Stretch your imagination for a minute and pretend you’re exploring the ruins of earth many years in the future, the human population has since perished, and all that is left are random artifacts in the ruins of what once was a brilliant culture. During your exploration you stumble upon a university campus and find a students differential equations textbook and homework; scary thought right? What do all those symbols represent? Was this a religious artifact? Was this artwork?
Given the scenario the question arises.. Does mathematics exist without people?
If earth remained and people vanished would gravity still have an average acceleration towards earth of 32.2 ft/s^2? Would the derivative of the function x^2 still be 2x? Yes of course relative to ‘us’; these may be concepts created relative to our system of mathematics, but is there a greater structure at hand?
Is math a vast creation of brilliant minds or is it a discovered code to our universe? The Greek philosopher Plato sided that math is discoverable, that it is what underlies the very structure of our universe. This view of the topic is known as the Platonist view. He believed a person would discover the truths independent of human observation and free of the transient nature of physical reality. The opposing view, argued by many modern professors, is that math is an invention of brilliant minds. Then there is the view that mathematics is purely a cultural artifact; which is more of a ‘realist’ theory. The view is that the unit square or a line segment is no more real than a dragon or unicorn. The theorems of math were derived merely by ‘game’ pieces used to model approximations in the so called “real world”.
Personally I don’t think the answer to the question is necessarily black or white. I believe the skeleton structure of mathematics lies somewhere in the spiritual realm of the unseen and unknown and we have discovered this structure. Although we have invented concepts and proofs based on this “mother ship” of mathematics to derive certain ideas which hold true. And when humans cease to exist the theorems, functions, and concepts left behind would be artifacts. Therefore we have discovered mathematics, invented mathematics, and some day will leave behind a cultural artifact relative to the human race which held the name mathematics.
What is your take.. is math invented, discovered, or merely a cultural artifact?
Thanks for reading.