Encyclopedias of various countries in references to B. L. Van der Waerden characterize him as an outstanding mathematician who predetermined the leading trends in the development of algebra of the 20th century. He was engaged in the application of the apparatus of algebra to the rigorous substantiation of algebraic geometry, and successfully used the methods of group theory to solve problems in topology, theoretical physics, and quantum mechanics. However, for historians of science, the name of B. L. Van der Waerden is associated with completely different results: he gained fame as a thoughtful source scholar and interpreter of ancient, primarily cuneiform, scientific texts. As if competing with Otto Neugebauer, his older contemporary, a native of Innsbruck, who has been constantly working in the USA since 1939, Van der Waerden opened many unknown pages in the history of the exact sciences of the ancient world. In the book "Awakening Science II. The Birth of Astronomy" worldwide the famous mathematician paints a picture of the development of astronomy in Ancient Egypt and Babylon. He relies on hard-to-find evidence from papyrus and cuneiform texts, including observations of the rising of Sirius, the rising and setting of Venus, and the mathematical theory of the Moon and planets. Considerable attention is paid to astrology and the influence of the astral religions of Ancient Mesopotamia on the relationship between the mathematical astronomy of the Babylonians and astrology, as well as the general influence of Babylonian science on the astronomy of Ancient Greece, early Indian astronomy and the astronomy of the Hellenistic era.