Ferdinand Minding went to the University of Halle where he studied philology and philosophy for two semesters. While he was a school teacher, he studied for his doctorate in mathematics which was awarded by the University of Halle in 1829.
Gallery of Ferdinand Minding
Unter den Linden 6, 10117 Berlin, Germany
Minding went to the University of Berlin where he continued his studies attending courses by Georg Wilhelm Friedrich Hegel who at that time was giving courses on aesthetics, the philosophy of religion, the philosophy of history, and the history of philosophy. He also attended lectures by the historian Leopold von Ranke, who was appointed to Berlin in 1825. Ranke opposed the views of Hegel on the philosophy of history so Minding received an interestingly different approach from these two teachers. He also listened to some lectures on natural sciences and mathematics but he concentrated his studies on philosophy. He graduated in 1827.
Career
Achievements
Membership
Saint Petersburg Academy of Sciences
1864 - 1885
In 1864 Minding was elected a corresponding member and in 1879 an honorary member, of the St. Petersburg Academy of Sciences.
Ferdinand Minding went to the University of Halle where he studied philology and philosophy for two semesters. While he was a school teacher, he studied for his doctorate in mathematics which was awarded by the University of Halle in 1829.
Minding went to the University of Berlin where he continued his studies attending courses by Georg Wilhelm Friedrich Hegel who at that time was giving courses on aesthetics, the philosophy of religion, the philosophy of history, and the history of philosophy. He also attended lectures by the historian Leopold von Ranke, who was appointed to Berlin in 1825. Ranke opposed the views of Hegel on the philosophy of history so Minding received an interestingly different approach from these two teachers. He also listened to some lectures on natural sciences and mathematics but he concentrated his studies on philosophy. He graduated in 1827.
Ferdinand Minding was a German-Russian mathematician. He was a professor of mathematics at the University of Dorpat.
Background
Ferdinand Minding (full name Ernst Ferdinand Adolf Minding) was born on January 23, 1806, in Kalisz, Russian Empire (now Kalisz, Poland) to the family of Gottlieb Minding from Breslau who, at the time of Ferdinand's birth, was a lawyer in Kalisz but also a musician who was a librettist. His mother was Modesta, the daughter of Johann Valentin von Holst, a lawyer in Riga, and Caroline Colins. The family moved from Kalisz to Hirschberg in Prussian Silesia when Ferdinand was one year old since his father, Gottlieb Minding, was appointed as a judge in that city. Hirschberg is now known as Jelenia Góra and today it is a town in Poland near the Polish-Czech border.
Education
Ferdinand Minding attended Hirschberg Gymnasium, graduating with his Abitur in 1824. From there he went to the University of Halle where he studied philology and philosophy for two semesters. At this time it was typical for university students in this part of the world to spend parts of their undergraduate years at different universities and so, after his two semesters at Halle, Minding went to the University of Berlin where he continued his studies attending courses by Georg Wilhelm Friedrich Hegel who at that time was giving courses on aesthetics, the philosophy of religion, the philosophy of history, and the history of philosophy. He also attended lectures by the historian Leopold von Ranke, who was appointed to Berlin in 1825. Ranke opposed the views of Hegel on the philosophy of history so Minding received an interestingly different approach from these two teachers. He also listened to some lectures on natural sciences and mathematics but he concentrated his studies on philosophy. He graduated in 1827.
Minding had not studied mathematics at university and self-taught in mathematics having studied the subject on his own while pursuing other topics at university. While he was a school teacher, he studied for his doctorate in mathematics which was awarded by the University of Halle in 1829 for his thesis De valore integralium duplicum quam proxime inveniendo on approximating the values of double integrals. For someone to reach the level of a doctoral thesis without having been formally taught mathematics is a quite remarkable achievement.
After graduation from Berlin Minding taught in secondary schools. In 1828-29 he taught mathematics, history and German at the Gymnasium in Elberfeld. Minding published his thesis, having made some minor changes to it, in Crelle's Journal für die reine und angewandte Mathematik, as Über die Berechnung des Näherungswertes doppelter Integrale (1830).
In 1830 Minding became a mathematics lecturer at the University of Berlin where he taught the barycentric calculus as presented in the works of August Möbius and published Auflösung einiger Aufgaben der analytischen Geometrie mittels des barycentrischen Calculs (1830). He also gave lectures on number theory which he wrote up as a textbook Anfangsgrunde der hoheren Arithmetik (1832). Minding announced the publication of his book in Crelle's Journal für die reine und angewandte Mathematik in 1831.
