I'm in maths not because I place a terminal value on understanding the subject better and more deeply, but because I find problems and the process of problem solving rather fun. Over the years I've come to notice that this is a trait I share with lots of people who first got involved with "proper" maths (or some approximation thereof) through high school Olympiads.
This in turn makes combinatorics a very natural field of interest, and indeed, I've been interested in combinatorics and related areas since before starting university. I thought that perhaps seeing university mathematics would move me towards fancier fields, but nah, 2010-11 me already knew what was up. I enjoy having a full picture of the maths I'm doing instead of playing a long, dragged out game of pure deduction. I like problems where the base object is very simple and the question can be explained to the curious non-specialist in full technical detail, and where the challenge is coming up with a fun new way to think
rather than to just keep learning till one knows
enough to make the problem trivial. I admire and respect the people primarily developing deep theoretical fields, but I know that given the way I think and operate I probably would not be able to contribute that much in those fields.
The question of what combinatorics actually is turns out to be kind of complicated; everyone has a feel for what counts, but it's surprisingly difficult to put in a neat box. If you have some time to spare I'd recommend Igor Pak's blog on the topic
, as well as his extensive collection of quotes
. Tim Gowers also has this fantastic essay called The Two Cultures of Mathematics
which everyone should read (if you want a stronger recommendation than mine: well, it's one of the suggested "Articles by Others" that appear in the left pane of Terry Tao's blog