A serious hurdle

After handing me the preprint of a paper he will be submitting/has submitted to a journal recently, my supervisor asked me to come up with an equivalent analysis of another — though related — classification of problem we have been looking at. The last week has been spent trying to put together such an analysis and has led to many a moment of dispair as my understanding of the problem all came crashing down around me, only for me to spend literally hours slowly rebuilding it with fragments taken from textbooks all over the place.

It all boiled down to one step that we pretty much know to be true but are lacking the rigourous proof to state for certain. Everything preceding the fundamental step is all written out nicely and the consequences following it all work wondefully, to the point where the analysis us the answers we know to be right; it's just the proof that everything is ok is currently, well, not there. And if there is one thing mathematicians can't do, it's wave their hands in the air for too long ignoring the lack of a proof — unlike, say, string theorists who do more waving than the queen.

The circumstances surrounding the missing step were made worse by my belief that the analysis of the step was already complete — it was just that I hadn't found it and my supervisor wanted me to find it. My meeting today revealed that that isn't the case, which came as some relief because I truly believed that I simply could not to it. Full stop. After a good discussion and yet more insight from my supervisor, the problem seems to have been circumnavigated and I am left for the rest of the afternoon/weekend working through the consequences of the workaround.

Funny as it may sound, such weeks make for exciting times and I'm glad to be sitting here working through such challenging problems.