While at Gottingen, this man served as a doctoral adviser to Grace Chisholm Young, the first female mathematics Ph.D. recipient there.
orientation-preserving automorphisms exist for this man's namesake Riemann surface quartic. This man proposed classifying geometries according to group theory and projective geometry in his 1872 manifesto, the Erlangen program. While at Gottingen, this man served as a doctoral adviser to Grace Chisholm Young, the first female mathematics Ph.D. recipient there. An immersion of another object named for this man resembles a twisted figure 8. That object only requires six colors for map coloring, making it the sole exception to the Heawood conjecture, and is a one-sided 2-manifold with no boundary that is non-orientable, like the Mobius strip. For 10 points, name this German mathematician who devised a namesake bottle.
orientation-preserving automorphisms exist for this man's namesake Riemann surface quartic.
Felix Klein [or Christian Felix Klein]