[1] He discovered Korselt's criterion, which provides a secondary definition for Carmichael numbers[2] and also contributed an early result in algebraic logic.
[3] The Korselts are a huge, widespread family that has been resident in the village of Mittelherwigsdorf near Zittau in Saxony (nowadays close to the Czech and Polish borders) since the early Middle Ages.
After a probationary year as a teacher at Nikolaigymnasium in Leipzig he taught from 1891 to 1898 at various schools in Pirna, Dresden, Keilhau near Rudolstadt, Löbau and Meerane.
His first scientific publication, a voluminous review of Ernst Schröder's lectures on the Algebra of Logic, fell into this time (finished 1893).
[1] Korselt's 1902 dissertation at Leipzig University (adviser Otto Hölder) was titled Über die Möglichkeit der Lösung merkwürdiger Dreiecksaufgaben durch Winkelteilung ("On the Possibility of Solving Strange Triangle Problems by Angle Dissection").