Ancient Greek mathematics represents one of humanity's most important intellectual achievements, fundamentally transforming how we understand and approach mathematical knowledge. Beginning in the 6th century BCE with figures like Thales and Pythagoras, Greek mathematicians revolutionized the field by shifting from practical computation to rigorous logical proof, establishing mathematics as a deductive science built upon axioms and theorems. Euclid's Elements, composed around 300 BCE, codified this approach in a systematic framework that remained the standard geometry textbook for over two millennia. Greek mathematicians made groundbreaking discoveries across multiple domains: Archimedes calculated areas and volumes using methods anticipating integral calculus, Apollonius developed the theory of conic sections, Eratosthenes measured the Earth's circumference with remarkable accuracy, and Diophantus pioneered algebraic methods for solving equations.
Beyond specific discoveries, the Greeks established the crucial principle that mathematical statements must be proven rather than merely observed or assumed, creating the foundation for all subsequent mathematical development. Their emphasis on logical rigor, systematic organization, and abstract reasoning not only shaped mathematics but influenced the entire Western intellectual tradition, making Greek mathematics indispensable to the emergence of modern science and philosophy.
The image in the header is from a page of the Latin translation by William of Moerbeke, ca. 1270 of Archimedes On the Sphere and Cylinder. You'll find these pages on 36v,37r. The manuscript is housed at the Vatican Library (Ott.lat.1850) and is available online. Like many old manuscripts it is bound with other material so don't expect the mathematical text to be at the font of the book.