Abraham Gotthelf Kästner (27 September 1719 – 20 June 1800) was a German mathematician and epigrammatist.
He was known in his professional life for writing textbooks and compiling encyclopedias rather than for original research. Georg Christoph Lichtenberg was one of his doctoral students, and admired the man greatly. He became most well known for his epigrammatic poems. The crater Kästner on the Moon is named after him.
Kästner studied law, philosophy, physics, mathematics and metaphysics in Leipzig from 1731, and was appointed a Notary in 1733. He gained his Habilitation from the University of Leipzig in 1739, and lectured there in mathematics, philosophy, logic and law, becoming an associate professor in 1746. In 1751 he was elected a member of the Royal Swedish Academy of Sciences. In 1756 he took up a position as full professor of natural philosophy and geometry at the University of Göttingen. In 1763, succeeding Tobias Mayer, he became director of the observatory as well. One of his doctoral students was the physicist and aphorist Georg Christoph Lichtenberg, who became a colleague of his at Göttingen. Other notable doctoral students were Johann Christian Polycarp Erxleben, Johann Pfaff (doctoral adviser of Carl Friedrich Gauss), Johann Tobias Mayer, Heinrich Wilhelm Brandes, Farkas Bolyai (father of János Bolyai), and Georg Klügel. Kästner died in 1800 in Göttingen.
Johann Christian Polycarp Erxleben (22 June 1744 – 19 August 1777) was a German naturalist from Quedlinburg.
Erxleben was Professor of physics and veterinary medicine at the University of Göttingen. He wrote Anfangsgründe der Naturlehre and Systema regni animalis (1777). He was founder of the first and oldest academic Veterinary School in Germany, the Institute of Veterinary Medicine, in 1771.
He was Dorothea Christiane Erxleben’s son, who was the first woman in Germany to be promoted to a medical doctor.
Johann Friedrich Pfaff (22 December 1765 – 21 April 1825) was a German mathematician. He was described as one of Germany’s most eminent mathematicians during the 19th century. He was a precursor of the German school of mathematical thinking, which under Carl Friedrich Gauss and his followers largely determined the lines on which mathematics developed during the nineteenth century.
He received his early education at the Carlsschule, where he met Friedrich Schiller, his lifelong friend. His mathematical capacity was noticed during his early years. He pursued his studies at Göttingen under Abraham Gotthelf Kästner, and in 1787 he went to Berlin and studied practical astronomy under J. E. Bode. In 1788, Pfaff became professor of mathematics in Helmstedt, and continued his work as a professor until that university was abolished in 1810. After this event, he became professor of mathematics at the University of Halle, where he stayed for the rest of his life.
He studied mathematical series and integral calculus, and is noted for his work on partial differential equations of the first order (Pfaffian systems as they are now called) which became part of the theory of differential forms; and as Carl Friedrich Gauss’s formal research supervisor. He knew Gauss well, when they both lived together in Helmstedt in 1798. August Möbius was later his student.
His two principal works are Disquisitiones analyticae maxime ad calculum integralem et doctrinam serierum pertinentes (4to., vol. i., Helmstädt, 1797) and “Methodus generalis, aequationes differentiarum particularum, necnon aequationes differentiales vulgares, utrasque primi ordinis inter quotcumque variabiles, complete integrandi” in Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin (1814-1815).
His brother Johann Wilhelm Andreas Pfaff was a professor of pure and applied mathematics. Another brother, Christian Heinrich Pfaff, was a professor of medicine, physics and chemistry.
