Is mathematics an invention or a discovery? – Whether you share my enthusiasm for mathematics or not, you cannot dispute its practicality. Its applications range from counting sheep and constructing pyramids to sending a rover to Mars, which is millions of kilometers away.
Even while these are not purely mathematical pursuits (item counting, engineering, and space travel all take place in the real world), they do provide evidence that mathematical concepts and procedures are useful in describing the physical world.
Unlike the physical sciences, mathematics does not rely on experimentation. As an illustration, a mathematician cannot examine the derivative of the tangent function in the same way that a biologist or physicist might observe and analyze cell division or planetary orbits, respectively.
The seeming contradiction between mathematics’ abstract nature and its ability to describe the world around us prompts the inquiry as to whether or not mathematics is something discovered or invented by humans. Finding the resolution to this age-old mystery could reveal more about our culture and history than it does about the development of mathematics.
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Math is innate
Because the cosmos is founded on the same order, mathematics serves as the natural language of science.
Mathematical structures exist innately in the natural world. And even if the cosmos vanished tomorrow, our timeless mathematical truths would remain.
The ability to forecast and understand the physical processes we aim to manage depends on our ability to further our understanding of mathematics and its workings. To provide a rough description, I’d call this mathematical Platonism, though it’s more of a romantic stance.
Mathematics was created by humans
Only because we made it to do so did mathematics prove to be remarkably well adapted to describing the physical world. Humans create mathematics to fit their needs as they go along; it is a product of the intellect.
Mathematical concepts and laws with related structures are entirely human inventions; if the universe were to vanish, they would disappear with it. True mathematical knowledge is created, not found. That’s the alternative view, which is not Platonism.
Math is not so successful
Those who find the widespread use of mathematics to be astounding may have been swayed by an exaggeration of the field’s achievements.
Analytical mathematical equations can only ever provide an approximation of the real world, and even then they can only ever describe a small subset of all the phenomena we observe.
Overemphasis on these results is a type of “cherry picking,” since we prefer to focus on physical problems for which we find a way to apply mathematics. This is the stance of realists.
