Is Mathematics Real? The Smart Question That Triggered a Vigorous Debate

​Recently, TikTok user @gracie.ham touched the ancient foundations of mathematics in-depth and asked a gem of a question: “How could someone come up with a concept like algebra?”

She also wondered what the Greek philosopher Pythagoras might have used maths for, and had other questions that gravitated around the ancient conundrum of whether mathematics is real or something humans just invented.

Many responded negatively to the post, but others, including renowned mathematicians, found the wondering rather insightful.

Is Mathematics Real?

Philosophers and mathematicians have actually been debating this for centuries. Some are inclined to believe that mathematics is universal, while others consider it man-made. Thanks to @gracie.ham, Twitter users have now joined the debate.

Part of the answer can be found in history. From one point of view, mathematics​ is a universal language used to define the world surrounding us. For instance, two cars plus three cars is always five cars, no matter the perspective.

But mathematics​ is also a language used by humans, so it is not free of culture. History shows that various cultures understood mathematics​ in their own way; however, most of this understanding is now lost. There’s one culture, though, that left numerous texts regarding their scientific knowledge.

Babylonian Mathematics​

Clay tablets from ancient Babylon have survived intact for thousands of years and are slowly being translated. What we took from them is that Babylonians were practical people who were highly educated and knew how to solve complex problems with numbers.

However, their arithmetic was rather different from ours. They did not use zero or negative numbers, and even mapped out the activity of the planets without using calculus. They knew was that the numbers 3, 4, and 5 correspond to the lengths of the sides and diagonal of a rectangle. They also knew these numbers gratified the basic relation 3² + 4² = 5² that ensures the sides are perpendicular.

The Babylonian view doesn’t use algebraic variables, theorems, axioms, and proofs simply because these theories might not have been developed back then. However, they did mathematics​ and solved problems without any of these allegedly modern concepts.

The Basics and the Rest

The Babylonians might have used their knowledge of right triangles for various purposes, but there’s no way of knowing now. There’s also evidence from ancient India and Rome suggesting that the dimensions 3-4-5 were employed as a simple but efficient way to create right angles in the construction of religious altars.

In addition, ancient Hindu religious texts provided instructions for making a rectangular fire altar using the 3-4-5 system with sides of length 3 and 4, and diagonal length 5. These measurements make sure that the altar had right angles in every corner.

Back in the 19th century, German mathematician Leopold Kronecker said: “God made the integers, all else is the work of man.”

Most mathematicians agree with this concept, at least for the positive integers, or the whole numbers we count with because the Babylonians didn’t use zero or negative numbers. Overall, mathematics​ has been used for a very long time.

Is it real, though? Most cultures agree with regards to some fundamentals, such as the positive integers and the 3-4-5 right triangle. But everything else in mathematics​ is rather set by the society in which you live.

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