Ancient mathematics; the beginnings of mathematics in Greece; Archimedes and Appolinius; mathematics methods in Hellenistic times; the final chapters of Greek mathematics; medieval China and India; the mathematics of Islam; mathematics in medieval Europe; interchapter - mathematics around the world; algebra in the Renaissance; mathematical methods in the Renaissance; geometry, algebra and probability in the 17th-century; the beginnings of calculus; analysis in the 18th century; probability, algebra and geometry in the 18th century; algebra in the 19th century; analysis in the 19th century; geometry in the 19th century; aspects of the 20th century.