# On This Day

• ### 12-15-1742

Euler gave the first clear statement of the Fundamental Theorem of Algebra: every algebraic equation of degree n has exactly n complex roots. Imprecise statements of the result were given earlier by Peter Roth (1608) and Albert Girard (1629). Incorrect proofs were given by d'Alembert (1746), Euler (1749), de Foncenex (1759), Lagrange (1772), and Laplace (1795), but a correct proof (and the name) had to await Gauss's doctoral dissertation of 1799. Gauss devised his proof in the fall of 1797 when he was 20.

Leonhard Euler
Carl Friedrich Gauss
The Fundamental Theorem of Algebra
• ### 12-15-1802

Janos Bolyai born in Kolozsvar, Hungary (now Cluj, Romania). Of his discoveries in non-Euclidean geometry, he would write to his father Farkas, "From nothing I have created another entirely new world."