Our popular Maths Circle Lectures continued last week. We were honoured to welcome Dr James Munro, Admissions and Outreach Coordinator, Mathematical Institute, University of Oxford and Stipendiary Lecturer at New College, Oxford. Dr Munro entertained and challenged his audience with an introduction to Évariste Galois and the field that is now named after him. Aditya, in Year Thirteen, recaps the event below:

Dr Munro's captivating lecture on the Quest for the Quintic and Galois theory took us on a thrilling mathematical journey through the vast realm of polynomials. While quadratic and cubic formulas are familiar to many, the absence of a quintic formula left us intrigued and eager to explore.

With a profound enthusiasm for polynomials, Dr Munro illuminated the perplexing absence of a quintic formula, contrasting it with the neat solutions of quadratics and cubics. Through a journey into Galois Theory, we explored field extensions and learned that the roots of quintic equations often defy expressions using basic arithmetic operations.

With the help of volunteers from the crowd and Desmos, Dr Munro helped illustrate the idea of ‘roots of unity’, revealing the intricate patterns and symmetries that underlie these elusive mathematical structures. By learning about complex numbers, we ventured into an entirely novel realm of mathematical understanding, unveiling previously unseen dimensions within the subject.

However, while the elusive quintic formula remained just out of reach, our journey left us with a newfound appreciation for the elegance and complexity of polynomials. Thanks to Dr Munro's guidance, we departed with a sense of accomplishment, having collectively delved into the depths of mathematical inquiry.

Aditya, Year Thirteen