My mathematics career (if you could even loosely call it that) was never likely to be stellar, I’m afraid. I muddled along OK for a while, taking in probability & basic calculus** pretty well, as well as imaginary numbers & matrix transformations. It got a little bit thicker in amongst trigonometric calculus, but I managed to hang on for long enough to get into uni – amid the endless cries of “But we’re never going to ACTUALLY USE this, are we?” from many of my contemporaries. Once at university I pretty well completely lost the plot however, due to a combination of having a tutor whose French accent was so thick that I couldn’t understand his explanations of telescoping series, and also in part because I stopped going to lectures. But mainly the French accent, I’m sure.
So having truncated a promising career in pure mathematics, I lost access to further knowledge in that field – as do many people who cast an area of study to the wayside. Previously this was a pity (he writes, inexorably steering towards another superfluous “Wow, isn’t Wikipedia amazing?!” post), however with the advent of modern communications technology it is now possible for a university dropout to learn of the existence of some truly mind-hurting things.
Yes trendsetters, thanks to Wikipedia even we non-intelligentsia can learn of:
- Tits Buildings – a geometric algebraic structure for generalising the structure of homogeneous spaces, postulated by Belgian mathematician Jacques Tits. This is, of course, useful to know if someones asks you to name a famous Belgian other than Hercule Poirot. You could also say Audrey Hepburn, but then you’d have wasted an opportunity to say Jacques Tits***.
- The Hairy Ball Theorem – The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on the sphere. Or, to put it another way, if you try to comb the hairs on a sphere flat you’re always going to wind up with a tuft. As the wikipedia article shows, this is not true of hairy donuts, which can be combed flat. In case you were wondering.
See kids, stay at university! It gets better.
** important note: I didn’t recreate the famous line by Aaron Warren-Thomas who, after completing the 10 week term’s work on Integration and being faced with the teacher’s enquiry of “Now class, are there any questions?”, raised his hand and asked, “I’ve got one – what does that squiggly line mean?”.
*** to be honest, once you’ve gone down the road of naming famous Europeans with amusing sounding names, you can then play the trump card of mentioning Wubbo Ockels – the first Dutch citizen to go into space. He also helped people escape under the Berlin Wall via a tunnel he and some of his mates built as students. What a guy.