Ethan Tan – Gold Medallist at IMO 2018
Math seems hard because most people have learned it in a way that is unintuitive and restrictive, and this is mainly the fault of the school system of teaching math.
The first issue with this is that people don’t understand what they’re doing when they solve problems. Students are taught a range of techniques and formulas that they’re told to accept as true, often providing little to no explanation or any fundamental reason as to why they should be true. To many, math can seem like magic, where solutions to problems appear out of nowhere with mystical and confusing reasons behind them. Countless students memorise the quadratic formula without understanding why it does what it does, or explain why differentiation and integration are inverses. All of these have simple and visual explanations but these explanations are never given in class. Students would be able to derive and understand formulas for themselves instead of having to memorise formulas and methods. Math is in reality an incredibly visual and intuitive art, but all of the intuition and visualisation are removed in favour of rote learning and boredom.
Students also aren’t taught proper mathematical thinking in school. Thinking in new and interesting ways is the essence and the joy of mathematics. With this removed, mathematics becomes boring and difficult and becomes a tedious task. School often emphasises endless repetition in order to regurgitate the same formula or task, but in reality math should be about using the tools you have to solve problems that you haven’t ever seen before, or inventing your own tools to attack a problem. Many people can understand how finishing a puzzle can be enjoyable and satisfying but few understand that math is at heart the same.
There are a range of other factors that are also at play, such as preconceptions, lack of understanding of use, uninterested or incompetent teachers, and the list goes on.
Despite the common belief, math can be quite beautiful. I’ll finish with a solution to a fairly simple algebra problem that I thought was beautiful.
Prove that 2(𝑎2+𝑏2)=(𝑎+𝑏)2+(𝑎−𝑏)22(a2+b2)=(a+b)2+(a−b)2.
The best solutions are those where you don’t even have to say a word.