Understanding yourself and the enemy in the context of Mathematics

In this philosophical expose Tristan Barnard and Sophie Marques combine forces to bring you a Socratic study on why being a Mathematician prepares you for a rich and rewarding inner life.

Illustration by Tristan Barnard

To know yourself can bring partial success, but to also know your enemy, “Mathematics”, can bring complete success.

One way that you might know yourself and achieve understanding is to be alone with yourself. This can be uncomfortable as you will encounter all that you ignore within yourself. Metaphorically, facing that which is difficult inside of yourself can make a part of you feel like your own enemy, but this part of yourself is what needs to be integrated. Struggling with Mathematics can mean that it too may be, metaphorically, an enemy; and one against which you battle consistently. In such a battle, you need helpful strategies. Thus, if you know yourself better, understand your feelings towards Mathematics and learn strategies for ‘battle’ – you are better positioned to achieve success in everything you do.  

Statement of the guiding principle by renowned strategist and author of “The Art of War”, Sun Tzu.

Sun Tzu said: “If you know your enemy and yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.”

If struggle is your enemy, don’t see it for the first time: gain an understanding of what you are going to face.

The truth about life is that it is difficult and that is something with which you will have to deal. One such way to deal with this problem is to know yourself and how you behave in difficult circumstances. In all the turbulence of life, the one constant variable is yourself. You carry your understanding of who you are with you all the time: thus, you experience both your past and future selves simultaneously within the present and you must cater to all of them simultaneously. A helpful strategy is to fix your past trauma in order to be at peace in the present. In the present, you need to take care of your health for longevity. In the future, you must plan for your best-imagined reality and execute this plan. The future holds all the potential in the world and this allows you to create a destination that is pleasant to envision. You can therefore have a better tomorrow than you had today. This journey towards success starts by knowing yourself.    

It is true that we might turn to distractions to escape a current reality that makes our suffering real. Such distractions include believing in falsehoods, choosing memorization over the struggle of understanding, cheating, and even distractions such as social media. However, such alternatives to hard work sacrifice the future as they result in us fooling ourselves and thus destroying our potential.

Mathematics and reality differ conceptually. Mathematics is determined by pre-established rules while reality is largely undetermined and open to interpretation. Mathematics functions on definitions and logical limitations, where it seems at times that our lived reality does not. This is partly the cause and result of the world around us being experienced and constructed through partial understanding and subjective interpretation – particularly through the use of language. Yet in Mathematics, you are placed within a framework where it may become possible to understand the material, the “enemy”, precisely and thus you are afforded the abilities of insight that are seldom compatible with the uncertainty of reality.   

So we can see how in such a situation as this, the guiding principle to Know Thyself can help you understand your own internal subjective reality so that you can face the certainty of Mathematics with greater confidence in yourself. Mastering the self first and understanding your own strengths and weaknesses can only help you pit yourself against any enemy.

So remember: Be attentive to yourself, care for yourself as though you were someone you loved and take time to be alone with yourself so that you might “know thyself”.

Illustration by Tristan Barnard

Failure to uphold the guiding principle in Mathematics

There are many ways in which we might fail, however there are some ways to fail that we have in common and from which we can learn: 

The first lesson in failure in  (the Ego):

Ego is inherently neither good nor evil. It can, however, become foolish arrogance. We might then delude ourselves into believing wrongly in our own excellence, which will leave us blind to our inadequacies or shortcomings.

If this happens we risk failure because we do not allow ourselves to recognize our lack of understanding. This may happen when we dismiss the feelings of something going wrong by justifying that we have time to still fix it alone, or that such failures will not happen to us. Then we risk falling into the trap of an arrogant ego.  

One way to overcome this from happening is to realize that change is challenging. The pathways in your brain are like well-traveled roads which are easy and convenient to take. It then stands to reason that building a new road through the bush is hard work and will involve voluntary effort or may even be painful. It is difficult to change or avoid well-established patterns of thought and behavior. Thus it also goes without saying that you should not lie to yourself and pretend that your ego has no hold on you. 

 Example of the first lesson of failure:

Imagine that you are a first-year university student who has successfully passed Mathematics at school with little effort and has been granted admission to the course of your choice. As University starts you sit in your lectures believing you understand, only later to discover tutorial after tutorial you do not and then subsequently fail the assessments. You, however, insist on believing in your own abilities to succeed without  help and so you fall down this pit to the inevitable conclusion of complete and utter failure of the module.

Consider that your failure could be due to your ego informing your reality, the use of false narratives and failure to look upon that of which you are afraid.

