How does a 3700-year-old Babylonian clay tablet rewrite the history of Mathematics? What was Archimedes’ approach for approximating pi? How is Ptolemy associated with the construction of the first analog computer? "Navigating the Paths of Mathematical Thinking: From Mesopotamia to Ancient Greece", a collection of the mathematical mysteries that troubled Babylonians and Greeks thousands of years ago, provides answers to all such questions. The story of mathematics is nearly as old as that of humanity itself. Since antiquity, mathematics has been crucial to advances in science, engineering, and philosophy. From the notched bones of the early man to the mathematical progress brought about by settled agriculture in Mesopotamia and Egypt and the groundbreaking developments of ancient Greece and its Hellenistic empire, the history of mathematics is an extensive and impressive one. Although mathematics has today reached far beyond the ancient achievements, it was the conscious imitation of ancient classics like Archimedes, Apollonius, Thales, and the competition with them, that in part drove the swift rise of mathematics in the 17th century. "Navigating the Paths of Mathematical Thinking: From Mesopotamia to Ancient Greece" explores the paths of thought of all those leading figures of antiquity. It navigates through the empirical mathematics of the Babylonians and the demonstrative approaches of the ancient Greeks, who advanced mathematics from an eclectic collection of practical techniques to a coherent structure of deductive knowledge, and delivered a remarkable legacy to the modern world, greatly contributing to mathematics as we know it today.