I'm currently completing my first year of A-Level Further Mathematics and the institution through which I'm completing it is offering supervision services for what is known as an "Extended Project Qualification", which involves a $5,000$ word essay in an area that you are interested in (for me this is obviously mathematics) now, I've considered picking a specific millennium problem such as the Navier-Stokes equations or the Yang-Mills theory and Mass-Gap hypothesis as my topic, but I'm undecided.
Alternatively, I find the ability in mathematicians to look at a problem in mathematics and understand the underlaying implications of what is written, and using these implications to solve the problem, a great feature of all mathematicians. That being said, a second topic I've certainly considered is the Role of Intuition in Mathematics.
I have no doubt that coming up with $5,000$ words regarding either of these topics is achievable, especially given their history, but ultimately I don't want to be blind to the other possibilities. So is there any area of mathematics that someone feels could produce an interesting EPQ?
Note: The main thing to consider is the availability of resources (and considering there is a sizeable amount of mathematics whose rigour I do not understand, this implies I will have to rely at least partially on articles if I were to choose a complex topic)