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Eduard Study (1862-1930) — Ein Mathematischer Mephistopheles Im Geometrischen G¨Artchen

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Eduard Study (1862-1930) — Ein Mathematischer Mephistopheles Im Geometrischen G¨Artchen Eduard Study (1862-1930) | ein mathematischer Mephistopheles im geometrischen GÄartchen Dissertation zur Erlangung des Grades Doktor der Naturwissenschaften\" am Fachbereich Mathematik der Johannes Gutenberg-UniversitÄat in Mainz Yvonne Hartwich geb. in Langen Mainz, im November 2005 Faust. Nun gut, wer bist du denn? " Mephistopheles. Ein Teil von jener Kraft Die stets das BÄose will und stets das Gute scha®t. Faust. Was ist mit diesem RÄatselwort gemeint? Mephistopheles. Ich bin der Geist, der stets verneint! \ (s. [Goethe's Faust], S. 39) Ich bin gewillt, ein BÄosewicht zu werden. \ " (s. Shakespeare's Richard III., 1 Aufzug, 1. Szene bzw. [Study 1908b], S. 125) Inhaltsverzeichnis 0 Einleitung 6 1 Prolog: Geometrie im 19. Jahrhundert als Vorgeschichte 10 1.1 Analytische vs. synthetische Geometrie . 10 1.2 Invariantentheorie . 12 1.3 Lie's Werke . 17 1.4 Grassmann und seine Werke . 20 1.5 AbzÄahlende Geometrie . 23 1.5.1 Chasles vs. de Jonqui`eres:Urheberstreit . 25 1.5.2 Halphen vs. Schubert: Debatte zweier nationaler Menta- litÄaten . 29 1.6 Liniengeometrie . 33 1.7 Axiomatik und Grundlagenkrise . 37 2 Eduard Study's Jugendzeit: Werden 41 2.1 Kindheit, Schulzeit und Studium . 41 2.2 Dissertation . 46 2.3 Preisarbeit . 48 3 Habilitation bei Klein: Gratwandern 50 3.1 Kontakte zu Klein . 50 3.2 Habilitation: Rettungsversuch der Chasles'schen Vermutung . 54 3.3 Mit Hilbert nach Paris zu Halphen . 61 4 Auf dem Weg zur Privatdozentur: Emanzipieren 65 4.1 Begegnungen mit Gordan, Engel und Lie . 65 4.2 VerÄo®entlichung der ternÄaren Formen\ als Privatdozent in Mar- " burg . 70 5 Auseinandersetzung mit Zeuthen ber die Chasles'sche Vermu- tung: Behaupten 74 5.1 Zeuthen's Briefe . 74 5.2 Study's Reaktion . 78 5.3 Abbruch durch die Redaktion der Mathematischen Annalen . 82 6 Der lange Weg zum ersten Ordinariat: Streben 90 6.1 SphÄarische Trigonometrie . 90 6.2 Amerika-Aufenthalt und Extraordinariat in Bonn . 91 6.3 Herausgabe der Grassmann'schen Werke und Artikel in der ma- thematischen EnzyklopÄadie . 95 6.4 Ordinariat in Greifswald . 100 6.5 Geometrie der Dynamen . 105 7 Die Bonner Zeit: Macht 114 7.1 Gestalten mit Personalpolitik . 114 7.2 Rezensionen der Lie'schen Werke . 122 7.3 Diskussionen mit Weyl . 130 7.4 Triumphe auf fremdem Terrain: Study's spÄate AusflugeÄ in die Philosophie . 136 7.4.1 Die realistische Weltansicht . 136 7.4.2 Mathematik und Physik . 147 7.4.3 Denken und Darstellung . 148 7.4.4 Prolegomena . 153 7.5 Emeritierung, Nachfolger und Nachrufe . 160 8 Epilog: Nachgeschichte, Vergleiche und Konsequenzen 167 8.1 Severi vs. van der Waerden: Ringen um die mathematische LÄosung der Chasles'schen Vermutung . 167 8.2 Hilbert vs. Study: Gemeinsamkeiten und GegensÄatze . 173 8.3 Polemik vs. Programmatik: Zum VerstÄandnis E. Study's . 176 9 Quellen 178 9.1 Literaturverzeichnis . 178 9.2 Archive . 201 9.3 Abbildungsnachweis . 