weber, un mathématicien à Strasbourg 1895 – 1913.

In La science sous influence. L'université de Strasbourg, enjeu des conflits franco-allemands 1872-1945 (sous la direction d'Elisabeth Crawford et Josiane Olff-Nathan).

Strasbourg: La Nuée Bleue 2005; pp. 37-47.

This article had actually been written quite a bit earlier, the file posted here is more complete than what is printed in the book. In the meantime, I also wrote the entry on Heinrich Weber for the Nouveau Dictionnaire de Biographie Alsacienne. – The book also contains a very brief report (pp. 253-256) which we wrote with Josiane Olff-Nathan, on then recent research concerning the Nazi Reichsuniversität Strassburg (1941-1944/45). This subject was taken up again in 2006b.


2005a    [XIX]  

David Hilbert, report on algebraic number fields (“Zahlbericht”).

In I. Grattan-Guinness (ed.): Landmark Writings in Western Mathematics.

Amsterdam - Boston - etc.: Elsevier 2005; pp. 700-709.

See also 1998c; cf. 2007a3.


2004b    [XIX] 

Birgit Petri & N. Sch. :

From Abel to Kronecker. Episodes from 19th Century Algebra.

In O.A. Laudal & R. Piene (eds.): The Legacy of Niels Henrik Abel.

Berlin, Heidelberg, etc.: Springer 2004, pp. 227-266.


2004a    [XX]

Lo político en matemáticas : un intento de rastreo.

La Gaceta de la Real Sociedad Matemática Española 8/1 (2004), 129-157.

This is the Spanish translation by José Ferreirós of 2003a.


2003b     [XIX]

Welche Rolle spielt ein Klassiker in der Mathematik? Das Beispiel von C.F. Gauß’ Disquisitiones Arithmeticae.

In L. Hedendehl-Hebeker, St. Hußmann (Hrsg.): Mathematikdidaktik zwischen Fachorientierung und Empirie. Festschrift für Norbert Knoche.

Hildesheim, Berlin: Verlag Franzbecker 2003 ; pp. 177-188.


2003a     [XX]

Politisches In der Mathematik. Versuch einer Spurensuche.

Mathematische Semesterberichte 50/1 (2003), 1-27.


2002b   [Hist] 

Diophante d’Alexandrie : un texte et son histoire.

In 4000 ans d’histoire des mathématiques : les mathématiques dans la longue durée.

Actes du 13e colloque inter-IREM d’Histoire et d’Épistémologie de Mathématiques.

IREM de Rennes, 2002

This is the French translation by Frédéric Métin of 1998c2.


2002a      [XIX]  

Jacqueline Boniface & N. Sch. :

« Sur le concept de nombre en mathématique ». Cours inédit de Leopold Kronecker à Berlin (1891).

Revue d’histoire des mathematiques 7 (2001) [printed July 2002], 207-275.

The original handwritten lecture notes edited in this paper are available here. – Incidentally, an unidentified quote (see p. 240, footnote 41) has meanwhile turned up : see footnote 80 of 2007a3.


2000      [Math]

Alexander Reznikov, N. Sch. (eds.) :

Regulators in Analysis, Geometry and Number Theory.

Progress in Mathematics 171 (Birkhäuser) 2000.


1999c     [Transl]

Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorrraine Daston, Joan Beatty, Lorenz Krüger,

Das Reich des Zufalls - Wissen zwischen Wahrscheinlichkeiten, Häufigkeiten und Unschärfen.

Aus dem Englischen übersetzt von Christa Krüger und N. Sch.

Heidelberg - Berlin :  Spektrum Verlag, 1999.


1999b     [Transl]

Jürgen Neukirch:

Algebraic Number Theory.

Springer Grundlehren 322, 1999.


1999a     [Math] 

Jan Nekovar & N. Sch. :

On the asymptotic behaviour of Heegner points

Turkish Journal of Mathematics 23/4 (1999), 549-556.

This result of mathematical armchairing with Jan was still a long way from proving Mazur’s Conjecture on Heegner points. The latter was, however, established within a few years, using Ratner’s theorems on closures of unipotent flows on p-adic Lie groups, by Nike Vatsal, and by Christophe Cornut in his Strasbourg thesis.


1998f       [XIX-XX]  

On the History of Hilbert’s Twelfth Problem. A Comedy of Errors.

In Matériaux pour l'histoire des mathématiques au XXe siècle. Actes du colloque à la mémoire de Jean Dieudonné (Nice, 1996).

Séminaires et Congrès (Société Mathématique de France) 3 (1998); pp. 243-273.


1998e    [XIX-XX]  

H.G.W. Begehr, H. Koch, J. Kramer, N. Sch., E.-J. Thiele (eds. on behalf of Berliner Mathematische Gesellschaft) :

Mathematics in Berlin.

Berlin - Basel - Boston: Birkhäuser 1998.  xii+200 pp.

Apart from being coeditor, I wrote two chapters for this booklet produced for historically interested participants at the Berlin ICM:

1998e1   

Gotthold Eisenstein, 16 April 1823 - 11 October 1852; pp. 55-60.

