Albert Einstein had once asked,“How is it possible that mathematics, a product of human thought, that is independent of experience, fits so excellently to objects of reality?”
His words seem to suggest a question that has been a raging debate since even the time of the Pythagoreans
Is mathematics an invention or a discovery?
Mathematics is a diverse language of science that has enabled mankind to understand the world we live in- like the patterns and structure found in nature as well as helped us improve our daily lives through technology.
But is math an invention of the human brain? Or does math already exist, with us simply discovering its truths?
Let’s try to answer this question in two ways:
If the universe disappeared tomorrow, along with us, 1+1 would still be equal to 2.
Mathematics is known as the natural language of science- it means that the structures of mathematics are intrinsic to the natural world. It means that even if we do not exist- mathematical truths will. It is up to us to discover mathematics- how it works and applies to the world. That assists us in gaining more knowledge about the way nature works, so that we can control it better and to our benefit. This suggests that math is discovered.
But if the universe disappeared it could also mean that there would be no mathematics at all- just like there would be no cricket, chess or an universal truth.
Mathematics can also be argued as a human expression of how we understand the universe- it is skillfully built by us to describe the world as we see it. It’s a product of the human mind and we make mathematics up as we go along to suit our purposes.
So which one is true? And is their just one true answer?
The answer doesn’t actually have to be just either. Mathematics can be both- an invention and a discovery. It can be looked upon as a combination of the two.
We invent mathematical concepts—numbers, shapes, sets, lines, and so on. We can look at them as our invention- we keep extracting them from the world around us. But we then go on to discover the complex connections among the concepts that we invent; these are the so-called theorems of mathematics.
Alternatively, 1+1=2 can be a universal truth- but to show that it’s true, a proof must be invented. This universal truth may disappear when we do- but they hold universally true as long as we don’t.
This debate over the fundamental nature of mathematics is not new, but the least we can do is to try to understand it.
What do you think mathematics is- a discovery, an invention- or both?