Kötter graduated in 1884 from the University of Berlin under the supervision of Karl Weierstrass and Leopold Kronecker.
[2] Kötter's treatise "Fundamentals of a purely geometrical theory of algebraic plane curves" gained the 1886 prize of the Berlin Royal Academy.
[3] In 1901, he published his report on "The development of synthetic geometry from Monge to Staudt (1847)";[4] it had been sent to the press as early as 1897, but completion was deferred by Kötter's appointment to Aachen University and a subsequent persisting illness.
[5] He constructed a mobile wood model to illustrate the theorems of Dandelin spheres.
[6][7] In a discussion with Schoenflies and Kötter, Hilbert reportedly uttered his famous quotation according to which points, lines, and planes in geometry could be named as well "tables, chairs, and beer mugs".