In this episode of The Mathematicians Podcast, Benjamin Cornish turns his attention to Apollonius of Perga—the ancient Greek mathematician whose work on conic sections shaped the way we understand curves, orbits, and even space travel. We explore Apollonius' life, his lesser-known contributions beyond geometry, and the deep mathematical ideas that earned him the nickname "The Great Geometer." From the invention of the terms ellipse, parabola, and hyperbola, to the legendary Apollonius Problem—a deceptively simple tangency puzzle with lasting implications—we trace his influence through history and into the modern age. Perfect for students, teachers, and lovers of mathematical storytelling, this episode offers technical depth, historical intrigue, and a few terrible puns on the side. Keywords: Apollonius of Perga, conic sections, ancient Greek mathematics, ellipse, parabola, hyperbola, Apollonius problem, tangency geometry, history of mathematics, mathematical storytelling Hashtags:#ApolloniusOfPerga#ConicSections#HistoryOfMathematics#GreekMathematics#Ellipse #Parabola #Hyperbola#GeometryPodcast#MathematicsEducation#AncientMathematics#TheMathematiciansPodcast#MathematicalStorytelling