December 2008 Archives

I often describe myself as “a late convert to mathematics” and it's about time I explained what I mean.

From my early teenage years, I was a radio ham and an electronics hobbyist. I was pretty certain that I wanted to be an electronic engineer from the age of about 15, but, somewhat unusually for a would-be engineer, I intensely disliked mathematics. Everything else came very easily to me, maths required effort, and I was very lazy. I was also somewhat unfortunate in having maths teachers who were, shall we say, less inspirational than, say, my physics and chemistry teacher. I regarded mathematics as something of a necessary evil. I had to repeat maths to get the grade needed to get into engineering, despite good grades in everything else.

For three years of engineering, I struggled with maths. Spending too much time in the bar and not enough in the library didn't help, but as in school, pretty much everything else came very easily. I broke up with a girl the night before my third year maths final, failed spectacularly, and had to repeat in the autumn. Then, while studying for the repeat, something happened…

I had a mathematical epiphany. I was studying moment-generating functions and noticed their similarity to Fourier transforms. Then I started seeing other previously unnoticed connections between areas of mathematics I'd previously studied and it was interesting. Before that time interesting and mathematics were not two words I would have in the same paragraph.

I passed my third-year repeat maths exam comfortably; not a stellar performance, but more easily than I ever had before. Then, in my final year, my continuous assessment grade in maths was 96.25%. For the 3.75% that I lost, the lecturer called me into his office: he told me that one of my solutions was wrong, so he couldn't give me that marks for that problem, but he was intrigued to know how in hell I'd come up with it; he dubbed it interesting and creative… but wrong. Not the worst way to lose a few marks, I think. The final was of the “8 questions, pick 5” type and there were 6 questions I was perfectly comfortable with. I was then, and still am, somewhat slow when writing and particularly when working with mathematics, and only got 4 questions done in the available time. It was frustrating not to have time to do another question, which would've been easy. My exam grade was bang-on 80%. I got everything I was able to answer right, something I'd never, ever done before. The only thing that stopped me getting 100% was a lousy half-hour.

Since then, I've been particularly interested in connections between different areas of mathematics. Fundamentals, category theory, logic. Last year I took courses in abstract algebra and advanced logic. I loved them, but basically didn't have the mathematical chops to develop my knowledge and skills in the available time to be certain of a 5 (a Swedish “A”) in the exam — I never sit exams to “just pass”, instead I regard them as tests of my own understanding of the subject matter, which I expect to be complete before I'll sit an exam — so I haven't sat either exam yet. Unfortunately, my mathematical background, and the 10 intervening years between the times I've studies mathematics seriously, means that there are huge gaping holes in my knowledge.

Finally, there's one more thing that I've come to understand. Mathematics is an intellectual botanic garden of transcendent beauty, and mathematicians are the custodians and botanists who tend the flowers and breed new orchids. The attitude of most engineering students to mathematics is akin to rudely tramping through the flower-beds in hob-nailed boots, uprooting ornamental flowers to use for pig fodder — mea culpa, mea culpa, mea maxima culpa — to all of the maths lecturers I had in college: I'm sorry. Really. I get it now. I'm sorry.