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Tobies, Renate:
The Mathematician Felix Klein and His Lasting Impact
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 10 (2025), fasc. n.3, p. 223-239, (English)
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Sunto

Il gentile invito a scrivere un articolo per questa rivista in occasione del centenario della morte di Felix Klein (22 giugno 2025) mi offre l'opportunità di evidenziare alcuni dei punti più importanti della vita e dell'opera di questo matematico, organizzatore scientifico e riformatore dell'istruzione. Felix Klein (1849-1925) ha spinto numerosi ricercatori ad analizzare il suo lavoro e ad esaminare la sua influenza sullo sviluppo della matematica e delle sue applicazioni. Ciononostante, c'è ancora molto di nuovo da scoprire (si vedano i recenti libri Ciesielska et al. 2025; Tobies 2025). Allo stesso tempo, ci sono ancora da correggere alcune inesattezze ed errori, dato che nella letteratura e negli archivi online leggiamo ancora informazioni errate e affermazioni congetturali.
Referenze Bibliografiche
[AdW Göttingen] Archiv der Akademie der Wissenschaften zu Göttingen.
[Oslo] Nasjonalbiblioteket, Estate of Sophus Lie I (Klein's letters to Lie).
[Paris] Bibliothèque de l'Institut de France, Faculté des Sciences de Paris, MS 2719 (Lettres de Klein à Gaston Darboux).
[Pisa] Scuola Normale Superiore Pisa, Biblioteca, Fondo Enrico Betti.
[StB Berlin] Staatsbibliothek Berlin, Sammlung Darmstaedter, Blumenthal, H 1910.
[UAG] Universitätsarchiv Göttingen.
[UBG] Niedersächsische Staats- und Universitätsbibliothek Göttingen. Handschriftenabteilung. Cod. MS. F. Klein.
[Protokolle] vols.1-29. Protocols of Klein's Mathematical Seminars.
[UBG], online: http://www.uni-math.gwdg.de/aufzeichnungen/klein-scans/klein/ ; and https://firsching.ch/klein/ , where Moritz Firsching (since the year 2014) and Henning Heller (since 2023) added biographical infos, and links.
[ZStA] Akten des Zentralen Staatsarchivs Merseburg, integriert in das Staatsarchiv Preuûischer Kulturbesitz Berlin-Dahlem (Records of the Central State Archives in Merseburg, integrated into the State Archives of Prussian Cultural Heritage in Berlin-Dahlem).
BINI, GILBERTO, ed.(2023). Algebraic Geometry between Tradition and Future. An Italian Perspective (Springer IndAM Series 53). Springer Nature. | fulltext (doi) | MR 4628113
BLUMENTHAL, OTTO (1928).`Gedenkrede auf Felix Klein." Jahresbericht der DMV 37, Abt. 2, pp.1-3.
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CIESIELSKA, DANUTA; HELLER, HENNING; TOBIES, RENATE; ZWIERZYNSKA, JOANNA eds. (2025). Felix Klein's Foreign students – Opening Up the Way for Transnational Mathematics (Trends in the History of Science). Cham: Birkhäuser/Springer Nature Switzerland. | fulltext (doi) | MR 4778703
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CREMONA, LUIGI (1992-1999). La corrispondenza di Luigi Cremona 1830-1903. 4 vols. Roma: Università degli studi di Roma `La Sapienza" (vol.1, 2); Milan: Univ. Bocconi (vol.3, 4). | MR 2307210
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EPPLE, MORITZ (1999). Die Entstehung der Knotentheorie. Braunschweig/Wiesbaden: Vieweg. | fulltext (doi) | MR 1716305
EWALD, WILLIAM (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Oxford: Oxford University Press. | MR 1465678
FANO, GINO (1894). "Sull'insegnamento della matematica nelle Università tedesche e in particolare nell'Università di Gottinga". Revista di Matematica 4, pp. 170-188. | MR 3524690
FURINGHETTI, FULVIA; GIACARDI, LIVIA eds. (2022). The International Commission on Mathematical Instruction, 1908-2008: People, Events, and Challenges in Mathematics Education. Cham: Springer Nature.
GARIO, PAOLA (2006). "Quali corsi per la formazione del docente di matematica? L'opera di Klein e la sua influenza in Italia." Bollettino dell'Unione Matematica Italiana 9-A.1, pp. 131-141. | fulltext bdim | fulltext EuDML
GIACARDI, LIVIA; LUCIANO, ERIKA; SCALAMBRO, ELENA (2023). "Gino Fano (1871-1952)." In BINI, ed. (2023), pp.137-190. | fulltext (doi) | MR 4628120
ISRAEL, GIORGIO, ed. (2017). Correspondence of Luigi Cremona (1830-1903). Rome: Brepolis.