In this example, you deluded yourself into thinking you were not alone in lack of understanding or struggle and that you would pass along with everyone else who felt the same. What you need to remember is that classes at university progress very quickly and that if you get left behind it is a tall ask to catch up. You may also have been affected by self-deceit and thus had an additional, internal, failure.

Illustration by Tristan Barnard

The second lesson in failure in Mathematics (falsehoods):

In this lesson, Truth and Deceit will be explored.

If you practice Truth, your truest self and your true goals go forward into the world and are reflected back to you. By practicing Truth, you will invite into your life that which is best for you. If you practice Deceit, then your true self is overshadowed by your deceit, making you a puppet directed by something else within your life. By practicing Lies and self-Deceit, you have no real control over the direction of your life. 

Be careful. The power of lies, manipulations and misdirections can be alluring. It is far easier to dupe yourself into believing that you have not achieved well for a range of other reasons other than because you needed to work harder and tell yourself the Truth. 

Example of the second lesson of failure:

Imagine that you are a student who asks to copy Mathematical answers from a peer or who allows your peers to do all the work while you take credit for it in group assignments. You therefore achieve good results in tutorials and group projects but fail in exams when stripped from the support of your peers.

In this example you have chosen the easy way out. However, by taking the easy road we fail to learn the lessons we need to grow: Do not copy work and do not rely on others to solve all your problems or do all the work for you. This will lead to a form of self-Deceit by making you believe that you understand the work. It will also result in alienating you from the group. If you are part of a group you need to pull your weight otherwise people will not want to work with you again.

Failure in the above example could be due to self-Deceit that made you believe that you understood the work when you did not and made you feel justified in taking the credit for work which was not yours.

Illustration by Tristan Barnard

The third lesson in failure in Mathematics (Inaction):

Inaction is a result of fear. A child who thinks that there is a monster under their bed or in their closet will never look because they cannot face the terror of it being true. Similarly, if we fear something we avoid it and do not look too closely at it- but the truth is that we must look. The scared child will only know if there is or is not a monster through confident investigation. If there is a monster they can plan how to deal with it. If there is not a monster then they no longer need to worry. We might also find that the monster is far scarier in our imagination than an actual threat, and so too it is true with Mathematics and with any struggles we face.  

Remember: If you are a child in the dark, all sounds are scary until you shine a light on them.

Example of the third lesson of failure:

Imagine that you are a University Mathematics student who has failed two tutorial tests and believes that you can still save yourself from failing the module or the course. Yet, in the back of your mind you have doubts and anxieties about your true ability and so due to the unpleasant nature of those fears you choose to look away and ignore them and never face investigating your strengths and weaknesses so that you can focus on managing the course properly. In such an example your fate has once again become an unnecessarily said but forgone conclusion.

Through this example we learn that if you cannot act in time to affect change, you have effectively relinquished your choices and decision making ability. Instead, you have allowed the randomness of life to decide your fate. This is no battle strategy for a confident warrior. Instead, always act before you think you are ready because if you wait, you will wait a whole lifetime.

Failure in this instance could be due to looking away from the monster in your closet and thus being unable to plan how to deal with it.

Illustration by Liani Malherbe

The culmination of all failures leads to Mathematical Anxiety:

The result of all the failures outlined above will be what is described as Mathematical Anxiety. This is a real and crippling fear of failure produced through the constant erosion of self-confidence through set-back after set- back. You might have arrived at this point by similar means as the examples above. The way through it and towards success? Know thyself and the enemy against which you are struggling in Mathematics. 

Reflection and Conclusion:

Absolutely nothing can be lost in the pursuit of understanding the self. This golden principle has no substantial counter-argument or negative outcome.

When you struggle with a lack of purpose or a sense of not fitting in, take heart and consult The Self so that you can undertake self-development. You are not a fixed point or unmovable destination. You can become all which you would dream for yourself, but you need to be willing to engage with yourself and work towards self-improvement. You can only benefit in the long run and the consequences of that will be attracting into your life all the excellence and beauty which you originally sought. Thus, “to know thyself is the beginning of wisdom” – Socrates.

Through Knowing Yourself you have won half the battle: Know what to expect, know how you will be tested and prepare yourself adequately by staying well informed. Another helpful metaphor is to strive to like water – infinitely adaptable but without concrete form; immensely strong and able to form, and flow around, all obstacles. And remember that if you understand yourself it will also help you understand others who are on the same journey. It will help you cross the halfway point between you and any enemy, and you and others, so that the rest of your journey might be an easy downhill.

Tristan Barnard

BSc Wood & Wood Product Science student, Stellenbosch University, South Africa


Department of Mathematical Sciences, Stellenbosch University, South Africa

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