25 November 2016

Is mathematics beautiful?

​​​​​It is a common question in maths classes "Where are we going to use this in real life?" Some students need to understand the utility of mathematics in their day-to-day lives. Some want to know where the mathematics they are learning is used and some evolve to a point where they understand and appreciate the elegance of mathematics as it is.

Society in general seems to be of the view that it is okay not to be good at basic numeracy. There are people from many different walks of life who say, often proudly, that they are hopeless at mathematics.

Often in the categorisations of the creative subjects, mathematics is not included. 

At the same time many mathematicians believe that mathematics is a creative endeavour and many mathematics teachers and students experience this creativity. We experience the beauty and elegance of mathematics and know intuitively that when calculations turn ugly, they cannot be right.

J H Poincare (1854-1912), a famous French mathematician observed that "The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."

And J Bronowski (1908-1974), a British mathematician, noted that " a form of poetry, which has the same relation to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process."

So when the mathematicians in our students delve into the abstract nature of the subject and play with and manipulate various formulae and equations out of curiosity (and often because they can), the understanding that this process generates, the engagement and exploration that go with it brings delight and an appreciation of the beauty of mathematics to some.

In 2014, experiments were conducted by neuroscientists to study the activities in the brain when the subjects did mathematics and it is reported that the experience of mathematical beauty correlates with activity in the same part of the brain areas that are active during "the experience of visual, musical and moral beauty". The difference being that in mathematics an understanding of the subject and an exposure to the material used was necessary to trigger this activity in that part of the brain.

At our school a group of Year 9 girls started an acceleration program in mathematics in 2014. They started the program with a lot of excitement and some trepidation but with a promise by none other than Archimedes, "Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty."

Through many highs and some lows in their often intense journey through the acceleration, they reminded themselves of this promise and persevered.

It is pleasing to note that 15 girls completed their HSC in Extension 1 Mathematics this year, while they are in Year 11.

Below is some feedback from some of these students on their experience of mathematics and accelerating through the course.


Mathematics is a simple representation of a complex reality. Its elegance lies in many proofs or formulas, short and unexpected, producing profound results. Mathematics' beauty extends into nature, the Fibonacci spiral of a nautilus shell or Einstein's formula, E=mc2, showing how matter and energy are interchangeable. However, as a student of mathematics, its true beauty and elegance is demonstrated when looking at an equation, feeling frightened by its complexity, and with hard work and dedication, being able to understand it. No matter how many times one struggles, questions, or even fails, nothing is able to beat the satisfaction of a single 'click' of understanding. So while mathematics may be beautiful through its profound results, as a student, its true beauty lies within its ability to teach one patience and persistence, producing a richer character.

Mathematics is beautiful despite the fact that it is more inaccessible than other forms of art. It is every bit as creative yet it's also logical. Maths is so logical that it's immutable. Maths doesn't care about how smart a person thinks they are, or how badly they might want to be right, or how easily they can appear to follow a concept. After a certain point, you cannot blame your inability to answer a problem on a poorly-written question or a teacher's grudge, or the fact that something wasn't covered in class. Maths isn't going to change for you. The beauty of mathematics is its certainty once you understand it. When you understand something is true in maths, you know its truth is unassailable.

Maths is rewarding because it teaches you a different way of thinking and of approaching challenges. The content may not be applicable to all aspects of life after school, but the principles of working on and logically solving problems that may seem unsolvable will be something I will definitely take away from maths. Doing the accelerated maths program has absolutely made me a more persistent person and allowed me to challenge myself and reach the potential that I never knew I had!

Maths is a very fascinating subject. It is more than just theories and calculations. The beauty of maths is that it has taught me logic and now the physical world around me makes so much sense. 

The maths acceleration program has really helped increase my love for maths, I have enjoyed learning new things and being challenged to understand difficult concepts. The support from class members has helped the experience to be enjoyable and worthwhile.

Accelerating in maths this year has been a really beneficial and enjoyable experience. Although our class has had its ups and downs, I have been able to explore the beauty of maths without six other subjects competing for all of my attention.

Well, mathematics is beautiful and as always the beauty is in the eye of the beholder.

Dr Shantha Bose
Head of Mathematics