Background

Abraham Gotthelf Kaestner was born on September 27, 1719, in Leipzig, Germany. His father Abraham Kaestner, a professor of jurisprudence, began early preparing him to enter that field but the young man’s interests turned to philosophy, mathematics, and physics.

Education

Kaestner studied law, philosophy, physics, mathematics and metaphysics in Leipzig from 1731.

Career

After his Habilitation at the University of Leipzig in 1739, Kaestner lectured there on mathematics, logic, and natural law as privatdozent until 1746, and then became an extraordinary professor. In 1756 he was appointed a professor of mathematics and physics at the University of Gottingen, where he remained for the rest of his life. In 1763, succeeding Tobias Mayer, he became director of the observatory as well.

Kaestner owes his place in the history of mathematics not to any important discoveries of his own but to his great success as an expositor and to the seminal character of his thought. His output as a writer in mathematics and its applications (optics, dynamics, astronomy), in the form of long works and hundreds of essays and memoirs, was prodigious. Most popular was his Mathematische Anfangsgriinde, which appeared in four separately titled parts, each going through several editions. Of lesser significance was his other four-volume work, Geschichte der Mathematik.

Achievements

• Abraham Gotthelf Kaestner went down in history as an influential figure through his writings and teaching at the University of Gottingen; Gottingen’s reputation as a center of mathematical studies dates from that time. Kaestner is also known in German literature, notably for his epigrams.
  
  From today’s point of view Kaestner’s historical significance lies mostly in the interest he promoted in the foundations of the parallel theory. The three men who independently founded non-Euclidean (hyperbolic) geometry in the early nineteenth century were all directly or indirectly influenced by Kaestner: Gauss had studied at Gottingen during Kaestner’s tenure there; Johann Bolyai’s father, Wolfgang, who personally taught his son geometry, had studied under Kaestner and had tried his own hand at proving Euclid’s postulate; Lobachevsky studied mathematics at the University of Kazan under J. M. C. Bartels, a former student of Kaestner’s.
  
  The crater Kaestner on the Moon is named after him.

Works

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  • Selbstbiographie und verzeichnis seiner schriften nebst Heyne's lobrede auf Kästner 1909
  • Geschichte der Mathematik 1796
  • Übersicht der Fortschritte verschiedener Teile der geographischen Wissenschaften 1790
  • Anfangsgruende Der Arithmetik 1774
  • Einige Vorlesungen in Der Königlichen Deutschen Gesellschaft Zu Göttingen Gehalten 1768
  • Encyklopädie Der Reinen Mathematik Und Praktischen Geometrie 1795
  • Geometrische Abhandlungen 1790
  • Epigramme 1815
  • Vermischte Schriften 1755
  • Compendieuse Physikalische Bibliothek
  • Erlaeuterungen ueber die Kaestnerische Analysis der Unendlichen 1778
  • Zum Theil noch ungedruckte Sinngedichte und Einfälle 1800
  • Aequationum Speciosarum Resolutio Newtoniana Per Series 1743

Religion

Kaestner was a devout Lutheran.

Views

As a student, Gauss is said to have shunned Kaestner’s lectures as too elementary. Yet the princeps mathematicorum shows the influence of Kaestner, not only in the matter of parallelism but in other areas as well. Kaestner opposed, as did Gauss, the concept of actual infinity in mathematics; and he felt the need, later clearly expressed by Gauss, for postulates of order in geometry. Indeed, Kaestner anticipated M. Pasch in explicitly postulating the division of the plane, by a line, into two parts, and in enunciating the needed assumptions concerning the intersections of a circle with a line or another circle.

Connections

Kaestner married Anna Rosina Baumann in 1757 after a 12-year engagement. She died on March 4, 1758, less than a year later, of lung disease. Later Kaestner had a daughter Catharine with his cleaning lady.

Father:

Abraham Kaestner

late spouse:

Anna Rosina Baumann

Daughter:

Catharine Kaestner

References

• Dictionary of Scientific Biography, Volume 7
  1973