1998e2   

The Nazi era: the Berlin way of politicizing mathematics; pp. 127-136.


1998d       [XIX-XX]  

Franz Lemmermeyer & N. Sch. :

Introduction to the first English edition of Hilbert's Zahlbericht.

In D. Hilbert, The Theory of Algebraic Number Fields.

Berlin, Heidelberg, etc.: Springer 1998; pp. XXIII - XXXVI.

See also 2005a. On some delicate points of Adamson’s translation, cf. 2007a3, p. 365.


1998c     [Hist] 

“Wer war Diophant?”

Mathematische Semesterberichte 45/2 (1998), 141-156.

This is essentially the talk I gave on 29 May 1998 at the Euler-Vorlesung in Sanssouci (Potsdam). It is an exercise in style about some basic methodological problems in the history of mathematics. I subsequently translated, reworked, and expanded the piece, but never published this improved version in print :

1998c2     [Hist]

Diophantus of Alexandria. A Text and its History.

See also 2002b.


1998b    [Math] 

Klaus Rolshausen & N. Sch. :

On the second K-group of an elliptic curve.

Journal für die reine und angewandte Mathematik 495 (1998), 61-77.


1998a     [XX] 

Beispiele und Gedanken zu den Auswirkungen des Kriegsendes auf die Mathematik in Deutschland. 

Sitzungsberichte der Berliner Mathematischen Gesellschaft 1993-1996 (published in 1998), 153-167.


1997     [XIX-XX]  

Some Milestones of Lemniscatomy.

In S. Sertöz (ed.) : Algebraic Geometry. Proceedings Bilkent Summer School, Ankara 1995.

Lecture Notes in Pure and Applied Mathematics Series 193.

New York: M. Dekker 1997; pp. 257-290.

The pdf-file linked to this entry is word-identical with the text printed in the volume, but differs in page layout.


1996    [XX]  

N. Sch. & René Schoof :

Beppo Levi and the arithmetic of elliptic curves.

Mathematical Intelligencer 18 (1996), 57-69.


1994b    [Math]

C. Kassel, J-L. Loday. N. Sch. (eds.) :

K-theory Strasbourg 1992.

Astérisque 226, 1994.


1994a    [Math]

CM motives and the Taniyama group.

In U. Jannsen, St.L. Kleiman, J.-P. Serre (eds.) : Motives.

Proceedings of Symposia in Pure Mathematics 55, part I, AMS 1994; pp. 485-508.


1993-94  [Popul]

Les 350 ans du « Grand Théorème de Fermat ».

L'Ouvert (Journal de l'A.P.M.E.P. d'Alsace et de l'I.R.E.M. de Strasbourg)

73 (déc. 1993), 1-9; 75 (juin 1994), 32-44.


1993    [XX]

Questions politiques dans la vie des mathématiques en Allemagne 1918-1935.

In La Science du Troisième Reich (sous la direction de J. Olff-Nathan).

Paris (Seuil) 1993; pp. 51-89.6.


1992   [XX]

Erhard Scholz & N. Sch. (Hrsg.) :

Oswald Teichmüller – Leben und Werk, mit Beiträgen von K. Hauser, F. Herrlich, M. Kneser, H. Opolka, N. Schappacher, E. Scholz.

Jahresbericht der Deutschen Mathematiker-Vereinigung 94 (1992), 1-39.


1991e     [Math]

N. Sch. & Anthony J. Scholl :

The boundary of the Eisenstein symbol.

Mathematische Annalen 290 (1991), 303-321 ; Erratum 290 (1991), 815.


1991d     [Math]

Les Conjectures de Beilinson pour les courbes elliptiques.

Actes des Journées Arithmétiques Luminy 1989.

Astérisque 198–199–200 (1991); pp. 305-317.


1991c    [Math]

Jean-Francois Mestre & N. Sch. :

Séries d'Eisenstein-Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q.

In van de Geer, Oort, Steenbrink (eds.) : Arithmetic Algebraic Geometry.

Progress in Mathematics 89 (Birkhäuser) 1991; pp. 209-245.

The pdf-file linked to this entry is word-identical with the text printed in the volume, but differs in page layout.


1991b     [XX]

Edmund Landau's Göttingen. From the life and death of a great mathematical center.

Mathematical Intelligencer vol. 13. no. 4 (1991), 12-18.


1991a     [XIX - XX]

Développement de la loi de groupe sur une cubique.

Séminaire de Théorie des Nombres Paris 1988/89,

Progress in Mathematics 91. Basel etc (Birkhäuser) 1991, 159-184.


1990      [XIX - XX]

N. Sch. unter Mitwirkung von Martin Kneser :

Fachverband – Institut – Staat. Streiflichter auf das Verhältnis von Mathematik zu Gesellschaft und Politik in Deutschland seit 1890 unter besonderer Berücksichtigung der Zeit des Nationalsozialismus. 

In G. Fischer, F. Hirzebruch, W. Scharlau, W. Törnig (Hrsg.) : Ein Jahrhundert Mathematik 1890-1990.

Braunschweig: Vieweg 1990; pp. 1-82.


