Mathematics! What a demonic word is this? Mathematics means different things for different people.
To some people, it is something to be avoided at all cost. It means pain, suffering, confusion and pure torment. Maybe they think that hell is a place where its inhabitants are forced to solve mathematics problem every day for eternity where heaven is the place where all traces of mathematics is banned forever.
Many others treat is as a necessity of life. They may need it in their jobs or to pass their examinations. They treated in with “professional” respect, learn what they can with the intention to use it to advance their career to the next level.
A small minority like myself see it as pure magic. It begins from nothing. You draw some lines, curves and numbers. Put them into equations, move the components around and a whole new universe is created. This is what I called “magic”. In this article, I shall elaborate more on this phenomena call “mathematics”.
Mathematics begin when people learned how to count. I don’t know much about tribes but based on what I have learned, some tribes do not have words for numbers above a certain limit. For example, they may have words for number 1, 2 and 3 only. Number 4 onwards are classified as “many”. Based on this limited vocabulary, one can deduce that such tribe could not have planned far. As far as they have the word for the largest number.
They could not have done much engineering and will be disadvantaged at war. Imagine this, when you organise an attack on them, what you have to do is to send in say 50 soldiers to set up a camp. The next day, hide 20 of them and order the remaining 30 men to leave. The tribesmen would have interpreted it as many people came and many left. They could not tell the difference between 50 and 30. Neither could they work out that there are 20 men still hiding.
No civilisation could have existed without the knowledge of basic mathematics which involves counting and arithmetic. If any of them really existed, they would have been replaced by the process of natural selection in mathematics.
In short, any civilisation that managed to exist knows the value of mathematics. Many of them developed it independently and yet it is consistent regardless of the culture it comes from. This means that regardless of which part of the world you are from, the rules of addition, subtraction, multiplication and division are all the same.
Mathematics is therefore absolute and independent of one’s culture, geography and history. This is the opposite of religion. All civilisations also created their religions which tell them how their world was created, what can or cannot be eaten, how to live their lives, fight their wars, what type of structures they have to build for their gods etc. However, all religions differ from one another and are dependent on the culture, geography and history that created them. Therefore, unlike mathematics, all religions are relative and non-absolutes.
What this means is mathematics is the anchor of stability in the midst of a changing universe. Through mathematics, we can be assured that there are absolutes in this universe that will not be changed and independent from changes in discoveries, technology breakthroughs and trends. In mathematics, we have the rights and wrongs clearly proven and defined. What was proven right will be right forever. It is the island of stability in the midst of chaos.
One may ask, “How about other branches of science?” The difference between mathematics and other sciences like physics, chemistry and biology is mathematics consists only of deduction and the manipulations of numbers. It does not depend on experiments or observations at natural processes. This means new discoveries have no impact on the established mathematical laws.
The above phenomenon is also a drawback for mathematics itself. Since it is independent from the natural processes in the world around us, it is useless by itself. All the equations and laws created from it are useless unless we can put meanings behind those variables. The only way to do it is to conduct experiments, observations and followed by precise measurements to produce raw data. Feed it in the equations and we will have working mathematics.
Then again, how accurate are those measurements from experiments and observations? This is where the problem lies. Whatever discovery we made based on the observations today may be proved false tomorrow because tomorrow we may have better instruments or new events. Science is in constant flux. What is true today may not be so tomorrow due to new discoveries.
However, I need to stress here is that the changing portion is in the raw data that comes from observations and not from the mathematical process. The mathematical laws, once proven true are true forever.
So much for the consistency.
What I find so fascinating about mathematics is, it is purely the product of the brain. It was conceived in our brains. The sketches and equations we see on papers and boards are merely the representations of it. When I study this subject, I don’t see numbers flying around. Instead I see the thought processes that transform one state to another in a series of logical steps. You don’t even need expensive equipment like particle colliders for that. Just a pencil and a few pieces of papers , the rest is up to your brain to create your own miracle.
Mathematics had brought me much joy when I was in my pre-university days. I was fascinated by it. When I saw my teacher transforming equations on the black boards, I was mesmerised. After the final answer was out, I wanted to stand up, clap and shout in joy but I never did that because I was afraid others might think I am crazy or something. When I repeat the same process on paper and successful in completing the steps, I felt like a wizard. I have created my own magic spell. Doing mathematical exercises is like practising my magic. I felt like I was god.
Unfortunately, my priority then was to secure a place in the university, not to appreciate any subject. When the time came, I got into engineering. In case you are wondering on why not mathematics, the answer is, it is purely out of practicality. How much can an mathematics and physics graduate earn compared to an engineer?
I was not born in a rich family. So money is a high priority to me. As I think back, I wonder what would have happened if I opted for physics and mathematics instead? I don’t know.
Another quality of mathematics is it is universal and consistent even among species.
Suppose we encounter an alien civilisation. How do we deal with the first contact? We cannot assume their norm as the same as ours. We think of oxygen and water as the necessities of life but it might be toxic to their biology. We can see lights within a certain band of wavelengths but they might see it in a separate band. Then we can see what they cannot and vice versa.
The only common ground we can establish is through mathematics. The fact that these aliens can create a civilisation shows that they know some mathematics. They should have the same laws on addition, subtraction, multiplication and division. They should have the same value for pi and natural number e. They should know the meaning of prime numbers. All these can be used as the common ground to establish the first contact.
Enough of aliens. As we move forward, I believe we can progress at a faster rate if we can have a mathematician in every research team. The reason is because no other non mathematical faculties or departments in institutions of higher learning can teach all the mathematical topics to their students. They are bound to leave out certain topics that they think as irrelevant. Those irrelevant could become relevant in specific cases. It takes fully qualified mathematicians to identify that.
In having an in-house mathematicians we can have a higher chance of constructing mathematical models to analyse and confirm new discoveries. In fact, software companies and hedge funds have already begun to appreciate the importance of mathematicians in their teams. It is my hope that the rest of the economic sectors can do the same.
If you are a mathematics graduate or undergraduate reading this, I want to tell you that I am envious for being in the studies that I truly desire. However, I am not so envious of your economic prospects compared to your engineering counterparts. My wish is for the society at large to have better appreciation on our talents.