An Algebraic Number Theoretic Proof of Quadratic Reciprocity by Chuckie Namoit ’25

Gauss’s Golden Theorem: An Algebraic Number Theoretic Proof of Quadratic Reciprocity, by Chuckie Namoit ’25, Monday October 28, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: This talk presents an algebraic number theoretic proof of the Law of Quadratic Reciprocity. First discovered by Carl Friedrich Gauss, who famously referred to it as the “golden theorem,” quadratic reciprocity reveals deep insights into the solvability of quadratic equations modulo prime numbers. Gauss provided the first rigorous proof in 1796, and since then, mathematicians have discovered over 240 different proofs. This talk will present just one of these proofs and will rely heavily on concepts taught in abstract algebra.