Thoughts On Maths

I'm approaching the end of the research time for my PhD studies. Soon I will have to close all my open lines of inquiry and focus solely on the task of writing up. With a bit of luck - and a lot of work - I hope to have my thesis finished soon into the new year. At the minute I have no firm plans for what I'll do after my studies are all complete (which in an ideal world would be some time around May), but I'm sure something will come along.

At the moment though I still have a few things that I'm trying to sort out. There are a few little questions that I'm sure I can answer with just a bit more thought and consideration (who knows, maybe some reading will help), but time is running out and I'm starting to doubt that I have enough time in the next month in order to get the answers that I'm hoping for.

As ever, I'm convinced that these answers, these truths, already exist in some abstract sense. I've spent some time thinking about my problems (in the mathematical sense - I'm in denial about the others) and I can almost touch what I'm looking for. It feels as if I can just stretch my arm a little further I'll be able to grab a hold of the proofs that I'm after; also I'm thinking about the results I already have and how they can be improved or how proofs that I already have can be written more elegantly.

Today was my first day back in the office from my holidays, and already I can feel that my sleep in the coming weeks will be less restful. At the same time I can't help but feel really excited about the challenge ahead. I find whenever I'm working creatively in this way that all kinds of other creative things and ideas start coming together in my head. I don't know about other areas of research, but over the last few years I have definitely found that maths research follows a cyclic pattern when it comes to productivity. I have a sense that I'm approaching a peak rather than a trough, I just hope that it will last a long time...

In the next few days I'll try to find some time to talk some more about my time in Edinburgh, but I think that tomorrow I might write about my thoughts on a film that I saw for the very first time yesterday, "Planet Of The Apes"...