202 4 0 Einleitung Mit Eduard Study und der Mathematikgeschichte in den Dekaden um die Jahr- hundertwende ist es wie mit dem Hase und dem Igel: Wohin man auch blickt, Study war schon da und hat etwas uberÄ das Thema geschrieben oder das bis- her dazu VerÄo®entlichte kritisiert. Trotz dieser vielseitigen PrÄasenz existierte bisher keine zusammenhÄangende mathematikhistorische Darstellung uberÄ sei- ne Person: Wurden biographische Details verÄo®entlicht, so gri® man auf den Nachruf seines besten Freundes Friedrich Engel zuruck,Ä der auch das einzige Bild enthÄalt, welches meist von Study in Umlauf ist. Thematisch bemuhenÄ sich einzelne Untersuchungen, wie z. B. [Czichowski/Fritzsche 1993] furÄ die Theo- rie der Di®erentialinvarianten oder [Wawer 1933] zum Realismusproblem, etwas mehr ins Detail zu gehen, jedoch bleiben sie gezwungenerma¼en auf ihr Thema beschrÄankt. Die wesentlichen Gesichtspunkte, die Study in seinem Leben und seinem Werk bestimmt haben, umfassend darzustellen, sie in ihren Kontext ein- zuordnen und sie erst in diesem Zusammenhang zu kommentieren, soll Ziel der vorliegenden Biographie sein, sodass nicht nur ein vollstÄandigereres Bild sondern auch ein umfassendereres VerstÄandnis von Eduard Study entstehen kann. Auf Grund der Vielzahl der Themenbereiche, die Study bearbeitet hat, sowie ihres teilweise sehr zeitspezi¯schen und somit heute nicht notwendigerweise noch prÄasenten Charakters ist der eigentlichen Lebensbeschreibung ein einfuhrendesÄ erstes Kapitel uberÄ die Geometrie im 19. Jahrhundert vorangestellt. So sehr man sich daruberÄ streiten kann, ob Study als ein Kind seiner Zeit\ anzusehen " ist, so eindeutig ist er von seinen VorgÄangern und deren Methoden beeinflusst worden: Er fuhlteÄ sich der Tradition von Monge, Poncelet, PluckerÄ und Reye ver- pflichtet und arbeitete sowohl mit der synthetischen wie auch der analytischen Methode (Kap. 1.1). UberÄ Klein kam Study in Kontakt mit der Invariantentheo- rie Clebsch-Gordan'scher PrÄagung (Kap. 1.2), der abzÄahlenden Geometrie von Chasles und Halphen1 (Kap. 1.5) und beschÄaftigte sich zusÄatzlich durch Engel's Anregung mit den Werken Lie's2 (Kap. 1.3). Schon fruhÄ begeisterte er sich furÄ Grassmann und seine Werke (Kap. 1.4); erst spÄater, aber dafurÄ nicht weniger heftig lieferte er seinen Beitrag zur Liniengeometrie (Kap. 1.63) und ereiferte sich uberÄ Axiomatik und Grundlagenkrise (Kap. 1.7). Ebenso prÄagend waren die Erfahrungen in Study's Jugendzeit, der wir uns im zweiten Kapitel widmen. Schon fruhÄ Halbwaise und somit allein vom strengen Vater erzogen, entwickelte er sich als EinzelgÄanger und somit auch meistens zum Autodidakten. An vielen verschiedenen Orten (Jena, Stra¼burg, Leipzig und Munchen)Ä studierend (Kap. 2.1), promovierte er in seiner letzten Station 1Dieses Gebiet wird sich im Folgenden sowohl inhaltlich als auch von seiner Streitkultur als so entscheidend herausstellen, dass hier eine sehr genaue Untersuchung angebracht ist. 2Da Streitigkeiten einen zentralen Topos in Study's Leben darstellen, wird hier auch auf die Auseinandersetzung zwischen Klein und Lie eingegangen werden. 3Hier werden wir auch auf die italienische Schule der algebraischen Geometrie eingehen. 