Mathematical talent can show itself early through ability in rapid computation. The story of Carl Friderich Gauss, then the youngest student in his arithmetic class, is famous. When the teacher, a certain Herr Büttner, to keep the students occupied for a long time ordered them to add all the numbers from 1 to 100, Gauss instantly threw his slate on the table with the remark “ligget se” and the number 5050. (From (n + 1)n/2. The solution was long known. How the young Gauss, who alone had the correct answer, figured it out so rapidly is left to the reader.) The fifteenth century was also an age of prodigies in languages and learning and the arts, of whom some, such as Alberti and Leonardo, amounted to something and many others did not. The most notable mathematical prodigy was Johannes Müller, born in the small Franconian town of Königsberg, according to his horoscope in 1436 on Wednesday, 6 June, at 4:40 PM, and later known, from the Latin form of Königsberg, as Regiomontanus. The horoscope published by Girolamo Cardano with its notorious interpretation is considered in the Appendix. In 1447, he computed an ephemeris of daily positions of the sun, moon, planets, and the moon’s ascending node for the year 1448, an unusual occupation for an 11-year-old; it contained no fewer than 2928 positions, most involving several tabular entries and computational steps. To the ephemeris, he added horoscopes for the entry of the sun into zodiacal signs and for true conjunctions and oppositions of the moon, but completed these fully only into March and in part through July. Throughout his life, he carried out a prodigious amount of computation, and was probably a lightning calculator, as did Gauss with the same ability; but he was far more than a calculator, for like Gauss he was also the finest mathematician of his age.