Journey Through the History of Mathematics

11 August, 2022

The history of mathematics is nearly as old as humanity itself. Since the beginning of time, mathematics has been essential to advancing philosophy, engineering, and science. Through abstraction, creativity, and logic, it has developed from straightforward counting, measurement, and computation to the comprehensive, intricate, and sometimes abstract subject we know today.

The history of mathematics is a long and spectacular one, starting with the notched bones of early man and extending to the mathematical innovations brought about by established agriculture in Mesopotamia and Egypt, as well as the revolutionary advancements of ancient Greece and its Hellenistic empire.

In this article, we will go over some of the most critical periods and cultures that made an impact on mathematics as we know it today:

Babylonian Mathematics
Egyptian Mathematics
Greek Mathematics
Chinese Mathematics
Modern Mathematics

Our prehistoric predecessors would have possessed a general sense of discrete quantity and understood, for example, the difference between one and two antelopes out of instinct. However, it required a very long time to make the conceptual transition from the physical concept of two items to the creation of a sign or word for the abstract idea of ”two.”

Early man kept note of recurring events like the phases of the moon and the seasons. Notched bones found in Africa between 35,000 and 20,000 years ago provide some of the first signs of human thought around numbers. But in reality, this is just counting and tallying rather than mathematics.

Who invented math first and why?

Naturally, the oldest communities of people on Earth would have been the first to discover mathematics. Some of the earliest mathematical writings have been found on ancient Egyptian papyrus. More advanced mathematics date back more than 2,500 years to ancient Greece – although we shouldn’t discount the discoveries made independently in ancient China either.

Babylonian Mathematics

Any Mesopotamian mathematics from the time of the ancient Sumerians (https://en.wikipedia.org/wiki/Sumer) to the Hellenistic era, practically to the beginning of Christianity, is referred to as Babylonian mathematics.

The majority of Babylonian mathematical work was produced between the last few centuries of the first millennium BC and the first few hundred years of the second millennium BC, known as the Old Babylonian era.

Because Babylon played a significant role as a learning center, it was given the moniker Babylonian mathematics. Later, Mesopotamia, particularly Baghdad, became a hub for Islamic mathematics research throughout the Arab Empire. In fact, this is the historical origin of Western Arabic numerals (0,1,2,3,4,5,6,7,8,9), the most commonly recognized set of symbols used to represent numbers around the world.

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Egyptian Mathematics

The old Kingdom of Egypt, in the period between 3000 and 300 BCE, until roughly the start of Hellenistic Egypt, saw the development and usage of ancient Egyptian mathematics. These concepts were used for counting and solving written mathematical problems—often including multiplication and fractions.

The few surviving documents written on papyrus are the only sources that provide evidence for mathematics in ancient Egypt.

It is known from this literature that ancient Egyptians were familiar with algebraic ideas like the false position technique and quadratic equations, as well as geometric concepts like calculating the surface area and volume of three-dimensional forms—all necessary for building and engineering.

Greek Mathematics

Greek mathematics refers to mathematical works and concepts that date back to the Archaic, Hellenistic, and Roman eras, most of which are from the 7th century BC to the 4th century AD. Greek mathematicians were dispersed throughout towns in the Eastern Mediterranean, from Italy to North Africa, yet they were bound together by Greek language and culture.

Spelled in Attic Greek as [má.tʰɛː.ma] and in Koine Greek as [ˈma.θi.ma], the name “mathematics” itself comes from Greek, Romanized as “mathima”, meaning “subject of instruction.” One significant distinction between Greek mathematics and other civilizations is the study of mathematics for its own sake and the application of broader mathematical theories and proofs.

Greek mathematics is a significant era in the history of mathematics because it was vital to geometry and the concept of formal proof. Greek mathematicians also contributed to number theory, combinatorics, mathematical physics, mathematical astronomy, and, at times, ideas that were somewhat related to integral calculus.

Archimedes, regarded as one of the most notable Greek mathematicians, is known as the “Father of Mathematics” due to his significant contribution to the development of mathematics. His contributions are being used in great vigor, even in modern times.

Chinese Mathematics

Researchers now believe that early Chinese mathematics developed fully independently after an examination of its evolution in comparison to other regions of the world revealed its distinctive nature, by the 11th century BC.

Algebra, geometry, number theory, trigonometry, and more were all independently established by the Chinese in their real number system, which also contains extremely big and negative numbers, base 2 and base 10 numeral systems, and trigonometry.

The Zhoubi Suanjing, which has been variously dated to between 1200 BC and 100 BC, is the earliest mathematical document from China that is still intact.

The Tsinghua Bamboo Slips, which dates to approximately 305 BC and may be the oldest Chinese mathematical work still in existence, has the first known decimal multiplication table.

The Chinese made significant advancements in the evaluation of polynomials beginning in the Han Dynasty, when diophantine approximation became a popular numerical technique. Since then, many people have utilized and extensively documented phrases like continuing fractions as well as algorithms like regula falsi. They purposefully locate equation roots as well as the major nth roots of positive integers.

Modern Mathematics

The range and complexity of mathematical ideas increased at an extraordinary rate throughout the 19th century. France and Germany both experienced the era of change that swept through Europe in the late 18th century, but they approached mathematics in quite different ways.

The idea of axioms as “self-evident truths” was largely abandoned to focus on such logical notions as consistency and completeness. The 20th century followed this trend of greater abstraction in mathematics.

Mathematics has developed into hundreds of specialized areas and fields of study. Some of them include knot theory, sheaf theory, topology, graph theory, functional analysis, catastrophe theory, chaos theory, model theory, category theory, game theory, complexity theory, and many more. At the same time, the profession of mathematics became significant, involving thousands of new PhDs each year and jobs in both teaching and industry.

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