Enjoy the fifteenth group of essays from the 2024 TRM Essay Competition, now proudly held in partnership with the Oxford University Department for Continuing Education. The showcase will take place throughout June and July with the winners being announced in August.

If you enjoy reading any of the essays, be sure to leave a comment to let the author know!

This essay provides a visual tour of the world of non-Euclidean geometry, from spherical to hyperbolic.

This essay presents the history of attempted proofs of the Twin Prime Conjecture, alongside the author’s own investigations.

This essay gives a detailed overview of the succession of results that ultimately led to the proof of Fermat’s Last Theorem by Andrew Wiles.

This essay derives the Fibonacci numbers and their relationship to the golden ratio using the technique of generating functions.

This essay explains the conceptual steps of chess algorithms used by artificial intelligence.

This essay describes a model that can be used to find your perfect romantic partner, and applies it to the contestants of TV’s Love Island.

This essay outlines the history of the Black-Scholes equation and how the more general concept of volatility was used to make a lot of money on the stock market.

This essay describes the author’s love of mathematical calculations.

This essay provides a solution to Zeno’s paradox of Achilles and the tortoise by carefully explaining how to correctly treat infinite series.

This essay explores the concept of surreal numbers, explaining how they are derived and the interesting properties that result.

This essay discusses the idea of mathematical axioms and how the work of Godel changed the landscape of mathematics forever.

This essay calculates the impact rounding your order up to the nearest pound at McDonald’s could have on the world.

This essay uses the tools of group theory to make sense of the concept of a negative harmony in music.

This essay presents some of the key properties of exponential and logarithmic functions.

This essay argues for the idea of maths as the language of the universe using the Mandelbrot set as an example of a greater intelligence.