Major Mathematical Advances in History

In this well-written piece, Hlumelo states some of the milestones of Mathematics namely use of a zero, Geometry, Algebra, Calculus, and Infinity. He gives good content as to why a character or the body of knowledge was added to Mathematics.

Illustration by Elhamghaedi


Mathematics has taken a great deal of time and effort from various different parties across large expanses of time to become what it is today. No one person can claim the development of maths by themselves and so too was there no one event that revolutionized maths in one fell swoop. Within this essay, there will be a brief recalling of the greatest advances in mathematics.


While the use of zero within mathematics is intuitive today, there was a time when the concept of zero didn’t even exist. Before the modern-day imagining of zero, ancient Babylonians used empty spaces to indicate the early concept of zero. It was in ancient India (when) that the concept of zero was adopted and refined among Islamic mathematicians and then spread throughout the Middle East and eventually Europe. Today, zero is a fundamental part of mathematics with practical applications in every part of our lives.


At least in my opinion, geometry has to be the prettiest mathematical branch to ever be made. That being said, its origin was actually very practical and not just for artistic expression. The Egyptians used Geometry to survey and build complex structures such as the pyramids (give some time frame as to when this happened). Euclid then later formalized the rules of geometry and its study in his work. His work was then later expanded on and that produced the field of trigonometry and so on. Geometry has been a fundamental part of mathematics since near the very beginning and that is still true today. From completing the square in ancient time to modern-day computer graphics, geometry shows its undoubtable utility for us all.


Algebra is the part of mathematics that deals with symbols that represent quantities and the rules for manipulating those quantities. The earliest known use of algebra was among the ancient Babylonians who used it to solve their problems ,. Algebra has then been developed over time to help in many various fields such as engineering and physics. The development of algebra was necessitated by the unbelievable expansion of various fields that need an increasingly detailed level of understanding to maneuver and analyse. It is also an exciting field to study that many believe still holds secrets we are yet to find.


Curb-stomping brains left right and center, you may think calculus was invented only to punish the young eager 19-year-old but that isn’t the case. The desire to analyze curves in a rigorous manner had always pestered mathematicians all the way since the ancient Greeks. The field was finally properly instantiated by Isaac Newton and Gottfried Wilhelm Leibniz in the seventeenth century. The development of this field allowed mathematicians all over the globe to understand, analyse and study the nature of curves in a far more comprehensive way than ever before and has played an integral (pun intended) role in advancement of modern-day technology.

Illustration by Liani Malherbe


The concept of Infinity has fascinated humans since it was first conceived. The earliest attempts to formalize the concept were made with the intention of proving its physical impossibility. Initially, infinity was very heavily tied to subjective symbolism from various different cultures, with many believing the universe was infinite or that there were an infinite number of gods. As mathematics progressed, we got more and more insight into infinity. In the 19th century, Georg Cantor considered different sizes of infinities. By providing an explanation about physical phenomena such as black holes, the study of infinity continues to play a crucial role in mathematics and physics.


There are obviously way more leaps in mathematics worthy of recognition without a doubt however the ones documented above are some of the most impressive feats of intelligence and coalition the world has ever seen. The development of such complex concepts is proof of human ingenuity and dedication to improving our models of the world, while the relentless gathering of knowledge is a testament to the human desire for understanding and exploration. May we continue to read learn and decode the universe around us for years to come.

Hlumelo Mekuto

Student (2nd Year), Computer Science, Stellenbosch, Wilgenhof

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