# Pure Maths EPQWatch

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#1
I have quite a few questions about doing a maths EPQ as I am having a lot of difficulty with it.

1) I want to do a pure maths EPQ but is this even possible as I've researched a lot and I can't find any really good topics.

2) I'm interested in number theory and history but I can't find that much information on it and I have no idea what the question would be.

3) The information on number theory that I have found all seems very different like perfect numbers and Fermat's theorem and I don't know a question that would link them as I don't want my EPQ to be really generic.
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5 months ago
#2
Yes, it's possible. I heard about someone who did an EPQ on elementary knot theory. You mentioned that you're interested in number theory and the history of mathematics: which topics in particular interested you? I did an EPQ on the invention of calculus, and my report focused on Newton and Leibniz's approaches with plenty of historical background.

You don't have to worry too much about mathematical complexity. You could quite easily get a project out of Fermat's Last Theorem just by talking a bit about Pythagoras, perhaps throw in a discussion of infinite descent for the case n = 4 (make sure you understand it), then summarise that Andrew Wiles BBC Horizon documentary on FLT. (You probably won't need to do any mathematics more sophisticated than, say, defining what an elliptic curve is, and perhaps an example of a modular form if you're feeling keen.)

There are plenty of beautiful pieces of mathematics you could use. The Riemann hypothesis is one (though, I suspect it has been done to death). The prime number theorem could be another, and is quite challenging, but you might like to read up on that too. (It's one of my favourite theorems.)
Last edited by spectral_theory; 5 months ago
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#3
Thanks, never heard of the prime number theorem so I'll look that up. I've heard of the knot theorem but I have no idea what its about so I'll look that up too
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