The word "mathematics" comes from the Greek μάθημα (máthema) which means "science, knowledge, or learning"; μαθηματικός (mathematikós) means "fond of learning". Today, the term refers to a specific body of knowledge -- the deductive study of quantity, structure, space and change.

Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments come to light only in a few locales. The most ancient mathematical texts available are from ancient India circa 1500BC-500 BC (Rigveda - Sulba Sutras) and ancient Egypt in the Middle Kingdom period circa 1300-1200 BC (Berlin 6619), Mesopotamia circa 1800 BC (Plimpton 322). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The Han Dynasty in ancient China contributed the Sea Island Manual and The Nine Chapters on the Mathematical Art from the 2nd century BC to the 2nd century AD. Ancient Greece and the Hellenistic cultures of Egypt, Mesopotamia and the city of Syracuse increased mathematical knowledge. Jain mathematicians contributed from the 4th century BC to the 2nd century AD, while Hindu mathematicians from the 5th century and Islamic mathematicians from the 9th century made major contributions to mathematics.

One striking feature of the history of ancient and medieval mathematics is that bursts of mathematical development were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an ever increasing pace, and this continues to the present day.