The Beauty of Mathematics

I previously wrote this blog entry in 2021, inspired by the news that Alan Turing will be featured on the new £50 British note. The codebreaker was credited with cracking the Enigma machine (the cypher device used by the Nazis to send encrypted messages in the military) in 1942, and whose name should be paralleled to Churchill, Eisenhower, and other wartime leaders. Some historians estimate that his work at Bletchley Park shortened the war by as much as two to four years. An incredible man, of amazing intellect, whose story is one of incredible highs and devastating lows, was a mathematical genius and has been called the “father of computing”.

Mathematics is all around us. Mathematics is beautiful. And its beauty is everywhere. It’s in the objects we design and create, in the works of art we admire, in flowers, and in bird songs.

I’ve always loved Mathematics, and how the subject is circular in its nature. In schools, we try to create a scheme of work that builds on prior knowledge, year after year, until students have a deep understanding of the inherent nature and connectedness of the subject. But often we fall short due to the time pressure of exams and university applications. I wish that, as educators, we could devote more time to teaching the beauty of Mathematics, and stories just like that of Turing.

I love that Mathematics is a subject that everyone can understand and comprehend. It appears in the most unexpected of places, and the strangest of ways. Take the Fibonacci numbers for example:

1, 1, 2, 3, 5, 8, 13, 21, …

This pattern is made by adding the previous two numbers in the sequence together. So 1+1 = 2, 1+2 = 3, 2+3 = 5 and so on. Simple enough to understand, this pattern appears surprisingly often in nature.

The ratio of the numbers (found by dividing successive numbers in the sequence) approaches the Golden Ratio, 1 to 1.618. Mathematically, this is written as:

Try this with some of the Fibonacci numbers, and see how close you can get to 1.618 (for example, try a = 610 and b = 377).

This number is sometimes called the “divine proportion” because of how often it appears in the real world. The arrangement of leaves on a plant stem and the scales on a pineapple will often be Fibonacci numbers.

But it doesn’t stop there. By drawing a rectangle in which the ratio of sides is equal to 1.618, we can draw the Golden Spiral. The Golden Spiral occurs in many pieces of artwork, bringing order and harmony to a scene seemingly chaotic in nature. It occurs in sunflowers, pinecones, petals in plants, shells on the beach, and even the arms of spiral galaxies.

One of my favourite YouTube videos that I show my students is Dr. Art Benjamin, talking about the beauty of Mathematics and this sequence of numbers. I love his passion for the subject and how he conveys his understanding with enthusiasm and vivacity.

Mathematics is also a subject that rewards hard work. With enough determination and perseverance, everyone can do Mathematics.

In closing, I hope that I have created a small amount of fascination in the subject that I love so dearly. As an educator, I teach my students to be life-long learners. Not only do I set them up to succeed academically, but I engender a love of learning, and Mathematics, through inquiry, investigation, and inspiration.