1989      [Popul]

Neuere Forschungsergebnisse in der Arithmetik elliptischer Kurven.

Didaktik der Mathematik 17 (1989), 149-158.


1988b    [Math]

M. Rapoport, N. Sch., P. Schneider (eds.) :

Beilinson's Conjectures on L-values.

Perspectives in Mathematics 4 (Academic Press) 1988.

Within these proceedings :

1988b1 

N.Sch. & Anthony J. Scholl : Beilinson's Theorem on Modular Curves; pp. 273-304.


1988a   [Math]

Periods of Hecke Characters.

Lecture Notes in Mathematics 1301 (Springer) 1998.

Except for minor changes, this was my 1986 Göttingen Habilitationsschrift.


1987        [XX]

Das Mathematische Institut der Universität Göttingen 1929 – 1950.

In Becker, Dahms, Wegeler (ed.s) : Die Universität Göttingen unter dem National-sozialismus.

München: K.G. Saur 1987; pp. 345-373.

1998g      [XX]  

Second, enlarged edition München: K.G. Saur 1998; pp. 523-551.

As far as my chapter is concerned, there is very little difference between the two editions. But the original paper that I wrote in 1983 – my first ever on a historical subject – was much longer and somewhat different in style from what appeared in the book. I reedited this original version in 2000, and post it here.


1985b      [XX]

Max-Planck-Institut für Mathematik. Historical Notes on the New Research Institute at Bonn.

Mathematical Intelligencer 7 (1985), 41-52.


1985a     [Math]

Günter Harder & N. Sch. :

Special Values of Hecke L-functions and Abelian Integrals.

In Arbeitstagung Bonn 1984.

Lecture Notes in Mathematics 1111 (Springer) 1985; pp. 17-49.


1984c        [Pol]

Gelber Regen. Zur Geschichte einer Kampagne.

Wechselwirkung 22 (1984), 39-42.

A report on my readings – partially prompted by exchanges with Neil Koblitz – on the American campaign about communist biochemical weapons allegedly tried out in South-East Asia. Cf. J.B. Tucker’s 2001 “Lessons for arms control compliance”.


1984b      [Math]

Tate's Conjecture on the Endomorphisms of Abelian Varieties.

In G. Faltings, G. Wüstholz et al. : Rational Points, Seminar Bonn/Wuppertal 1983/84.

Aspects of Mathematics E6 (Vieweg) 1984; pp. 114-153.


1984a      [LectNotes]

John Tate :

Les conjectures de Stark sur les fonctions L d'Artin en s=0. Notes d'un cours à Orsay rédigées par Dominique Bernardi et N. Sch.

Progress in Mathematics 47 (Birkhäuser) 1984.


1983c      [Math]

Catherine Goldstein & N. Sch. :

Conjecture de Deligne et gamma-hypothèse de Lichtenbaum sur les corps quadratiques imaginaires.

CRAS Paris, t. 296 (25 Avril 1983) Sér. I, 615-618.


1983b      [Math]

L'inégalité de Lojasiewicz ultramétrique.

CRAS Paris, t. 296 (14 Mars 1983) Sér. I, 439-442.


1983a      [Math]

Propriétés de rationalité de valeurs spéciales de fonctions L attachées aux corps CM.

Séminaire de Théorie des Nombres Paris 1981/82, Progress in Mathematics 38 (Birkhäuser) 1983; pp. 267-282.


1982b      [Math]

Rationalité de valeurs spéciales de certaines fonctions L.

Séminaire de Théorie des Nombres 1981/82, exposé 23. Université de Bordeaux I, UER Mathématique.


1982a      [Math]

Une classe de courbes elliptiques à multiplication complexe.

Séminaire de Théorie des Nombres Paris 1980/81, Progress in Mathematics 22 (Birkhäuser) 1982; pp. 273-279.


1981       [Math]

Catherine Goldstein & N. Sch. :

Séries d’Eisenstein et fonctions L de courbes elliptiques à multiplication complexe.

Journal für die reine und angewandte Mathematik 327 (1981), 184-218.

As John Coates was the first to point out to us in February of 2010 (!), the very first numbered formula of the paper, i.e., the definition (1.0) of the Kronecker double series on page 186, is actually wrong : the first argument of the character χ on the right hand side has to be ω instead of z. In the sequel of the paper, the Kronecker series are almost always employed with the second argument z0 equal to 0, which makes the χ-factor disappear. This may explain why the mistake went undetected for so long.


1980       [Math]

Some Remarks on a Theorem of M.J. Greenberg.

In Proceedings of the Queen's Number Theory Conference 1979.

Queen's Papers in Pure and Applied Mathematics 54 (1980); pp. 101-113.


1978       [Math]

Eine diophantische Invariante von Singularitäten über nichtarchimedischen Körpern.

Dissertation Göttingen 1978.


1977       [Math]

Zur Existenz einfacher abelscher Varietäten mit komplexer Multiplikation.

Journal für die reine und angewandte Mathematik 292 (1977), 186-190.


Note. Only a few selected book reviews are posted on this. Between 1993 and 2006 I have written lots of others, esp. for Mathematische Semesterberichte.