An Ode to Mathematics
I was standing on the balcony of my friend's apartment staring out over an empty Johannesburg street. Usually full and bustling with energy, this night was eerily still. Everyone, it seemed, had migrated down to the coast to take advantage of the beach weather for the holiday period. The wind played wistfully around us, bringing a chill that was completely out of place on a summer evening. The lack of streetlights made the night seem damper and dingier than usual - reminding me a little bit of what Shanghai felt like. Time was standing still.
It was here that me and my friend, James, were debating the esoteric as we usually do when we get together. We talked physics, philosophy, artificial intelligence, economics and then we spoke at length about the discipline of mathematics. It was prompted by a discussion on South Africa's decision to lower the requirements to pass mathematics to 20% for grades 7, 8 and 9. (13-15 year olds) The decision was a highly controversial one that sparked a lot of debate, at least in the bubble that I live in. Lowering the standard for progressing through school always seems like a defensive move and one that damages the quality of the education long-term - so it is always met with some fierce push-back. However, I have also heard some very compelling reasoning on the other side of the debate that argues that this move was in fact a good thing for the long-term success and employability of the kids moving through our school system. It is for this reason that I don't want to discuss the reasonableness or levers behind this debate. We'll save that for another time - I don't know what the right answer is.
What I found more interesting, and why I wanted to share this experience with you, was our discussion on mathematics itself as a discipline. So with James' permission I am going to try and summarise what we spoke about, to hopefully bring you some value as a reader.
I believe that mathematics is a disproportionately important subject. I really do think that it is the bedrock of this world whether you think you use it or not. Right off the bat, I am fully aware of my own bias here. I enjoyed mathematics and was very good at it. I entered into a field where mathematics was a crucial part and I still use it every single day. I am aware of the fact that you might tune me out now because of that - because your experience may not be like mine was. A large proportion of people hated mathematics and really struggled with it day after day in school and university. It can be a cruel, heartless subject when things don't seem to click for you and it is true, I think, that some have a natural affinity for the subject and some don't. But I hope to persuade you that even if you hated mathematics or if you don't go anywhere near a number in your professional life right now - that mathematics still remains the foundation on which you build a career and a life.
The reason that mathematics is the foundation is not because of the content itself. Outside of certain fields, knowing how to use calculus or trigonometry is in itself completely useless. But that argument hides the real gem of the subject and it is used as an excuse all the time.
"When I am ever going to use this?" "What is the point of this?"
The content that you learn in mathematics is in itself insignificant. It is the Trojan horse, the skeleton of what really matters. What mathematics brings is instead a method of thinking, reasoning and problem solving that fundamentally alters the way we think and live. That's why it is so crucial.
The beauty of mathematics is in its objective reality. When we look at a mathematical equation, it is either right or it is wrong. There is no room for subjective choice, no room for pandering or politicking around the answer, the answer is in black and white. It is the first subject that shows us absolute truth. 2 + 2 = 4. That is the absolute truth. There is no argument that you can make that will dissuade me of that fact. This certainty is what makes mathematics so worthwhile. We live in a world governed by change and uncertainty. It is a world changing so fast that knowledge that you may gain in school or university becomes irrelevant and out-of-date in no time and so intellectually it is possible to float around a topic with a bunch of theories and ideas but without ever actually solving something, without ever discovering the truth. Mathematics gives us that opportunity. It allows us to see, interact with and come up with a piece of rock-solid intellectual work that can hold up to time and to the changing winds of public opinion or even one's one opinion.
For me this certainty gives me hope. It shows me that even when everything else seems to be completely dependent on perception and is subjected to a war of opinions, we do have absolute truth. It is possible. It extends to a hope that we can find objective moral truths about how we live our lives. That we can find objective truths in physiology or in anatomy.
This truth is what has allowed technologies such as block-chain technology to revolutionise the way we think about value transfer. This truth has given us the confidence to develop neural networks within artificial intelligence that delivers us information we can use, purely on the basis of statistical pattern recognition.
Mathematics allows us a glimpse of certainty, a glimpse of truth. And whether you appreciate it or not at the time, the subject gives this to you so that you may have a hold on the world. So that you do not float through eternity wondering what it is real.
Logic and Reason
The second nugget of gold that mathematics offer us is a way of thinking that grounds every other decision that we make in this world. As a devotee of reason myself, this seems fairly self-evident, however I know that this topic is not one that typically comes up around the dinner table and so most of us have never really appreciated its importance and its significance. In mathematics, we learn for the first time - the meta-skills of logic and reason.
We learn what it is to build up an argument for some state of affairs and then use the absolute truth mentioned above to prove that the argument makes sense and can hold up when exposed to the light. Indirectly we learn to gauge what makes for a strong argument and what makes for a weak one. We learn to identify a valid set of assumptions or variables and how to distinguish those from tainted ones. Over time, our minds are fundamentally changed by mathematics as we come to understand how a rational, logical problem-solving method is what is required to find truth.
Again, the context is irrelevant here. The way of thinking that is embodied in our children is what is so powerful. At that age our brains are developing fast and doing everything they can to acclimatise to this strange world that we find ourselves in and the reasoning that you learn when solving mathematics problems is the reasoning that then carries forward to every other part of our lives. It is the foundational mode of rational thought that we hopefully all aspire to and it enables us to communicate, emphathise, collaborate, disagree, debate and create with the other humans that inhabit our space.
It is hard to understate the importance of reason in this world. We so desperately need more of it. And mathematics is where it all starts.
Lastly, mathematics gives us a roadmap and a set of tools to go and tackle problems with. I think its safe to say that problem-solving is a skill that is so widely applicable that it often is the thing that sets apart those who succeed and those who don't. It is the skill that has enabled our species to so effectively adapt to our environment and evolve to a point in time where there is truly no limit to the problems that we can solve. Given enough time and resources, the human race will figure it out. Optimistic, I know, but I truly believe it. Problem-solving is Archimedes' lever and we have moved the world with it.
Mathematics is the first subject as a kid where you are given a problem to solve and over time you are given the toolkit needed to do just that. With one equation, a teacher can teach resourcefulness, resilience, focus, lateral thinking, creativity and even empathy. It is the ultimate sandbox through which a child can learn how to tackle something that they don't understand and how they can come out the other side with a piece of absolute truth. It goes hand in hand with the scientific method taught in chemistry, physics, biology and the like. It is such a fundamental building block of the way we think that it applies to every single problem that we face from that moment on.
Mathematics offers us this toolbox and modality in a safe environment, allowing us to practice liberally before we tackle the real problems of the real world. That's special.
So as you can see, I am kind of a nerd with this stuff, so I may have over-indulged. But I hope that I have persuaded you of the fundamental importance of the study of mathematics, independent of trigonometry, calculus, geometry or any of those scary words. It's not about them, I promise. Mathematics changes the way your mind works from the inside. It is everything, in my opinion.
I implore you, when you have kids, do whatever you can do ensure that their mathematical foundation is solid. They may hate you in the moment, they may go through serious struggles and hardships. But I believe they will turn out as better people, and hopefully thank you for it.
Photo Credit: Smoochi