Whether you are studying mathematics in school or university, it is always a good practice to know the history of the discipline that has come to define our lives. The history of mathematics is almost as old as humanity itself. Since ancient times, the study and understanding of mathematics have been fundamental to advances in science, engineering, and philosophy.

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Mathematics, with all its branches (algebra, arithmetic, geometry, trigonometry, and others) has evolved from simple counting, measurement, and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination, and logic, to the broad, complex, and often abstract discipline we know today.

Historical artefacts testify to the evolution of Mathematics through time. From the notched bones of early humans to the mathematical advances ushered in by settled agriculture in Mesopotamia and Egypt and the revolutionary developments in ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.

The East was never far behind. Indeed, ancient China, India, and the medieval Islamic empire were ahead of Europe in the development of certain mathematical concepts and principles, before the focus of mathematical innovation moved back to Europe in the late Middle Ages and Renaissance. Then, revolutionary developments in 17th Century and 18th Century Europe set the stage for the increasing complexity and abstraction of 19th Century mathematics. These were eventually followed by the audacious discoveries of the 20th and 21st centuries.

maths in everyday life
Mathematics is all around us, even if we are unaware of it. | Image source: Reuben Teo on Unsplash

To understand the history of modern mathematics, it is necessary to start in ancient Mesopotamia and Egypt, ancient Greece and India, and Islamic civilization from the 9th to the 15th century. These civilizations influenced one another. India’s contributions to the development of contemporary mathematics stemmed from her considerable influence on Islamic mathematics during the latter's formative years.

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History of Mathematics: An Overview

Nature has its way with mathematics, just like every other aspect of life on this planet. Soon after language develops, humans begin counting, with the fingers and thumbs acting as nature's abacus. The decimal system is no accident. Ten has been the basis of most counting systems in history. Let us explore some of the milestones in the chequered history of Mathematics.

Ancient Mathematics

Archaeological evidence suggests that prehistoric people understood simple mathematics as well as astronomy. The oldest evidence comes from the Lebombo bone, which is about 37,000 years old and was found in Swaziland. It has 29 notches carved into it, which could have been used to record numbers, making it a tally stick.

Stronger evidence comes from the Ishango bone, which was found on what is now the border between Uganda and the Democratic Republic of Congo. The Ishango bone is about 20,000 years old and has a series of notches carved into it in three columns. Patterns in these numbers show that they were probably made by someone who understood addition, subtraction, multiplication, division, and prime numbers.

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The Sumerians in southern Mesopotamia, now part of modern-day Iraq, developed a written language in about 3000 BCE. This was around the same time that they developed the first school of mathematics. People developed an understanding of geometry and algebra by about 2000 BCE, by which time Sumer had become part of Babylon.

Around this time, both the Babylonians and Ancient Egyptians were aware of π (pi), the ratio of a circle's circumference to its diameter. By about 1500 BCE, the Babylonians were also aware of Pythagoras' theorem, which shows how the lengths of the sides of right-angled triangles are related.

Progress of Mathematics in Ancient Greece and Medieval Italy

Thales and Pythagoras could be jointly hailed as the Father of Ancient Greek Mathematics. Thales was born in about 624 BCE and contributed to geometry. Both Thales and Pythagoras were inspired by the Babylonians and Ancient Egyptians.

Pythagoras was fascinated by the connections between mathematics and nature. He found comfort in the certainty that mathematical knowledge provides, especially when compared to sensory knowledge, which is sometimes unreliable. Pythagoras is thought to have been the first to discover that music can be expressed mathematically. He believed that objects in space obey the same physical laws as on Earth, and so suggested that planets create music as they follow trajectories determined by similar mathematical equations.

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Pythagoras coined the term 'mathematics', which meant 'learning', and founded a religious movement called Pythagoreanism. Pythagoreans believed that the whole universe is composed of mathematics and that numbers are real entities that do not exist in space and time. The Pythagoreans were reportedly shocked to discover irrational numbers. Irrational numbers cannot be expressed as a fraction or written down in full because they contain an infinite amount of numbers with no known repeating pattern. They considered irrational numbers to be a flaw in nature.

