I remember how back in our university, almost all the first year students that have the high-level math (the “laaja”) keep asking older students questions like “Was it worth it?”, “Did you learn anything?” and “Will it be hard?”. My answers to these would be yes, yes, and yes. But that’s not today’s point. More interesting would probably be asking “Why? especially related to the first two.
As background information, I didn’t come from a math-specialized high school. I felt confident about math and had some successes in high school, especially towards the end. I was invited to participate in the higher math at our University – as you might know, it’s not mandatory for automation students – so I got to choose if I wanted to do it or not. After some deliberation, I resolved to do it. Mainly, I was curious about how I’d do inside that peer group and how I’d feel about “proper math”. Secondly, I thought I could always switch back to normal math if I didn’t like the high-flying version.
To cut a long story short, it was a hard track. I remember sitting with friends and doing exercises late into the evening. I remember spending about 50% of my studying time just on math. It worked and my results were pretty good, although in no way top class. Solid 4s and a 5 Three courses were enough for me, as switching to Industrial Management meant I didn’t need the 4th course, so I dropped it as unnecessary.
Anyway, what was the learning experience? Honestly, I don’t think I remember half of the stuff we went through. The pace was fast, exercises were not always so plentiful – or understandable – and most of the stuff I haven’t needed since. Maybe it’s somewhere in the back of my mind, but I couldn’t recall it without some supporting material.
The most important thing for me was to learn not to run away. I remember staring at problems that seemed completely incomprehensible and thinking there’s no way in hell I’ll figure this out. But in most cases I finally got it. Actually, we got it. Since I was almost always solving the stuff with friends, and that was also a key ingredient to success. Four minds thinking along slightly different lines made for a better solving process, and naturally decreased erroneous calculations.
Anyway, if you think don’t run away is an obvious principle, you’re probably right. It’s not the principle that was hard for me, it was – and sometimes still is - applying it. The math courses were a valuable experience in the field of really confusing problems. Problems, which make you think “the solution must be really hard – how will I ever think of it?” Normal problems don’t do that. The confusion leads thoughts into a sort of meta-level, thinking that since you can’t see the outline of the solution right away, it must be something outside your current knowledge. This naturally induces a thought that if the solution is outside your knowledge, how on Earth can you come up with it in the first place? Needless to say, you start focusing more on freaking out about the problem than solving it, which is a terrible spiral to get into.
In retrospect, freaking out about a problem is very unnecessary – never mind useless. For every problem, there’s always a solution. The problem might not be solved by the end of the night, but slowly you’ll get there. Every step is a step towards the solution. Just keep taking those steps.
A practical application of the don’t run away principle are my German skills. Since high school, my German skills had started seriously deteriorating. In active vocabulary I’d already fallen down to the “Ich bin” level, meaning I couldn’t really have a decent conversation anymore. At some point, I realized the situation would only get worse with time. The vocabulary wasn’t going to magically pop back in my head. Improving my German would mean I’d need to, you know, actually try to learn it. It was time to face the issue and stop running. So I decided to plan an Erasmus year in Austria (to combine language with beautiful sights), which worked as a motivation pump to take some German courses in university before the Erasmus. Well, now I’m here in Graz with the year nearly behind me, and my German is better than ever. Problem solved.
These days, whenever I face a problem, I remind myself: don’t run away. If I feel imprisoned by the problem, I just think oh well, just have to start chipping away with this spoon. The wall will crumble eventually.