Nikolai Nikolajevich Stuloff (1914–2006)

Historia Mathematica 35 (2008) 273–276 www.elsevier.com/locate/yhmat In Memoriam Nikolai Nikolajevich Stuloff (1914–2006)

The mathematician and historian of mathematics Nikolai N. Stuloff, of Mainz, Germany, was a remarkable person- ality in many respects. He was born in Moscow on 7 November 1914 (20 November in the Gregorian calendar), the youngest son of a wealthy mercantile family with close relations to the court of the Tsar. The Revolution forced the family to leave Russia in the spring of 1919. After an odyssey through several countries, the mother with four children eventually arrived in Paris, where the family was again reunited. Two years later, the Stuloffs settled in Berlin. Thanks to the ingenuity of his mother, who had studied cosmetics in Paris and established a cosmetics business with clients in wealthy Berlin circles, the family was again well-off. Nikolai, now fluent in Russian, French and German, attended the French Gymnasium. Because of his strong interest in science, he spent the last two years of his undergraduate education at the Oberrealschule am Hindenburgplatz, from which he graduated in 1934. At the Technische Hochschule in Berlin-Charlottenburg, Stuloff studied engineering, obtained his diploma in 1941, and then—against family tradition—turned to the study of mathematics at the University of Berlin. His dissertation was nearly completed at the end of World War II, when the approach of the Russian army caused the family to flee to Southern Germany. Under the extreme difficulties of a Germany divided into four occupation zones, the stateless Stuloff succeeded in finding poorly-paid engagements at the universities in Göttingen (1946) and Munich (1948). Having obtained his doctoral degree from Göttingen in December of 1947 with a dissertation on differentiation of

0315-0860/2008 Published by Elsevier Inc. doi:10.1016/j.hm.2008.07.002 274 In Memoriam / Historia Mathematica 35 (2008) 273–276 an arbitrary real order, his Habilitation followed in 1954 in Munich. There he attended courses by the well-known historian of mathematics Kurt Vogel (1888–1985); previously he had already heard lectures by Joseph Ehrenfried Hofmann (1900–1973) in Berlin during the War. These had awakened his interest in the development of mathematics. Meanwhile in 1946 the Johannes-Gutenberg-University had been founded in Mainz, where the mathematician Hans Rohrbach (1903–1993) was very interested in having history of mathematics represented within the department of mathematics. This offered Stuloff a chance for a more promising position. After having received a scholarship from the Deutsche Forschungsgemeinschaft (German Research Foundation) in 1955, he was promoted to Diätendozent for the history of mathematics in 1957, although he continued to lecture on pure mathematics until 1967. However, he now regarded as his main task transmitting to future teachers of mathematics an understanding of its historical development, in connection with pedagogical training. Eventually, a special Abteilung für Geschichte und Didaktik der Mathematik und exakten Naturwissenschaften (Division for History and Teaching of Mathematics and the Exact Sciences) was created in Mainz, and Stuloff was promoted to a professorship. Thanks to his successful teaching, Mainz was the first German university in which history of mathematics could be chosen as a minor field of study for students of mathematics. When Stuloff reached the age of retirement in 1980, no qualified successor for the combination of history and pedagogy of mathematics could be found, and so he continued to offer his courses until 1984, and in reduced form again from 1989 to 1994. Not only students from many different disciplines but also his colleagues were attracted to his fascinating lectures. The department arranged for the publication of transcripts of his lectures, so that students and teachers of mathematics would be able to profit from them on their own (see the bibliography). When Stuloff occasionally offered public lectures on general themes, the audience easily filled a large lecture hall. For him, the careful preparation of lectures was one of a professor’s foremost duties. What interested Stuloff most was how historical approaches to mathematics could assist present-day understanding of modern mathematical systems, theorems and problems. Among his publications along these lines are articles about mathematical methods in the 19th century and their interrelations with questions from physics, the concept of mathematics in the first half of the 19th century, and the philosophical critique of mathematics in this period. But the question how mathematics was understood in different historical periods also became the object of his research, as reflected in his papers about Byzantine mathematics, its philosophical and religious background and its tradition, as well as articles about the sources of the elements of mathematics of Nicolaus Cusanus and the influ- ence which Byzantine mathematics had upon him. Byzantine mathematicians, living in an era dominated by the thoughts of the Church Fathers, developed a retrospective attitude towards mathematics. They concentrated on com- mentaries and emendations of the Hellenistic heritage and did not, as modern mathematicians since the Renaissance have done, search for path-breaking new results. Stuloff further showed that the belief of Cusanus that mathematics is an excellent means for attaining higher spiritual knowledge was rooted in Byzantine texts. But Cusanus’ occupation with the problem of squaring the circle also led him to ponder the limit concept and the actual infinite, anticipat- ing ideas that later were studied by Kepler, Desargues, and Leibniz. Such considerations pioneered the way towards the ideal of the modern research mathematician whose central task is to develop new concepts, methods and theo- ries. Supported by his wife Maria, née Giani, Stuloff appointed his home on Rheinstrasse in the spa of Wiesbaden with numerous pieces of furniture and household artifacts reminiscent of the old-Russian atmosphere of his childhood. There, from 1964 on, the Stulloffs entertained colleagues, students and friends with conversations about science, literature, art, philosophy—and religion—in this very congenial setting. The couple was actively engaged, too, in the Russian-orthodox St. Elizabeth Church in Wiesbaden (built in 1847–55 in the Russian style), which was a center of Russian emigrants in the 1920s. Nikolai Stuloff, who died after a short serious illness in a hospital in Wiesbaden on 5 December 2006, will be remembered as a remarkable man who in certain ways represented a culture that perished long ago. He undoubtedly will never be forgotten by all who had the good fortune to know him.1

