The Birthday of Gauss’s Disquisitiones Arithmeticae (1801)

Carl Friedrich Gauss published his masterpiece ‘Disquisitiones Arithmeticae’ on this day? Actually the publication year is 1801, but the day is unknown. This book founded modern number theory: it introduced modular arithmetic, the law of quadratic reciprocity (proved by Gauss), the theory of cyclotomic fields (constructible polygons), and the first proof of the fundamental theorem of arithmetic. Gauss also gave the first rigorous proof of the prime number theorem (though not the final form). He wrote ‘Mathematics is the queen of the sciences, and number theory is the queen of mathematics’.