Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla.
The earliest mathematical texts available are from Mesopotamia and Egypt – Plimpton 322 (Babylonian c. 2000 – 1900 BC) All of these texts mention the so-called Pythagorean triples.
The study of mathematics as a “demonstrative discipline” began in the 6th century BC with the Pythagoreans. Ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, and even arts and crafts.
Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus.
The origins of mathematical thought lie in the concepts of number, patterns in nature, magnitude, and form. Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in hunter-gatherer societies.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be more than 20,000 years old. It consists of a series of marks carved in three columns running the length of the bone. It may have influenced the later development of mathematics in Egypt.
It has been claimed that megalithic monuments in England and Scotland incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.