It all began, supposedly, when humans first needed to keep track of their possessions. But it never ceases to amaze me how something that began with markings of 4 lines with a fifth striking across them, has become so powerful and fundamental that it rules our life and our intellect. It is mathematics and everything from your computer to money and rockets counts on math to work. Yet what a lot of us may not know is that math has its own Achilles’ heel.
First, the glory of math can never be sufficiently captured and expressed. It is simply everything and everywhere. This is because math is not merely a discipline or study – it is a way of life and the thing that makes us rulers of the planet. To think is often to be a mathematician albeit we seldom realize this. We count things, measure physical attributes and weigh alternatives. All of this is basically mathematics. But this is only what mathematics is, and not what it gives us. The applications of mathematics are limitless. It can help you figure out how probable it is that you win the lottery, how much a diet-conscious person should eat every day, how the job prospects are given the state of the economy and what makes the universe the way it is. A lot of the greatest intellects ever have been mathematicians – Newton, Einstein, Galileo and to mention our very own genius – Ramanujan. So what is it that makes mathematics what it is? To me, it is the fact that everything mathematical is logical and rational. There is no room for exceptions at all, although we will later consider how a very important theorem – a product of mathematics itself is its own nemesis. But when it comes to comparison with the sciences it becomes clearer. Physics is rife with approximations – hardly anything is actually what it predicts it will be. (This is obviously because the real world is so complex – physics does an amazing job nevertheless as long as the minute differences can be neglected.) Chemistry has always been my least favorite – there are exceptions and unexplained phenomenon or often it just goes back to physics to help itself out. For example, I have never been able to figure out why oxygen exists as O2 yet carbon is just C (Or maybe it’s just that I have not learnt enough). But rules in mathematics are hardly ever broken and that’s because everything is logically related to what mathematicians call axioms – the irrefutable truths that do not require proof.
But since the 20th century math has been suffering from a plague. In 1931, a brilliant and enigmatic mathematician by the name of Kurt Gödel conclusively proved that math is not perfect. In simple terms, Gödel showed that there could be no mathematical theory that was complete and consistent (with its axioms). It was a death blow to the perfection of math and at the time it was proved, people just outright declared that Gödel was insane. Yet, it is now widely accepted to be as true and as fundamental to math as arithmetic. But this in no way means that math is worthless or useless – it just means that there cannot be an all-encompassing formal math theory that can prove everything.
The most extraordinary thing is that we don’t even know where math exists. It is all in our intellects – an abstraction so ideal it is impossible for anyone to see the real mathematical circle, point or the number 4. Mathematics is an enigma to most, including me, but it inspires great awe in me that it is what rules our lives. As Gauss once remarked, “God does arithmetic”.
[Image courtesy: http://www.mostlymath.com/images/at-the-blackboard.jpg]