*I couldn’t pick between my 2 favourite essays so I’ve decided to award joint-winners who will split the cash prize.

A huge congratulations to Amelia Tan for their essay entitled “A Tangent about Tangents” which has been awarded joint-first prize in the student (under-18) category for the 2025 Tom Rocks Maths Essay Competition.

“A fascinating piece of mathematical history, not only well-explained, but written with plenty of personality and humour. I did not know the story of Descartes and Fermat beforehand and on my first read through found myself skipping ahead to learn what happened next! All of the mathematics is clearly described and explained at an appropriate level for the intended non-specialist audience, which is no mean feat given the use of geometry and calculus. Overall, just an excellent read that leaves the reader with a smile on their face.”

And a huge congratulations to John Winmill-Briggs for their essay entitled “Coprime by chance: Probability to ζ(n)” which has also been awarded joint-first prize in the student (under-18) category for the 2025 Tom Rocks Maths Essay Competition.

“A fascinating result, set up perfectly through an easily understood question that piques the curiosity of the reader – I did not expect the outcome, but I am so happy with the answer! Just one of those glorious mathematical problems that sound simple, but require a great deal of complexity from a wide range of topics to arrive at a solution. Exactly the type of problem that draws you in to the beauty of the subject and sets you on the path to becoming a mathematician. I loved it.”

Both winning essays will be published on the university website, and the winners will receive a cash prize courtesy of Oxford Lifelong Learning.

Read both winning essays by clicking the links below.