Was Mathematics Invented or Discovered?
As human beings, we have often begun to take for granted our ability to understand and use applied mathematics. It may sometimes be difficult to comprehend how we are capable of understanding our number systems and what they represent (albeit to varying extents) whereas all other species on this planet, as far as we are aware, do not share this apparently necessary trait. But this prompts an important question: if other organisms have not yet “discovered” mathematics, does this suggest that it was never present in the first place? If so, does this mean that maths was invented by us?
This millennia-old debate has haunted the minds of many great scientists and mathematicians alike – therefore, many different views on this have been expressed throughout the years respectively. One idea that came about was mathematical realism, which has ideas often intersecting with more complex branches of philosophy (such as Platonism, for instance).
“Mathematical realism is the view that the truths of mathematics are objective, which is to say that they are true independently from any human activities, beliefs or capacities.” Essentially, this idea supports the view that maths was discovered and not created by any means.
Realism has often been referred to as the most “natural” philosophical idea in relation to mathematics since ordinary mathematical statements do not make explicit mention to human activity, which therefore means that any arguments that go against it would have most likely been formed due to perceived flaws with the concept rather than a separately emerging idea. These arguments are often collectively referred to as “anti-realism.”
With that being said, there has been a recent increase in research done into anumeric languages that may counter realism: for linguists, “anumeric” is the term used to describe a language that does not have words for specific numbers. A great example of this is the Pirahã tribe in South America, for whom the only numeracy they need can be expressed by words meaning “a large amount” or “a small amount.” Studies conducted on the Pirahã also show that their inability to communicate numbers caused them to perform very poorly in basic numerical skills, such as counting. If this information were to be thought about logically, then it surely must be indicating that mathematics (and numeracy) was invented, as without the (mostly undisputed) invention of language that accommodates numeracy there would be none in the first place?
Another argument in favour of mathematics being invented can be credited to the Greeks: “mathema,” meaning knowledge, is the derivation of the word mathematics, and many people believe that the Greeks, building on from earlier concepts, were the “inventors” of this topic, coming up with complicated (relative to their time) ideas and ways of describing our world that are now fundamental facts that many branches of mathematical have been built upon.
However, many scientists look to the natural world instead of the human tongue or the Greek thinkers instead to find an answer to the question. Mario Livio, a leading astrophysicist at the Space Telescope Science Institute in Baltimore, comments on the symmetry of nature: “This careful selection of problems and solutions only partially accounts for mathematic’s success in describing the laws of nature. Such laws must exist in the first place! Luckily for mathematicians and physicists alike, universal laws appear to govern our cosmos…”
He goes on to say that mathematicians and physicists have invented the concept of symmetry to describe immunity to change in our universe – but the takeaway message from this is that the invention of mathematical terminology was only done due to the pre-existence (and therefore, discovery) of these fundamental laws than determine the world we live in. Physics has proven the existence of tangible laws across our universe with respect to space and time that we can represent numerically; this is to say that these factors do not alter the existence or permanence of these laws. Therefore, the existence of them has to have always been present, but later translated into equations and numbers that humans are able to comprehend.
My personal belief strongly mirrors that of the argument just described, mostly due to its lack of controversy or relative factual subjectivity. Therefore, my conclusion is that although individual mathematical terminology was, in itself, invented, this could only have been done if there was ever any need for it, such as to describe the symmetrical and solvable nature of our universe in a cohesive manner.