567 words on Uni
That conjecture is one of those easy-to-understand problems that was unproven for ages. All it says is that except for 2 and 3 there are no positive integers a, b, p, q such that ap - bq = 1. In other words, 8 and 9 are the only powers that are adjacent. Sounds easy – but apparently isn't. Looks a bit like Fermat's last theorem as well. In the talk we were given a lot of historical background on how progress on proving this was made and finally pointed towards theorems that lead to the proof of the conjecture. Sadly, these looked quite easy and it wasn't made clear which part exactly made finding the proof so hard.
Today, we heard two other interesting talks. Sadly both were made using projection facilities. The first speaker was a bit embarassed that his video beamer didn't work right away (requiring the computer a restart to use it) and then he was embarassed again because he used Windows – actually apologising for that, mumbling that Linux didn't do as well for displaying the files (although he seemed to be using something called GSView to display the slides). Mathematicians can be so ... civilised.
The later talk used analogue slides and both of them made obvious that, despite the speakers taking care not too rush through the material too quickly, projecting slides is a very poorly developed technique. The main shortcoming is that you aren't able to see the previous slide – meaning that you lose important context and possibly can't finish copying the interesting facts. Things that aren't a problem with the good old blackboard.
The solution used for this in the analogue age is using two projectors to keep the previous transparency or slide around. This, of course, leads me to demand Powerbooks with two video outputs, now.
But this may point us to another fact. Namely, the fact that software for making presentations is not only delivering utterly useless and ugly results in most cases but also completely fails to embrace the power of freely programmable computers and thinking out of the box.
Doing that they may have realised that having separate slides is actually a limitation caused by the traditional, analogue way of presenting things (and even in the analogue world, overhead projectors with a kind of 'infinite' roll of transparency exist). In many situations it would be beneficial to have the contents of the presentation scroll by – thus giving the maximum possible context on one screen – rather than starting with a blank page over and over again.
But then, of course, people might say that the programmers of Keynote & co. got it absolutely right as presentations made with those programs are made to people whose brains are starting to overflow at the third bullett point in a row.
In fact, when people are trying to actually work with these technologies rather than just playing them to show off your corporate gadgets, they see that problem right away. That's why the computer people in our department came up with a solution for this when using an electronic blackboard. This involves a software reading the board's files and displaying the previous pages on a secondary projector.