I was a newcomer to maths. I spent all my school and most of my undergraduate days hating maths and never bothering to learn it. Now I do maths daily in my work and research – not just statistics, but pure mathematics. Students are very surprised when they hear of this, as there is a fairly popular fallacy that people are either into maths or not into maths, so my late “conversion” seems rather odd.
In fact, there is nothing strange about it. I belong to the group of scientists who are completely hedonistic about their science. I do what I do because I’m curious and I have questions that are as-of-yet unanswered to my satisfaction, so I figure it’s up to me to get those answers. That’s really the only thing that drives me forward. I have no dreams of helping humanity or progress (how research into the early evolution of arthropods and mutation-driven speciation could have any sort of broad applicability is a mystery to me).
At one point, I realised I had hit a brick wall. I’ve always been an avid programmer since I was a teenager (culmination was a full-fledged videogame, unfortunately a niggly bug didn’t allow it to move past the start screen…), and I used that ability to cover up my lack of mathematical skills. But then I realised that I was limiting myself by not bothering with maths. And by “not bothering”, I mean I couldn’t even solve basic algebra two years into my undergrad. The integral sign was just proof to me that all mathematicians are illiterates unable to even write a S properly. That limitation meant I couldn’t get the answers I wanted.
So I set about changing that, enrolling into all the basic mathematics courses I could and selectively into the more advanced ones I perceived would be useful to me, all this coupled with a stringent self-study program. I already gave the reason for the transition, but many people who were like me struggle with the practicalities due to an ingrained horrible perception of maths. And it really is a problem of perception, as there are really only two factors at play when it comes to the fear of maths, and both are purely mental problems.
A fear of mathematics as “alien”. To the untrained eye, equations are long strings of symbols and it’s hopeless to try to make sense of them. You know what else is a long string of symbols? Every single written language. If I look at any Cyrillic writing, or Tagalog, or any of the many Indian scripts, I can’t make heads or tails of anything. This is exactly the feeling that I had when looking at maths.
But there is a critical difference between mathematical language and other languages: logic. There are several symbols that need to be learned in maths, but by and large it really is just a language that is completely logical with no learning necessary. If you see any equation from any mathematical field, you can, theoretically, go through it and work with it. There are no special exceptions, there is no jargon or dialect. It’s all identical. That’s why mathematics is universal. And as soon as you learn how to process the sight of an equation and not be deterred by it, you’ll find yourself gliding across maths. Just take everything one step at a time rather than trying to take it all in.
The second problem is one of expectations. Maths has a reputation for ultra-precision, especially in the ultra-messy biological sciences. So it’s no surprise that a fledgling biologist like myself went into maths expecting it to give me exact numbers that will prove key to solving my problem.
For one thing, this is absolutely not the way to do biology. Biology is messy, and any “precise number” is fallacious. Biology, by the very virtue of what biology is, demands ranges and probabilities and fuzziness. So you shouldn’t expect exactness and precision.
And this ties into the second point, that maths is not about precision and exactness. At least not numerical maths. As soon as the problem becomes larger and more complex – as the most basic biological problem will be – numerical analysis will only fetch approximations. This is ideal for biology, of course, but it’s something that must be grokked, and the original dream of ultra-precision discarded as soon as possible. This is somewhat problematic though, given that the things one typically learns first and that serve as building blocks for more advanced analysis, e.g. linear algebra and one-dimensional analysis, do deliver precision, keeping the mirage of precision alive.
I hope this post helps out any high school kids and undergrads. Don’t be like me and do bother with maths. At the very least, it will save you several weeks of non-stop catching up that will make you feel like an utter moron.