mathkaveli

Carl Friedrich Gauss once wrote that “Mathematics is the queen of the sciences and number theory is the queen of mathematics.” Every time I teach or revisit introductory number theory, I feel the truth of that line settle in. There is something dignified, almost royal, about working with the integers—these simple, familiar numbers that somehow hide endless surprises and patterns. In this post, I want to walk through the major ideas you would encounter in a first number theory course for math majors, and share a bit of the joy behind each topic. After all, number theory isn’t just a subject to study; it’s a subject to savor. Number theory begins with **divisibility**, and even the most basic idea that “a divides b” if b can be written as a times some integer. It feels small at first, but suddenly this tiny definition opens up entire landscapes. The Euclidean Algorithm, for example, takes two integers and dances backward through divisions to reveal the greatest common divisor. There is ...

Every November 5th, the night sky glows with bonfires and fireworks across the United Kingdom. Children recite the familiar words: Remember, remember the Fifth of November, Gunpowder, treason, and plot. I see no reason why gunpowder treason Should ever be forgot. This short rhyme—known as the Bonfire Prayer —dates back over four centuries to the failed Gunpowder Plot of 1605 , when a group of English Catholics, including Guy Fawkes , attempted to blow up the Houses of Parliament and assassinate King James I. Their goal was to end Protestant rule and restore a Catholic monarchy. The plan failed, and Fawkes was captured, tortured, and executed. From Thanksgiving to Tradition In the years that followed, November 5th became known as Guy Fawkes Night or Bonfire Night . The government declared it a national day of thanksgiving for the King’s survival. Communities lit bonfires, rang church bells, and later burned effigies of Guy Fawkes in public squares. The annual celebrati...