In addition to teaching at the University, in 1834 Minding began teaching at the School of Architecture in Berlin, taking over courses that had been taught up to that time by Lejeune Dirichlet. Minding gave courses of lectures on the theory of curves, on analytical dynamics, and on analysis at the School of Architecture.
In 1842 Lejeune Dirichlet proposed Minding for election to the Berlin Academy of Science but he was not elected at this time and this may have prompted Minding to seek a position away from Berlin. An additional factor in deciding to leave Berlin must have been the fact that he had, on two occasions, attempted to gain promotion to extraordinary professor, both attempts have ended in failure. In the following year, 1843, he left Berlin when he was appointed as professor of mathematics at the University of Dorpat, a post he held for 40 years. This university was in a slightly unusual position since Estonia had been controlled by Sweden and by Russia at different periods and, at this time, it was controlled by Russia. However, teaching at the university was in the German language and, although the finance and administration of the university was from Russia, its academic leanings were towards Germany with the majority of the professors being German.
From 1843 to 1883 Minding was at the University of Dorpat as a full professor, giving both general and special courses in algebra, analysis, geometry, the theory of probability, mechanics, and physics. In 1850 the Faculty of Philosophy was divided into that of physicomathematics and that of history-philology, and in 1851 Minding was elected to a four-year term as dean of the former division. In 1864 Minding and his family became Russian citizens.
Minding’s most important discoveries were in the differential geometry of surfaces; in these works, he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss’s (1825).
Minding’s studies on the bending or the applicability of surfaces were especially remarkable. He first examined the bending of a particular class of surfaces (1838); incidentally, in the case of surfaces of revolution, he studied an example of the “applicability on a principal basis,” which later became a preferred research topic for his disciple K. M. Peterson and for Peterson’s followers in Moscow. He then proceeded to the general problem of determining the conditions for the applicability of surfaces. Gauss had discovered (1828) that if one surface can be isometrically applied to another (so that the bending does not alter the lengths of curves), then the total curvature will be the same at all corresponding points.
Minding also investigated the corresponding problem for surfaces with variable total curvature. Today “Minding’s theorem” is found in all textbooks of differential geometry. Minding’s papers, as well as Gauss’s work of 1828, were great influences on the development of this branch of mathematics. In the article “Beiträge zur Theorie der kürzesten Linien auf krummen Flächen,” which was published in Crelic’s Journal für die reine und angewandte Mathematik (1840)ю
Starting from Euler’s ideas, Minding proposed the method of solving the differential equationю Minding’s method, expounded in the paper “Beiträge zur Integration der Differential-gleichungen erster Ordnung zwischen zwei Veränderlichen,” for which he received in 1861 the Demidov Prize of the St. Petersburg Academy of Sciences, was developed further by A. N. Korkin and others. Darboux (1878) worked independently, followed by E. Picard and others, in the same direction. Minding also published works on algebra (the elimination problem), the theory of continued fractions, the theory of algebraic functions, and analytic mechanics.
Ferdinand Minding's religious views are not widely known.
Politics
Minding neither was involved in politics nor made political statements.
Views
Minding pointed out that when the trigonometric functions are replaced by corresponding hyperbolic ones, the trigonometric formulas in spherical trigonometry for the geodesic triangles on the surfaces with constant positive curvature are converted into the hyperbolic formulas for the surfaces with negative curvature. In 1837, Lobachevski showed (in an article that also appeared in Crelle’s Journal) that the same relation exists between the trigonometric formulas for the sphere and the formulas in his “imaginary” (hyperbolic) geometry. The confrontation of these results might have led to the conclusion that two-dimensional hyperbolic geometry can be (partly) interpreted as the geometry of geodesics on a surface of constant negative curvature, but it was not until 1868 that Beltrami established this connection.
In his article “Wie sich entscheiden lässt, ob zwei gegebene krumme Flächen auf einander abwickelbar sind oder nicht …” (1839), Minding stated the following sufficient condition for applicability: Two given surfaces of equal constant total curvature are applicable to one another isometrically, and this can be done in infinitely many different ways.
Membership
In 1864 Minding was elected a corresponding member and in 1879 an honorary member of the St. Petersburg Academy of Sciences.
Saint Petersburg Academy of Sciences
,
Russia
1864 - 1885
Interests
Philosophers & Thinkers
Carl Friedrich Gauss
Connections
In 1836 Ferdinand Minding married Auguste Regle in Berlin. Auguste was the daughter of Carl August Regler and Henriette Kempsky. Ferdinand and Auguste Minding had one son, Karl Bernhard Minding (born 1839), and two daughters.