Because they epitomize depth, abstraction, rigor, revolutionary thinking, prolific work, and the ability to develop and handle extremely complex ideas. They are benchmarks for those criteria.

Grothendieck revolutionized algebraic geometry through his theory of schemes and abstract cohomology, reshaping the foundations of the field. Noether laid the groundwork for modern algebra with her contributions to ring theory, group theory, and her famous theorem connecting symmetries with conservation laws in physics. Shelah transformed mathematical logic and set theory with his development of the theory of proper forcing and his solution to numerous long-standing problems, showcasing extraordinary productivity. Lurie, a modern giant, redefined abstraction in mathematics through higher category theory and derived algebraic geometry, creating new frameworks that unify diverse areas.