Writes Lochlan P. (U6th)
Every good maths lesson provokes the question: “How is this work relevant in real life?”. Imagine a topic where the teacher answers: “It’s not!”. This topic is called Group Theory.
Group Theory is a topic in Extra Pure A-Level Further Maths, which seems rather distant from the familiarity of quadratic equations and trigonometric identities. This abstract branch of maths puzzles even the best mathematical minds at Merchant Taylors’. This week, we proved that two different groups of order ten were isomorphic, meaning they possess identical mathematical structures despite appearing different. After spending hours drawing Cayley tables (the format in which groups are represented) I naturally became curious as to the utility of this isomorphic property beyond the classroom.
In practice, isomorphisms are used in chemistry. They allow mathematicians and scientists to predict the properties of chemicals without analysing every molecule separately. Multiple molecules that appear to be different can exhibit identical behaviours, much like the structure of isomorphic groups. Other applications include cryptography and quantum physics. So, there is a purpose for this part of maths (and for all the others) after all, as mathematics is a subject with endless applications!
