Pioneers of Mathematics – From Pythagoras to Isaac Newton

Illustration from 1913 showing Pythagoras teaching a class of women. Many prominent members of his school were women and some modern scholars think that he may have believed that women should be taught philosophy as well as men.

Mathematics has gone a long way since its major development. Its beginnings is traced profiling scientists and philosophers who pioneered maths.

Mathematics is equated to counting, measurements and calculations. Prehistoric people counted on their fingertips, and today, computations use nanoseconds by high speed computers. Behind the study of maths are great thinkers who pioneered mathematics for what it is now. It is essential that maths courses or degrees highlight these thinkers who brought forward mathematics as another language whereby humankind can communicate.

Early Development of Mathematics, from Pythagoras to Euclid

Mathematics is a word derived from the Greek “mathema,” meaning “learning, study or science.” To reach conclusions and devise systems, it relies on the principles of logic.

A major development of mathematics came around 3000 BCE, when Egyptians developed the decimal system that made the value of pi.

Around 2100 BCE, the Babylonians put a system in place that used the number 60 as a base. This is used conveniently to divide time to hours then minutes to seconds.

Greek philosopher Pythagoras (550 BCE) defined a right triangle – the sum of the squares of the two sides must be the same as the square of the hypotenuse.

A century and a half later, the Greeks found the irrational numbers – those that could not be expressed as a ratio of two whole numbers.

Euclid, a figure in mathematics and author of The Elements, arrived around 300 BCE to devise geometry, a system defining how different figures and shapes relate to one another in space.

Archimedes and the Number Pi

About a hundred years later, Greek Archimedes discovered a constant without end. He formed 96 different sides into the approximate shape of a circle and compared the circumference to the diameter. So the number known as Pi was born. This was amazing – in which a circle’s circumference is always the same as the length of the circle’s diameter times pi.

The pi though is never exact, 3.14159… Modern computers have stretched pi for a quadrillion digits to confirm something more – that the numeral patterns on the right side of the decimal point never repeat themselves.

The Chinese Abacus and Numerical Decimal System of the Arabs

In the first century BCE, the Chinese devised their decimal system. They used sticks, and eventually invented the abacus, consisting beads arrayed on a frame device. By moving the beads, one can count in decimal divisions such as ones, tens, hundreds, etc.

By 825 BCE, the Arabs popularized the modern numerical system of zero through nine, and advanced algebra in which in equations, letters stand for unknown numbers. They also gave trigonometry, the study of right angles.

Fibonacci Numbers

Italian Leonardo Fibonacci (c. 1170-c. 1250), is regarded as the greatest mathematician of the Middle Ages. He introduced the Arabic number system around 1202. In his famous sequence (0, 1, 1, 2, 3, 5, 8, etc), the two previous numbers add up to the next one.

The significance of Fibonacci numbers is that dividing any number in the series by its predecessor (as in 5 divided by 3, for example) yields something around 1.6, called the “golden ratio.”

René Descartes, Isaac Newton and Gottfried Liebniz

In 1637, French thinker René Descartes theorized that math was an ideal model for the process of reasoning.

By late 1660s, Sir Isaac Newton invented calculus, a way to figure the rates at which different quantities change. Newton’s work was highly developed by German philosopher and mathematician, Gottfried Wilhelm Liebniz.

Mathematics in Modern Times

By 1960s, the so-called new math has bred a modern generation of mathematicians doing much more complicated tasks specific to different industries, for example, programming computers and designs for insurance policies and actuarial tables. With the advent of the Internet and latest technologies, anything is possible, including new mathematical discoveries.

Whatever evolution mathematics undergoes in the future, it is important that mathematics courses especially higher-level masters degree maths inculcate pioneers’ discoveries as foundation and philosophy, for within its various branches and mathematical applications, mathematics is an essential tool for many other scientific fields.


  1. Farndon, John, etal. The Great Scientists. London: Arcturus Publishing, 2005.
  2. Moore, Pete. E=MC². London: Quintet Publishing Ltd., 2002.