1 A volume with reminiscences by Fritz Krafft, a complete bibliography, and several of Stuloff’s papers will be published in the series Algorismus, edited by Menso Folkerts, in the near future. In Memoriam / Historia Mathematica 35 (2008) 273–276 275

Bibliography of Stuloff’s historical articles and lecture transcripts

1. Articles

Der Exaktheitsbegriff der Mathematik und sein Wandel in der Neuzeit [Kurt Vogel zum 70. Geburtstag]. In: Sud- hoffs Archiv 42 (1958), 245–259. Mathematische Tradition in Byzanz und ihr Fortleben bei Nikolaus von Kues. In: Rudolf Haubst (Ed.), Das Cusanus-Jubiläum in Bernkastel-Kues vom 8.–12. August 1964. Die wissenschaftlichen Referate. (Mitteilungen und Forschungsbeiträge der Cusanus-Gesellschaft, vol. 4.) Matthias Grünewald-Verlag, Mainz, 1964, pp. 420–436. Die mathematischen Methoden im 19. Jahrhundert und ihre Wechselbeziehungen zu einigen Fragen der Physik. In: Technikgeschichte 33 (1966), 52–71; reprinted in: Wilhelm Treue (Ed.), Naturwissenschaft, Technik und Wirtschaft im 19. Jahrhundert (Studien zu Naturwissenschaft, Technik und Wirtschaft im neunzehnten Jahrhundert, vol. 3) 2 parts. Vandenhoeck & Ruprecht, Göttingen, 1976, pp. 716–735. Die Herkunft der Elemente der Mathematik bei Nikolaus von Kues im Lichte der neuzeitlichen Wissenschaft. In: Mitteilungen und Forschungsbeiträge der Cusanus-Gesellschaft 6 (1968), 55–62. Über den Wissenschaftsbegriff der Mathematik in der ersten Hälfte des 19. Jahrhunderts. In: Alwin Diemer (Ed.), Beiträge zur Entwicklung der Wissenschaftstheorie im 19. Jahrhundert. Vorträge und Diskussionen im Dezember 1965 und 1966 in Düsseldorf. (Studien zur Wissenschaftstheorie, vol. 1.) Anton Hain, Meisenheim am Glan, 1968, pp. 7–89. Die Mathematik in philosophischer Kritik zu Beginn des 19. Jahrhunderts. In: XXe Congrès International d’His- toire des Sciences, Paris 1968. Actes, Tome IV: Histoire des mathématiques et de la mécanique. Librairie Scientiﬁque et Technique Albert Blanchard, Paris, 1971, pp. 171–174. Mathematik in Byzanz. In: Kurt Vogel in memoriam. Vier Vorträge von Wolfgang Kaunzner, Helmut Gericke, Karin Reich, Nikolai Stuloff. (Algorismus. Studien zur Geschichte der Mathematik und der Naturwissenschaften, No. 1.) Institut für Geschichte der Naturwissenschaften, München, 1988, pp. 39–62.

2. Lecture transcripts2

Von der antiken zur modernen Axiomatik. Mit allgemeinen Abschnitten aus der Mathematik-Geschichte. Durchge- sehene mathematik-geschichtliche Vorlesung von Prof. Dr. N. Stuloff, Winter-Semester 1973/74. Bearbeitet von F.-J. Kaesberger. Mainz, 1974, 312 pp. Die Entwicklung der Mathematik. Teil I: Von den Anfängen bis Cardano. Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im WS 1982/83. Ausgearbeitet von A[rmin] Führer. Mainz, 1989. X and 284 pp. Die Entwicklung der Mathematik. Teil II: Von Vieta bis Euler. Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im SS 1983. Ausgearbeitet von A[rmin] Führer. Mainz, 1988, VIII and 197 pp. Die Entwicklung der Mathematik. Teil III: Von Gauss bis Hilbert. Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im WS 1983/84. Ausgearbeitet von C[ornelia] Geiß. Mainz, 1989, XIV and 275 pp. Die Entwicklung der Mathematik. Teil IV: VonHilbert bis Bourbaki. Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im SS 1981. Ausgearbeitet von R[alf] Kneuper. Mainz, 1990, VIII and 113 pp. and 2 pages of bibliography. Die Geometrie im 19. Jahrhundert. [Die Entwicklung der Mathematik, Teil V.] Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im SS 1982. Ausgearbeitet von B. Rosbach. Mainz, 1994, IX and 172 pp. Entwicklung der Analysis. [Die Entwicklung der Mathematik, Teil VI.] Skriptum nach der mathematikgeschichtlichen Vorlesung von Prof. Dr. N. Stuloff im WS 1983/84. Ausgearbeitet von A[rmin] Führer. Mainz, 1994, VIII and 307 pp.

2 Imprint in all volumes: Mathematik. Mainz: Universität, Fachbereich 17, Mathematik. 276 In Memoriam / Historia Mathematica 35 (2008) 273–276

Acknowledgments

The authors are grateful to Prof. J.W. Dauben for thoroughly revising their English draft.

Fritz A. Krafft Philipps-Universität Marburg, Institut für Geschichte der Pharmazie, Roter Graben 10, D-35032 Marburg, Germany E-mail address: [email protected] Christoph J. Scriba Universität Hamburg, Geschichte der Naturwissenschaften, Bundesstr. 55, D-20146 Hamburg, Germany E-mail address: [email protected]