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pi
A study of the history of mathematics gives us interesting insights into fascinating concepts such as the pi. | Image source: Gerd Altmann from Pixabay

A century after the founding of Pythagoreanism, ancient Greek philosopher Socrates repeated Pythagoras' argument, that numbers are abstract entities that represent real things. Socrates' student, Plato, claimed that we can only be certain of knowledge that originates from the mind, not the senses, which can be tricked. Plato believed that there are two realms, the 'realm of the forms', which contains perfect concepts, and the physical realm we perceive with our senses. The physical world contains imperfect copies of the true forms.

In about 387 BCE, Plato set up an academy in Athens, which became the mathematical center of the world. Its' students included the ancient Greek philosopher Aristotle, ancient Greek astronomer Eudoxus of Cnidus, and possibly the ancient Greek mathematician Euclid. The latter made a number of discoveries in geometry shortly after 300 BCE.

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Euclid was the first to suggest that there are an infinite amount of prime numbers. Euclid's proof is contained in Elements, which became one of the most popular geometry textbooks for the next 2000 years. The concept of infinity had previously been discussed by ancient Greek philosopher Zeno of Elea. He considered how one infinity could be larger than another.

Ancient Greek astronomer Hipparchus is believed to have discovered trigonometry in about 150 BCE. Indian mathematician Brahmagupta was the first to use zero as a number in 628 CE. This was a controversial idea since it suggested that 'nothing' represented something that is real. An even stranger new number, i, was devised almost one thousand years later. i equals the square root of -1.

The laws relating to i were first introduced by the Italian mathematician Rafael Bombelli in 1572 and the symbol was introduced in the 18th century. i was first referred to as an imaginary number by Rene Descartes in 1637. Descartes and Pierre de Fermat devised the Cartesian coordinate system independently that year. This was used to plot graphs, which helped Isaac Newton and German mathematician Gottfried Leibniz develop calculus in the latter half of the century.

India's Contributions to Mathematics

The cultural milieu of the ancient Indian subcontinent had a significant impact on the evolution of mathematics. India's contribution to mathematics has a rich history going back over 3,000 years. The power of analysis and a scientific bent of mind allowed Indian thinkers to thrive for centuries before similar advances were made in Europe, China, and the Middle East.

Indian mathematics of the ancient and medieval eras not only gave the world the concept of zero, but Indian mathematicians also made seminal contributions to the study of trigonometry, algebra, arithmetic, and negative numbers. The decimal system is, perhaps, the most significant of India's contributions to the world of mathematics.

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Zero

The first recorded zeros, in what is known as the Bakhshali manuscript, were simple placeholders – a tool to distinguish 100 from 10. Similar marks had already been seen in the Babylonian and Mayan cultures in the early centuries AD and arguably in Sumerian mathematics as early as 3000-2000 BC. But only in India did the placeholder symbol for nothing progress to become a number in its own right. The advent of the concept of zero allowed numbers to be written efficiently and reliably.

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India and Maths
Ancient India contributed significantly to mathematical development with the concepts of zero and the decimal system. | Image source: Scott Rodgerson on Unsplash

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Calculus

The Kerala school of astronomy and mathematics, founded by Madhava of Sangamagrama in the 1300s, was responsible for many firsts in mathematics, including the use of mathematical induction and some early calculus-related results. Although no systematic rules for calculus were developed by the Kerala school, its proponents first conceived of many of the results that would later be repeated in Europe, including Taylor series expansions, infinitesimals, and differentiation.

Solutions of Quadratic Equations

In the 7th century, the first written evidence of the rules for working with zero was formalized in the Brahmasputha Siddhanta. In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations and for computing square roots.

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Maths Classes Online

There are many compelling reasons to study the history of mathematics. Under the guidance of online Maths teachers, school and university students can develop a deeper understanding of the mathematics they have already studied by seeing how it was developed over time and in various places. A study of the history of different branches of maths, such as geometry, algebra, or trigonometry encourages creative and flexible thinking by allowing students to see historical evidence for perfectly valid ways to view concepts and to carry out computations. Find Maths tutors near me and enrich your understanding of the fascinating discipline that is Mathematics!

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Shreyanjana

Shreyanjana is an archaeologist who ironically finds the written word to be the most powerful means of storytelling. A travel buff and a photography enthusiast, she has been writing and sharing stories of all sorts ever since she can remember.