Humans once believed that the sun revolved around the Earth, and they were convinced that the Earth was flat, so if you sailed a boat in one direction, you would eventually fall off the edge. These theories and many others were later proven to be wrong, so how do we know our current mathematical concepts are all absolute? Are they the “truths” in mathematics or will they be proven false in the future?
Ever since we were little, we have always wondered, “what is this biggest number in the universe, infinity?” How big is it really? A billion? Trillion? Googolplex? I would try and picture how big the number really was but in the end, it would just give me a headache. After realizing that it actually had no definite amount, I gave up. But in my opinion, infinity is real. The amount of infinity, if you count forever, will never end and even though we don’t know that exact number, will always continue on.
Even though there are absolutes in mathematics, such as addition, subtraction, multiplication, and division, things such as the area of a sphere, how do we know it’s actually an area? What even is an area? Humans have made hundreds, even thousands of different rules, from multiplying exponents to calculating the volume of an object from measuring with meters or inches, but all these “laws” in mathematics which are studied by people all over the world may not have any meaning outside the human brain.
A mathematician named Euclid once said that all forms of math were found in nature, but others believed that math was definitely created by man, otherwise based on rules that we invented. Not only have we not yet figured out the secret behind how math started, but it also makes us wonder more and more about the topic, making it a definite question for students and philosophers.
Although, there are some differences between mathematics and philosophy. When we think of philosophy, we see people discussing a certain topic and their opinions on it and although math is not completely absolute, we still use the created concepts in our everyday lives. Things such as the Fibonacci sequence and the golden ratio are considered absolute because they are found in many things in the nature such as seashells.
I think of mathematics as a language… we would never say “Spanish” is true or false… it is just a system we use to describe and model their world. However, there are many unexplainable concepts and ideas brought up by mathematics so rather than solving these issues we can only explore them from various angles and that’s what makes math worth talking about.