Mathematics: A Discovery or Invention | Sunday Saga #1

 Mathematics describes the real world of atoms and acorns, stars and stairs. Simple abstract equations define complex physical things elegantly. Why should this be? The more I think about it, the more astonished I get.

Albert Einstein said: “The most incomprehensible thing about the universe is that it is comprehensible.” Physicist Eugene Wigner wrote of “the unreasonable effectiveness of mathematics” in science. So is mathematics invented by humans, like chisels and hammers, cars and computers, music and art? Or is mathematics discovered, always out there, somewhere, like mysterious islands waiting to be found? The question probes the deepest secrets of existence. We are going to look at this question deeply in the upcoming passages.

We are going to look at this dilemma by taking a common problem encountered by electronic board manufacturers and designers of computers. They use laser drills to make tens of thousands of holes in their boards. In order to minimize the cost, the computer designers do not want their drills to behave as "accidental tourists." Rather, the problem is to find the shortest "tour" among the holes, that visits each hole position exactly once. As it turns out, mathematicians have investigated this exact problem, known as the travelling salesman problem, since the 1920s. Basically, if a salesperson or a politician on the campaign trail needs to travel in the most economical way to a given number of cities, and the cost of travel between each pair of cities is known, then the traveller must somehow figure out the cheapest way of visiting all the cities and returning to his or her starting point. The travelling salesman problem was solved for 49 cities in the United States in 1954. By 2004, it was solved for 24,978 towns in Sweden. In other words, the electronics industry, companies routing trucks for parcel pickups, and even Japanese manufacturers of pinball-like pachinko machines (which have to hammer thousands of nails) have to rely on mathematics for something as simples drilling, scheduling, or the physical design of computers.

Is this some mischievous trick played on us, such that all the human struggles to grasp and comprehend ultimately lead to uncovering the more and more subtle fields of mathematics upon which the universe and we, its complex creatures, were all created? Is mathematics, as educators like to say, the hidden textbook the one the professor teaches from while giving his or her students a much lesser version so that he or she will seem all the wiser? Or, to use the biblical metaphor, is mathematics in some sense the ultimate fruit of the tree of knowledge? As I noted briefly at the beginning of this blog, the unreasonable effectiveness of mathematics creates many intriguing puzzles: Does mathematics have an existence that is entirely independent of the human mind? In other word, are we merely discovering mathematical verities, just as astronomers discover previously unknown galaxies? Or, is mathematics nothing but a human invention?

These are not easy questions. As I will show in this(and upcoming) blogs, even modern-day mathematicians, cognitive scientists, and philosophers don't agree on the answers. Below are some of the scientists view on this topic-

Martian Gardner, the famous author of numerous texts in recreational mathematics, also takes the side of mathematics as a discovery. To him, there is no question that numbers and mathematics have their own existence, whether humans know about them or not. He once wittily remarked: "If two dinosaurs joined two other dinosaurs in a clearing, there would be four there, even though no humans were around to observe it, and the beasts were too stupid to know it."

Carl Sagan (1934-96)  used to think that the answer to the last question was in the affirmative. In his book Cosmos, when he discussed what type of signal an intelligent civilization would transmit into space, he said: "It is extremely unlikely that any natural physical process could transmit radio messages containing prime numbers only. If we received such a message we would deduce a civilization out there that was at least fond of prime numbers."

If you think that understanding whether mathematics was invented or discovered is not that important, consider how loaded the difference between "invented" and "discovered" becomes in the question: Was God invented or discovered? Or even more provocatively: Did God create humans in his own image, or did humans invent God in their own image?

I will attempt to tackle many of these intriguing questions (and quite a few additional ones) and their tantalizing answers in my upcoming blog(so keep following my blogs). In the process, I shall review insights gained from the works of some of the greatest mathematicians, physicists, philosophers, cognitive scientists, and linguists of past and present centuries. I shall also seek the opinions, caveats, and reservations of many modern thinkers. We will start this exciting journey with the groundbreaking perspective of some of the very early philosophers.

Till then share your ideas about these questions in the comment section. And keep loving maths, have a good day😁.