Évariste Galois died in a duel at 20, the night after writing the foundations of group theory in a single letter

Heliocentrism

Galileo Galilei was placed under house arrest for nine years for defending heliocentrism

Tractatus Logico-Philosophicus

Tractatus Logico-Philosophicus: 'Whereof one cannot speak, thereof one must be silent.'

Grigori Perelman

Grigori Perelman solved the Poincaré conjecture

Richard Feynman's diagrams turned quantum field theory calculations from intractable algebra into picture-bookkeeping

Feynman diagrams simplified quantum field theory from complex algebra to visual bookkeeping

Emmy Noether

Emmy Noether proved Noether's theorem connecting symmetry and conservation laws

Karl Popper

Karl Popper founded the Department of Philosophy at the London School of Economics and Political Science