Galois & Abel — Tragedy and Algebra
Two young geniuses who revolutionized algebra before dying tragically young
16.1 Niels Henrik Abel
Niels Henrik Abel (1802–1829) proved in 1824 that there is no general algebraic formula for polynomial equations of degree five or higher. He died of tuberculosis at 26, just days before a letter arrived offering him a prestigious professorship.
16.2 Évariste Galois
Évariste Galois (1811–1832) developed a complete theory explaining which equations can be solved by radicals — creating group theory. The night before his fatal duel at age 20, he wrote a letter summarizing his ideas that would transform all of algebra.
16.3 The Legacy of Group Theory
Group theory proved to be one of the most universal concepts in mathematics. Groups describe symmetry in all its forms and are essential today in particle physics, crystallography, cryptography, and pure mathematics.