JACOBS, KONRAD (1977). Felix Klein: Handschriftlicher Nachlass. Erlangen: Mathematisches Institut der Universität (Facsimiles and transcriptions of some of Klein's handwritten records, including Klein's Erlangen inaugural address). | MR 3362211
KAY, LESLIE D. (2023)."Felix Klein, Sophus Lie, contact transformations, and connexes." Archive for History of Exact Sciences 77, pp. 373-391. | fulltext (doi) | MR 4604371
KLEIN, FELIX (1914). "Bericht übber den gegenwärtigen Zustand des mathematischen Unterrichts an der Universität Göttingen." Jahresbericht der DMV 23, pp. 419-28. | fulltext EuDML
KLEIN, FELIX (1921/1922/1923). Gesammelte mathematische Abhandlungen, 3 Bde. [GMA I, II, III]. Berlin: Julius Springer. (https://gdz.sub.uni-goettingen.de/id/PPN237839962) | MR 389518
KLEIN, FELIX (1923a). "Göttinger Professoren (Lebensbilder von eigener Hand): Felix Klein." Mitteilungen des Universitätsbundes Göttingen 5(1), pp. 11-36. | MR 3362211
KLEIN, FELIX (1926/1927). Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Part I (ed. R. Courant and O. Neugebauer); Part II: Die Grundbegriffe der Invariantentheorie und ihr Eindringen in die mathematische Physik (ed. R. Courant and St. Cohn-Vossen). Berlin: Springer. – Engl.Trans. (only) Part I (M. Ackerman) Development of Mathematics in the 19th Century. Brookline, Mass.: Math Sci Press, 1979. – Russian Trans. Par t I Moscow/Leningrad: 1937, 21989; Part II Russian [The basic concepts of invariant theory and its penetration into mathematical physics]: Moscow-Izhevsk: Institute of Computer Studies, 2003. | MR 529278
KLEIN, FELIX (31928). Elementarmathematik vom höheren Standpunkte aus, III: Präzisions- und Approximationsmathematik. Für den Druck fertig gemacht und mit Zusätzen versehen von Fr. Seyfarth (Grundlehren der mathematischen Wissenschaften, 16). Berlin: Julius Springer (based on the autograph titled Anwendung der Differential- und Integralrechnung auf Geometrie, eine Revision der Principien (summer semester 1901, ed. Conrad Müller 1902, 21907). (First) English trans. Martha Menghini and Anna Baccaglini-Frank (2016). Elementary Mathematics from a Higher Standpoint, Vol. III: Precision Mathematics and Approximation Mathematics. Berlin/Heidelberg:Springer. | MR 225615
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POINCARÉ, HENRI (1886). "La correspondance d'Henri Poincaré avec des mathématiciens de A à H." Cahiers du séminaire d'histoire des mathématiques 1re série, tome 7, pp. 59-219. (Latest ed. NABONNAND et al. 2024). | fulltext EuDML | MR 836583
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SIEGMUND-SCHULTZE, REINHARD (2021). "The First Mathematically Serious German School of Applied Mathematics? Richard von Mises in the Field of Tension Between Pure and Engineering Mathematics in Post-WWI Berlin." In L. Mazliak and R. Tazzioli, eds., Mathematical Communities in the Reconstruction after the Great War 1918-1928. Trajectories and Institutions (Trends in the History of Science). Cham: Birkhäuser/Springer Nature Switzerland, pp. 191-225. | fulltext (doi) | MR 4240591
STUBHAUG, ARILD (2002). The Mathematician Sophus Lie: It was the Audacity of My Thinking. Trans. Richard H. Dale. Berlin: Springer. | fulltext (doi) | MR 1876528
TERRACINI, ALESSANDRO (1926). "Corrado Segre (1862-1924)." Jahresbericht der DMV 25, pp. 209-250.
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TOBIES, RENATE (2023). Felix Klein und Georg Pick Mathematische Talente fordern und fördern. Berlin: Springer Spektrum. | MR 672110
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TOBIES, RENATE; ROWE, DAVID (1990). Korrespondenz Felix Klein - Adolph Mayer. Auswahl aus den Jahren 1871 bis 1907. Leipzig: B.G. Teubner. | MR 672110
TOLLMIEN, CORDULA (1993). "Der `Kriegder Geister' in der Provinz - das Beispiel der Universität Göttingen 1914-1919." Göttinger Jahrbuch 41, pp. 137-209.
TOLLMIEN, CORDULA (2023). "Eine der schönsten Verbindungen, die zwischen der wahrnehmbaren Welt und ihrer wissenschaftlichen Beschreibung besteht" - die Noether-Theoreme (Die Lebens-und Familiengeschichte der Mathematiker in Emmy Noether in Einzelaspekten, 3). Ahrensburg: tredition. | MR 4822969
VOSS, AUREL (1919).`Felix Klein als junger Doktor." Die Naturwissenschaften 7, pp. 280-287. | fulltext (doi) | MR 1549084

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