5 (Kap. 2.2), wo auch durch Bearbeitung einer Preisaufgabe seine ersten Lorbeeren einheimste (Kap. 2.3). Im dritten Kapitel kommen wir mit der Habilitation bei Klein zu einer der wichtigsten Personen wie auch einem der folgenreichsten Abschnitte in Study's Leben. Dazu wird zunÄachst auf das bisherige VerhÄaltnis zu Klein eingegangen, den Study schon seit seinem ersten Aufenthalt in Leipzig schÄatzen gelernt hat- te (Kap. 3.1), bevor die eigentliche Habilitation im Jahre 1885/86 zur Spra- che kommt, nicht ohne deren ursprunglichÄ geplanten Gegenstand, den Beweis des Prinzips der Erhaltung der Anzahl, zu diskutieren (Kap. 3.2). Quasi eine Zeitreise zu dem tatsÄachlichen Gegenstand seines Habilitationsschrift, der Chas- les'schen Vermutung, stellt sein anschlie¼ender Aufenthalt in Paris zusammen mit Hilbert dar, welcher auch furÄ seine kunftigeÄ Beziehung zu diesem Mathema- tiker nicht zu vernachlÄassigen ist (Kap. 3.3). Eher eine Zwischenphase, in der Study sich seine ersten eigenen Forschungs- schwerpunkte sucht und umfassenderere Kontakte knupft,Ä stellt das vierte Kapi- tel dar. Im letztgenannten Zusammenhang stehen die Begegnungen mit Gordan, Engel und Lie (Kap. 4.1), wobei erstere aus fachlichen, die beiden anderen auch aus sozialen Gesichtspunkten gewinnbringend sind. Fast seinen gerade verstor- benen Bruder ersetzend, korrespondiert Study mit Engel ein Leben lang, was dank der fast preussisch zu nennenden akribischen Archivierung Engel's eine der wenigen und somit auch sehr wichtigen, fast tagebuchartigen Quellen darstellt. Lie hingegen entwickelte sich ein wenig als alternativer Mentor und Gegenpol zu Klein. Durch eine Privatdozentur in Marburg sich auch von Letztgenann- tem lÄosen wollend, gab Study im Jahre 1889 seine erstes dunnesÄ BuchleinÄ zu ternÄaren Formen\ heraus, vor allem in der Motivation verfasst, sich zu pro¯- " lieren und zu positionieren (Kap. 4.2). Wieder auf sein Habilitationsthema zuruckgeworfenÄ wird Study durch seine Auseinandersetzung mit Zeuthen uberÄ die Chasles'sche Vermutung zu Beginn der 1890iger Jahre, sodass diesem funftenÄ Kapitel zusammen mit dem dritten eine geradezu weichenstellende Bedeutung zukommt (und dies nicht nur, weil es sich hier um eine der bedeutendsten Debatten in den Mathematischen Annalen handelt, sondern auch in Bezug auf Study's weitere Entwicklung). Somit lohnt es sich, zunÄachst die Rolle Zeuthen's an Hand seiner Briefe an Klein genauer zu untersuchen (Kap. 5.1), vor allem auch, da sich dabei ein anderes Bild zeigt als das den Lesern der Mathematischen Annalen dargestellte. Die HintergrundeÄ sind auch bei Study's Reaktion einzubeziehen (Kap. 5.2), in der wir ein ab- solutes Paradebeispiel des Triumvirates seiner Streitkultur beobachten kÄonnen (nur diesmal in umgekehrter Reihenfolge): eigene Alternativtheorie, sachliche Kritik der vorliegenden Meinung und polemische Bemerkungen zu derselben. Die UmstÄande, die zum Abbruch durch die Redaktion der Mathematischen An- nalen (Kap. 5.3) gefuhrtÄ haben, erhellen gleichzeitig die Rolle Kleins in einer Debatte, in der mathematische oder sogar mathematikhistorische Argumente die persÄonlich-gesellschaftlichen zu verschleiern suchten. 6 Mit der Hypothek dieser Auseinandersetzung geht es in den nÄachsten Zwi- schenabschnitt (dem sechsten Kapitel), in welchem Study verzweifelt versuchte, sich zu etablieren: Sein zweites Buch uberÄ sphÄarische Trigonometrie ist wieder ein Misserfolg. Alles andere (auch seine seit 1889 bestehende kleine Familie) hinter sich
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