Practical mathematical ability, like other parts of the body (since it is encoded somewhere in the brain), atrophies over time. By the end of high school, I was able to score a 5 on the AP calculus BC exam, which allowed me to skip Calc I & II at Tulane. Freshman year, I learned more math, although I didn’t really like it and was going through a major adjustment to college life, and I didn’t pick it up very well. By sophomore year, I’d forgotten most of the integration tricks I knew, and some of the derivatives.
From time to time, I’ve re-learned this stuff. Experience (and scientific studies) have shown that it’s normal to re-learn things much more quickly that the initial learning time, which is nice. My research places me in kind of an odd spot though.
If I were doing purely theoretical work, I’d have pencil to paper all of the time, integrating, derivatizing (as we said in HS), solving differential equations, substituting variables, etc, etc. But I don’t do purely theoretical work.
On the other hand, were I an experimentalist or a clinician, my work would be much more hands-on, so my math skill would atrophy a great deal, but it wouldn’t matter as much.
I work somewhere in the middle. Our software is sufficiently advanced that my work is a lot like hands-on experimental work. It’s important for me to understand the underlying theory, and I do, but understanding it and sitting down to work out math problems (especially if you’ve gained the understanding by doing so already in the past) is a different story. I go through long periods without serious math work, punctuated by short bursts where I have to dig all the way back in. Lately it’s been for a class.
I used to feel guilty about this — I probably wouldn’t have even posted it on this blog a couple of years ago. However, after hearing many other academics — several of whom are much more advanced in their careers than me, and well respected — lament a similar problem, I no longer feel guilt. It’s a common problem. For professors that teach university classes, the problem is somewhat alleviated, as they have to teach classes on this stuff and it keeps them fresh.
Not to say that I want to have to teach any classes right now, mind you.
I’d be interested to hear if you have any suggestions for staying sharp when I’m in a mathematical lull.
I wish I had some advice on this. This happens to me all the time. In college I did linear algebra and up through multivaruable calculus and actually really enjoyed math. After transferring to Tulane I didn’t take any more classes and my skills atrophied both in math and physics. However, today, when i need it it’s fairly easy to go back to a textbook and the derivations of formulas and theorems come flowing back. It’s not instantaneous, but it’s easier. I wish I could keep it with me all the time. But with me, if it’s not in constant use, the knowledge just goes. Which is why I remember nothing of Japanese and Swahili any longer. Sad.
Rob emailed me this because comments were broken:
Just thought you would like to know.
My math skills have never atrophied, but I’ve never gone a year
without math of some kind.
I battle math rot by by memorizing big concepts. For every sub-
discipline in math, usually every idea you need is one or two easy
steps away from some big ideas. If you memorize the core concepts,
you can re-derive everything else on demand.
I have no solutions, only commisserations. I haven’t had to do any math more complex than taxes or calculating tips since 2001. I got a four in my AP class which let me skip some calc in college, but when I got into college, I found out that calc was as far as I’d ever need to go in math. Subsequently, I’m proud of myself that I even remember the concepts involved in calculas, even if I’ve forgotten how to be begin most of those problems. I’m actually really sad because I really enjoyed learning mathematics. For all it’s dry and sometimes tedious exercises, it revealed a very elegant way of looking at the world.
To whit, I’m pretty excited I’ll get to take a stat class for anthropology. I get to crunch some numbers again.