In this episode of pplpod, we calculate the immense legacy of Johann Carl Friedrich Gauss, the 19th-century German scholar known as the "Prince of Mathematicians". Born into a family of low social status in Brunswick, Gauss was a child prodigy who—according to famous anecdotes—astonished his elementary teacher by instantly summing the integers from 1 to 100.
We explore his transformation from a poor student to the director of the Göttingen Observatory, a position he held until his death. We break down his most significant contributions, including his 1799 doctoral thesis on the fundamental theorem of algebra and his 1801 masterpiece, Disquisitiones Arithmeticae, which consolidated number theory as a discipline. The episode also covers his "astronomical" rise to fame after he successfully predicted the location of the dwarf planet Ceres using his newly developed method of least squares.
Beyond pure mathematics, we look at Gauss's practical inventions, such as the heliotrope for geodetic surveying and the first electromagnetic telegraph, constructed in collaboration with physicist Wilhelm Weber.
Finally, we discuss the complex personality behind the genius. We examine his rigorous perfectionism—encapsulated by his motto Pauca sed Matura ("Few, but Ripe")—which led him to withhold revolutionary work on non-Euclidean geometry because he felt it wasn't yet perfect. We also touch on his dislike of teaching and the bizarre posthumous discovery that his preserved brain had been accidentally swapped with that of a physician for over 150 years.
