Felix Klein

Felix Klein was born in Düsseldorf in 1849 and spent most of his working life at the University of Göttingen, where he was a dominant administrative figure alongside Hilbert. His 1872 Erlangen Program reorganised geometry around the notion of invariance under groups of transformations: each geometry is characterised by the transformations that leave its defining properties unchanged. This was a deep conceptual rearrangement whose echoes run all through twentieth-century mathematics and physics — including Noether's theorem, which is in effect an Erlangen Program for mechanics.

Klein was also a powerful advocate for improving mathematical education in Germany and for recruiting exceptional talent to Göttingen. Together with Hilbert he invited Emmy Noether to Göttingen in 1915, backed her against the faculty's refusal to appoint her, and helped bring her work on invariance in general relativity to Einstein's attention. He died in 1925, aged 76.