Tristan Barnard encourages young students of Mathematics to persist through challenge and hardship, to master the discipline of mind that sees all failure as part of the journey to establishing a firm foundation of understanding and to seek support from teachers and knowledgeable others.
An Odyssey is described as a long series of wanderings or adventures, especially filled with notable experiences or hardships. A Greek epic poem by this name, attributed to Homer, describes Odysseus’s adventures in his ten-year attempt to return home to Ithaca after the Trojan War. Such a long wandering or voyage is usually marked by many changes of fortune, much like life, and as such each of us have a story of our journey in mathematics. This journey perhaps punctuates our entire lives. I recall a time from my past where my fellow students would often ask “Why do we need to learn mathematics? What is the point?”. This sentiment seemed to be so widespread that it occasionally developed into a discussion with the teacher concerned where both parties left feeling as though they were justified in their thinking.
The one argument most often made when people don’t have a good answer is at worst that it counts for marks and at best because mathematics holds beauty. I have always found the former argument lacking in all aspects, as it simply places the question to the side in favour of what can be called more relevant for concern and so the latter argument is perhaps far more interesting. But more importantly, mathematics itself is a tool of the mind and much like any tool it holds no inherent beauty unless used in the process of creation, much like a hammer is not beautiful – yet. It can be used to mould steel into a perfect arc or forge a perfectly balanced blade, which are then held in awe. Yet it is the craftsmen which we praise and not the tool, for the tool allows for the focusing of the mind into precise, dedicated work which leads to the road of mastery and from mastery comes the ability to manifest abstract ideas into the world. This holds true for artists such as Da Vinci, Picasso and for scientist-mathematicians such as Einstein, Newton and Hawking. These individuals are often both artist and scientist-mathematician. They are forever curious as to the inner workings of the fabric of the universe. From this curiosity sprouts a dream or an idea which results in a creative solution. When this understanding is conveyed to others through the medium of mathematics, we praise the enlightened viewpoint of such solutions. Much like art conveys understanding of emotions, mathematics conveys understanding of our surroundings. Therein lies the inherent beauty, the craftmanship of humanity and the ability to share, understand and convey ideas which may very well change the world forever.
A blank sheet of paper is often not described as beautiful until an artist places onto it a creation from their mind and mathematics is the same. It too is a blank sheet of paper that allows for the expression of the mind. That in truth is the importance of mathematics: it allows us to take abstract ideas from the mind and manifest them into meaningful solutions and observations. But this can be a pitfall, too. mathematics is a mental tool of deductive reasoning and it may fall prey to the inner workings of the mind; thus, a critical juncture must be crossed within one’s own mind: we all have to make a choice to not fall into self-doubt, often encountered early at school. To believe that one is incapable of doing mathematics flies in the face of what mathematics is. It is a medium through which ideas are exchanged and understood. I nearly fell into this very trap in my Grade 2 year, but fortunately I had a teacher who was set on encouraging me to believe in myself, when I had yet to learn that I needed to be the one to believe in myself and that my results in mathematics would forever be tied to my perception of those who taught me that one fundamental lesson.
This then leads into the discussion of what happens to those who fall and have no one to pick them up. Do they forever dwell in a spiraling current of doubtful thoughts, pulling them away from the belief that they are able to do what others seem to do with ease? This may lead to resentment towards the subject material, or to forfeiting further challenge or entirely admitting defeat.
In such situations it is important to remember that the mind can be both a powerful ally and enemy. It is the governing force that allows for mastery in all things and one must be disciplined when faced with the dark abyss of failure which has forever permeated mathematics. Failure is integral to mathematics in the same way that it is to life. It is through failure that growth and learning come about. As Winston Churchill once said, “Success is not final, failure is not fatal: it is the courage to continue that counts”. One can then say that success is an ever-moving goal while failure is the path to that goal and that courage in the face of the dark thoughts of one’s own mind is that which will propel one forwards. Failure in mathematics can be large or small, yet each failure is necessary and each is as unique as the individual to whom it occurs. To fail at an equation is to learn to never fail the same way again and eventually to learn intricacies, and then mastery. To fail at a test is to learn about oneself and that which governs us, to skirt the void of the mind and pass through the eye of self-doubt into the tempest of a raging storm through which you may break, for a time, or find your strength. To fail a module is to be broken down into your fundamental elements and watch as things seem to crash around you, only to learn that that which does not break forms the sturdiest foundation to success. As you are faced with your own unique failures remember this old metaphor: There are two wolves warring within oneself and the one that wins, is the one you feed.
In closing, on this Odyssey, I point out that the ocean is a recurring symbol. It is, in effect, the sea of life. An Odyssey represents our journey through life with all its victories and heartbreaks. Part of the appeal of the Odyssey is this universal journey that we all undertake in ways great or small. Each of us are on a journey through an ocean of possibilities, forever changing, not always calm, with the only certainty being the path that we have walked. But have faith in that the destination is not yet known and that all the potential the world has to offer still exists before you despite the path you have taken. I know not your path nor your destination and your future is your own to create, and I know not the hurdles that life may throw in your path nor your struggle, but I know that it is within you to succeed. It is also up to you to discern your way to success, but know that it is not a path which needs to be walked alone. Perhaps one of the bravest things which can be done is to ask for help.
I wish you good luck on your journey and leave you with a quote by Henry Ford: “When everything seems to be going against you, remember that the airplane takes off against the wind, not with it”.
Fourth year BSc-student in Wood and Wood Product Science