The University of Oxford have set up a small competition for 'maths essays' which is now open for submissions. Everyone is eligible to enter, regardless of mathematical ability, as long as you have an interesting mathematical story to tell.
All entries will be showcased on tomrocksmaths.com and the winners will be published on the university webpage. There is also a prize of £50 for the best overall essay, and a separate prize of £50 for the best essay from a student aged 18 or under. You can see the winning entries from last year (both high school students) along with more details of the competition here: https://www.seh.ox.ac.uk/study/outreach/teddy-rocks-maths
The closing date is 26 March 2021 and the winners will be announced in April.