# Historical Development of Mathematics

Instructor: Kathryn Thomas

Kate teaches college math, statistics, and computer science. She has 2 master's degree: (1) computers and (2) accounting and finance.

This lesson gives a brief overview of the historical development of mathematics from pre-historic times to today. Math is a truly international creation with significant contributions from Africa, Asia, and Europe.

## History of Math

The history of math goes all the way back to pre-historic times when hunter-gatherers created words to identify one, two, or more than two animals or objects. As you can imagine, it was critical for them to know how many saber-tooth tigers were outside the cave! Archaeologists have found artifacts showing early math development in Africa that are more than 20,000 years old. Other archaeologists have found multiplication tables on clay tablets that they date to the Babylonians in 2500 BCE; some of these tablets may have even been geometry homework!

## Math During the Classical Period

Pre-historic Africans started using numbers to track time about 20,000 years ago. The Rhind Papyrus (1650 BCE) shows how ancient Egyptians worked out arithmetic and geometry problems in the first math textbook.

Babylonian mathematicians were the first known to create a character for zero. Hypatia worked with her father Theon to translate math texts into Greek. The Greeks expanded the math developed by the ancient Egyptians and Babylonians to promote a systematic study of math. Pythagoras developed his famous theorem about right triangles around 530 BCE and even inspired a religion and school that worshipped numbers.

Today's geometry textbooks are direct descendants of Euclid's Elements written by the famous Greek mathematician. Meanwhile, thousands of miles away in what would one day be Mexico, Mayan mathematicians independently developed a number system sophisticated enough to predict astronomy-related events.

## Math During the Golden Ages

### Golden Age of Chinese Mathematics

The development of math in Europe almost came to a stop during the medieval centuries but continued to progress quickly in China. Liu Hui used a 192-sided polygon to calculate the value of pi to five decimal places around 263 CE. The first abacus was probably created in China to help civil servants calculate taxes, wages, and engineering solutions. During the 13th century, Qin Jiushao used approximations to solve quadratic and cubic equations. These solutions were unknown in the West until the 17th century.

### Golden Age of Indian Mathematics

Mathematicians in India were also centuries ahead of those in Europe. Many historians believe that Pythagoras learned his geometry from an Indian textbook, the Shulba Sutras, which may have been written as early as 700 BCE. Jain mathematicians recognized different types of infinities a couple of hundred years later. Indian mathematicians were also the first to see zero as a number rather than just a placeholder and develop trigonometric concepts like sine and tangent to calculate distances. By the 12th century, Indian mathematicians developed the early foundations of calculus.

### Golden Age of Islamic Math

Mathematicians at the House of Wisdom in Baghdad began translating Greek and Indian math scrolls around 800 CE. Hindu mathematicians developed the numbers (0-9) that we still use today. Al-Khwarizmi developed many of the techniques that would later be known as algebra around 900 CE. By the 10th-century, Persians applied mathematical induction to prove theorems; about 200 years later, Persian mathematicians developed the foundations of algebraic geometry.

## Math in Renaissance Europe

European intellectual life regained momentum in the 14th century. Mathematicians in central Sudan attracted scholars from all over the world to study their work on magic squares in the early 17th century. European mathematicians also studied translations of Greek and Arab texts. In Italy, Luca Pacioli published a book of math puzzles near the end of the 1400s, while Rafael Bombelli explained how to use complex numbers combining real and imaginary numbers to solve equations in the 1500s. The math symbols for plus, minus, and so on were standardized during the Renaissance.

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