“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein
April is Mathematics Awareness Month. This an annual event that was created to increase public understanding of, and appreciation for, mathematics. It began in 1986, when President Reagan of the USA issued a proclamation establishing National Mathematics Awareness Week. Activities for Mathematics Awareness Month generally are organised on local, state and regional levels by college and university departments, institutional public information offices, student groups, and related associations and interest groups. Although this is a USA event, it is now spilling out to other Anglozone countries and to some other countries as well.
This year, Mathematics Awareness Month will focus on the Mathematics of Sustainability. Being human means continually balancing our needs with the world’s resources while operating within the laws of nature. Mathematics helps us better understand these complex issues and is used by mathematicians and practitioners in a wide range of fields to seek creative solutions for a sustainable way of life. Society and individuals will need to make challenging choices; mathematics provides us with tools to make informed decisions.
Students often start to question the need for learning mathematics at school. Once arithmetic has been mastered, and the more abstract mathematical concepts begin to be taught to them, it is not uncommon to hear in a school: “What is maths good for? Why should I learn it? How on earth is this relevant to me in my future as a..?” It is not difficult to answer these questions, especially if one is a maths teacher, however, putting the answers in the right language and right context for a class of malcontented young people to appreciate is a challenge.
Ever since there were humans in existence, there have been problems that required immediate and practical solutions. Whether the problems were over basic requirements like sustaining sufficient amounts of food or major accomplishments like constructing functional and durable buildings, problems such as these remain with us to this day. Successful problem solvers are able to understand what is expected of the problems they face by understanding the details surrounding the question at hand, which is the most important step to solving problems. After patiently examining the details, paying attention to the details, intelligent choices are made as well as the beginning steps of developing a strategy. The plan must be carried out in an order that makes sense. So careful planning, possibly by justifiable experimentation, must take place. Once an actual solution is obtained, it must be tested to determine whether or not it is reasonable. This is what maths is all about.
Maths problems that are covered in class force us to use many, if not all, of the detailed methods of problem solving. The theory provides us with the methods of arriving at solutions in the most efficient way. Each individual problem becomes a small but important lesson for solving problems in general. Maths is traditionally learned by first doing many smaller problems. Then the small problems are put together to solve bigger problems. For instance, in order to solve algebraic equations, being knowledgeable about arithmetical operations, i.e. addition, subtraction, multiplication, and division, is a must. Ordering the steps to be carried out, evaluating expressions, and learning how and when equations are used must be learned, too.
The world is facing a range of serious challenges on issues such as the environment, energy, and climate change. The finances of a globalised economy, the complex budgets of the world’s major countries, international trade, all require mathematics. Especially where sustainable practice is concerned, mathematical modelling is essential. Mathematics plays an important role in understanding and addressing these sustainability problems.
You may not need maths to survive in your every day existence. Pocket calculators taught us that you don’t even have to know arithmetic. Mobile smart phones tell us immediately the answers to simple maths problems: Google can tell you how many square kilometres 12.4 square miles is, or the volume of a hemisphere with 25 cm diameter. In any case, these are simple arithmetical, geometrical and mensuration exercises. Higher mathematics teaches to appreciate the beauty of reasoned thought, the value of logic, and the power of proofs. Mathematics is the foundation of all science: For example, physics, economics, computing, astronomy. How can one understand the world without knowing what calculus is about, without knowing what optimisation is? Without knowing about Noether’s theorems or chaos?
Even if one looks at the arts, and music is an obvious example, you don’t need to know maths to like a concerto or enjoy a symphony. However, maths helps us understand why we like the sound of an interval and why another sounds unpleasant. Why jumping from one note to another is pleasing and why another pair of notes sounds grating. Maths tells us why the composition of one canvas is pleasing to the eye and why another painting’s composition may look “wrong”. Counting and simple arithmetic, ratios, sequences and series may help us understand why a poem doesn’t scan right. Mathematics is the language of nature and learning it provides our connection to the universe.