By Arvin Charles
Dubbed by many as the cradle of all creations, there is no doubt that mathematics is indeed the tool that built civilization to what it is today. Galileo Galilei, a famous mathematician and astronomer in the 17th century once said that mathematics was the language in which God has written the universe. This language can be observed in the most miniscule of things, be it the hexagonal structure of snowflakes falling in the winter breeze or the simple transaction when you buy your cup of coffee in the morning. Mathematics can be perceived in almost everything around us and it would be inconceivable to live in a world without it. Many great minds throughout history from the famous Pythagoras to Sir Isaac Newton, have contributed to our understanding of mathematics to date, tackling many problems and successfully finding solutions in systematic ways. That being said, there is yet one problem of sort that has puzzled the world for more than 4000 years and is still being debated without having a consensus among mathematicians and scientists – was mathematics discovered or created?
Necessity, the mother of invention.
One theory behind the epoch of mathematics that has been debated for centuries would be the notion that mathematics is the fruit of mankind’s thoughts. Mathematics could have merely been created by mankind to represent phenomena as a theoretical ideal and have no existence outside the conscious thought of humans. It could be that mathematics is simply a method in which we bring artificial order to a world of chaos. Many people deduce that mathematics is an invention due to the fact that it is not always successful. Based on a paper written by Derek Abbott, a professor from the University of Adelaide, mathematics as an invented language, only appears to be successful because we tend to select problems that we have found a way to apply mathematic principles to solve them. He also adds on by stating that there is a high chance that many mathematical models would have failed to describe a certain phenomenon but they are simply ignored.
Many people who defend the idea of mathematics being an invention also claim that certain mathematical laws like calculus were not discovered by physical means like counting or observations from the physical world, but were designed as a language to solve particular problems. For instance, to model the mechanics of motion, Newton knew that he would have to break up motion into small changes with time and observe these changes but there was no mathematical method to describe the motion of the object at any moment at his time. Hence, through trial and error, Newton foresaw the need for a whole new branch of mathematics which lead to his creation of calculus. This primitive form of calculus was then refined over centuries by adding limits and other features to what it is today.
Suppose that there were a number of rocks on a beach. If there were nobody to count them, would that number still exist? Based on Plato, a Greek philosopher and mathematician, the existence of mathematics is independent of our thoughts. In other words, mathematics would still subsists even without the presence of human beings, much like how atoms and electrons would. Hence, the more we discover mathematics and relationships between numbers and quantities, the more we unravel the mysteries of nature. This ideology is called Platonic Theory which agrees with the argument that mathematics was a discovery and it is our duty to decipher patterns and relationships to understand phenomena in nature.
A good example of mathematics being a discovery rather than an invention would be Fibonacci’s sequence. Similar to other discoveries, Fibonacci had his “Eureka” moment unexpectedly by studying the breeding of rabbits in an idealized population. Suppose a pair of rabbits mate and the female rabbit gives birth to another pair of rabbits (both male and female) at the end of every month, and the new pair of rabbits follow the same pattern monthly. The Fibonacci sequence can be derived by considering the number of rabbits at the beginning of each month which would give the sequence 1,1,2,3,5,8,13,21,34,.. which goes on forever. Fibonacci then realized that the numbers followed a certain pattern whereby the subsequent number in the sequence is the sum of the two previous numbers. Later on, Robert Simson deduced that the ratio of a number in the sequence to its previous number converges to a ratio of 1:1.618033987 to great accuracy, especially with larger numbers in the sequence. This is known as the Golden Rule and oddly enough, after the discovery of the sequence, people started noticing the Golden Rule everywhere in nature, from humble flower petals in gardens and pine cones in the forest to the colossal spiral galaxies in space. The intrinsic characteristic of mathematics in nature as shown in Fibonacci’s great sequence, further supports the fact that mathematics originated from discovery.
The argument about whether mathematics was created or discovered has been debated for centuries and is still raging on today. The hunt for the answer to the question often tends to be so deep and immersed in philosophy that they almost appear to be spiritual. Nevertheless, the question is not as important as the results we obtain from the application of mathematics. The bottom line is that as engineers, we must know the rules of the game and use mathematics to our advantage. We need not worry about the origins of mathematics but rather keep calm and calculate!