I'm still studying maths at undergraduate level, but intend to continue exploring topics in pure maths after I have graduated, so am thinking already about what directions I'd like to persue now, (as I like to be several steps ahead of myself!)
One area which seems particularly interesting is 'reverse mathematics'. I'd be interested to learn what the prerequisites would be for understanding it. Presumably it is a part of logic, and is related in some way to proof theory? If say, I wanted to explore questions such as, 'are there a finite number of ways of proving something?', would this be the right direction to take? (In fact, is there already an answer to this question?)
Apologies if the above is a bit broad/vague. This is my first post, and I plan to add to it as I learn more!
Update 1: Can anyone recommend a good introductory text on reverse mathematics and/or proof theory?