Edmund Husserl began as a mathematician but turned to philosophy in search of a rigorous foundation for knowledge. He founded phenomenology, which describes how things appear to consciousness. Of Jewish origin, he was sidelined by the Nazis late in life, but he trained students such as Heidegger and Edith Stein.
Core ideas
Philosophy should describe experience as it appears, without presuppositions
All consciousness is always consciousness of something
The everyday life-world is the forgotten foundation of the sciences
The tradition: Phenomenologist
Phenomenology studies phenomena, that is, things as they appear to consciousness, describing that experience with rigor. Husserl is the founder of this method.