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Southern Asia, mathematics in Asia has a rich tradition in mathematics. Persian, Hindu, and Vedic scholars, among others in this area, contributed to the body of mathematics knowledge. Some of the achievements that have been historically credited to Arabic or Islamic mathematicians may have been influenced by pre-Islamic Persia. From ancient times, the rise and fall of various empires, wars, migration, and colonial influences have resulted in shifting cultural and geographical boundaries. As a result, many countries and regions in southern Asia have changed over time. The United Nations statistical classification for southern Asia contains Afghanistan, Bangladesh, Bhutan, India, Iran (Islamic Republic of), the Maldives, Nepal, Pakistan, and Sri Lanka. In the twenty-first century, these Asian nations continue to make advances in mathematics and mathematics education.

North Africa, mathematics in Africa, comprised of Algeria, Egypt, Libya, Morocco, Sudan, Tunisia, and Western Sahara, has long been geographically and culturally distinct from the rest of the continent because of the Sahara desert (which includes most of the region) and the proximity to southern Europe and the Middle East. The mathematics of ancient Egypt is among the oldest known mathematics traditions, and the Egyptian city of Alexandria was an important center of learning in the ancient world. Centuries later, Egyptian mathematicians were among the contributors to the Islamic Golden Age, translating classical works, which also helped bring about the Renaissance and Age of Enlightenment.

The Pythagorean school Religion Pythagorean School is the name given to a number of mathematicians and followers of Pythagoras. Pythagoras founded the school in the sixth century b.c.e. in what is now southern Italy. It appears to have been a religious sect built around the proposition that reality was revealed through numbers. It was one of the earliest philosophical schools, and at the time there were no rigid boundaries between philosophy, religion, and politics.

In Mathematics, applied the 1920s, the German military adapted, from a then recently developed business device, and began using an encryption code device known as the “Enigma” machine. Believing it to be an unbreakable encryption device, they continued to employ it into World War II. A significant effort to crack the Enigma code was undertaken, first by Polish mathematicians prior to the German invasion of Poland and then by British mathematicians at Bletchley Park, culminating in the breaking of the code in 1940. This success was instrumental in the ultimate Allied victory and in shortening the war significantly.

Our knowledge of Babylonian mathematics (2100–200 BCE) is based on extensive mathematical calculations found on clay tablets in the area of Mesopotamia (now Iraq), surrounding the ancient city of Babylon between the Tigris and Euphrates rivers. Because only a fraction of the tablets have survived—and only a small fraction of those have been translated—our knowledge of the depth and breadth of Babylonian mathematics is limited. Mathematics historian Otto Neugebauer likens the situation to tearing a few random pages out of a few textbooks and then trying to reconstruct a representation of modern mathematics. Nonetheless, Babylonian mathematics did involve complicated mathematics, and was used primarily to solve practical problems. These mathematical problems ranged from arithmetic calculations, to algebraic rules, to geometrical formulas, to numerical ideas.

Vedic Vedic mathematics mathematics is a system of mathematics associated with India’s upper Indus Valley prior to 1000 b.c.e. Originally transmitted orally, the Vedic mathematics known in the twenty-first century was abstracted from ancient Sanskrit texts, known as “Vedas.” Sri Bharati Krsna Tirthaji rediscovered the Vedas in the early 1900s, but his scholarly results were not published until 1965.

The Roman mathematics Roman period for mathematics could be said to have started when a Roman soldier was sent to seize Archimedes during the capture of Syracuse. Told by Archimedes to wait as he finished his diagrams, the soldier lost patience with the old man and slew him. The popular stereotype of the Romans is that they did little to advance Greek discoveries in mathematics, instead merely applying Greek methods to practical problems. This conception is not entirely fair. The Roman Empire was not one homogenous zone, but was rather a collection of culturally diverse provinces. For this reason, many works produced during the time of Roman rule, like the books of Ptolemy, writing in Alexandria, Egypt, are written in ancient Greek rather than Latin. Therefore, these books could be considered Greek, Roman, or Greco-Roman depending on the context. However, despite this diversity, the Roman period led to the dominance of some mathematical practices that still have an influence in the twenty-first century.