{Research}

I have no content here. When I decide what I'm writing my thesis about, I probably will put stuff up here, including, possibly, drafts as they come into being.

If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Godel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.
- John Barrow

In any non-trivial axiomatic system, there are true theorems which cannot be proven.
-Kurt Godel

Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
-Bertrand Russell