Abraham Gotthelf Kästner's father was a university professor of jurisprudence. He hoped that his son would follow in his footsteps and Kästner started out on a university course with the intention of studying the philosophy of law, but he soon found other topics more to his liking and began to concentrate more on philosophy, physics and mathematics.
Kästner wrote his habilitation thesis at the University of Leipzig, and was awarded the qualification which allowed him to teach there in 1739. He taught at the University of Leipzig as a Privatdozent until 1746 when he was appointed as an extraordinary professor. Ten years later, in 1756, he was appointed as professor of mathematics and physics at Göttingen where he succeeded to Segner's chair. He was an excellent expositor of mathematics although it is reported that Gauss did not bother to go to his lectures as he found them too elementary. However he did influence Gauss, in particular with his interest in Euclid's parallel postulate.
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Perhaps his two most famous works, both in four volumes, were Mathematische Anfangsgründe
Perhaps the most important feature of Kästner's contributions was his interest in the parallel postulate which indirectly influenced Bolyai and Lobachevsky too. Kästner taught Bolyai's father and J M C Bartels, one of Kästner's students, taught Lobachevsky. Folta writes in [
Kästner [is] among the mathematicians of the 18th century whose broad interests compelled [him] to concern [himself] with the principal problems of geometry. [His] results included new features that more precisely formulated the traditional interpretation of elementary geometry. In fact, [he] began the conscious attempt to make a precise axiomatisation of the fundamental concepts. Kästner, in spite of his rather great inclination for Euclid's Elements, based his version of the axiomatics of geometry in his Kompendium on other principles (e.g., on motions) and attempted both to seize on other fundamental properties (continuity, ordering) and to determine the selection of the parallel axiom as a foundation.The article [
Kästner is also known in German literature, notably for his epigrams. He was a devout Lutheran. Kästner married twice and had a daughter by his second wife.
Article by: J J O'Connor and E F Robertson