Wednesday, August 13, 2008

Emotion and mathematics

It would be easy for people outside of mathematical areas to assume that the exercise of mathematics is an austere and unemotional activity, and that as a result mathemamaticians are, whether by nature or by habit, cold and disinclined to emotion.

Having observed many people (including myself) doing mathematics and discussing mathematically-related topics, this is far from the case.

I have had many congenially heated arguments with colleagues, and I have even caught myself grinning in delighted anticipation of going another round with a valued fellow-traveller.

(I've been called crazy a lot of times - but more times in mathematically-related discussions than anywhere else - and with unstinting good humour to boot. "You're crazy! You can't do that." "No, really, it's right. You can do it here..." "No, no, it's nuts to do it that way even if it's right." -- and so on back and forth; in fact, I think that's how a lot of mathematical arguments get polished)

Even as a solitary activity, mathematics is for me, intensely emotional, even visceral. Many times, equations I have worked with have various kinds of symmetry, and many of those symmetries will carry through the equations as the argument develops.. this is, I presume, what produces a strong sense of rightness that I often feel as the steps progress. There's also a corresponding sense that there is some mistake - for me a feeling something like that moment on a roller coaster as it begins to descend, though it is sometimes even stronger than that - before being aware of exactly what is wrong, or precisely where it lies.

If you work with particular kinds of expressions a lot, you built up a sense of what they "should" look like, and it becomes easier to recognize that something is wrong before you can say precisely what the problem is; because the intellectual cognition is behind the pattern-recognition, it has an emotional quality.

A really clever manipulation (I can't help but think of them as "tricks") or an inspired substitution that makes a difficult problem easy can produce a tingling sensation up the back of my neck and head. A particularly beautiful piece of mathematics can, on occasion, move me almost to tears.

Then there's joy and delight. On occasion I have had the fortune to look at some neat, if modest, just-derived result and wonder if perhaps I am the first to have ever seen it (it is, obviously, rarely the case that I am - it is not unusual to find that my result has been tucked away in some mathematical corner for many decades ... on one occasion I found I had been beaten by Gauss - but the thrill of discovery is there all the same).

There's also what I call the "stupid feeling". When I'm working on something new or unfamiliar (or even, on occasion on what ought to be familiar), I can spend long periods - days, weeks, or even, shamefully, months - where I feel intensely incompetent, like I'm reaching around in the dark for something that I know is right there, but can't seem to locate it - and then there's a fleetingly brief moment of joy as I see how to do it (often barely long enough to say "Yes!"). Then quickly after, in retropspect (sometimes as I see an even better way to do it), it is all so utterly obvious, so agonizingly plain, that the prior feeling of incompetence seems, if anything, far too mild.

For me, that feeling is occasionally so intense I cannot even bear to write it up properly, or sometimes even to mention it, because the whole thing is so painfully facile. (I doubt that most people feel this quite so keenly; I'd be curious to know.)

Mathematicians don't discuss emotion much; a kindly supervisor might have a few words on dealing with the disappointments that naturally come with trying to get some result to come out, or those that come with trying to get something published. But outside of that, the preference is almost always to talk about the mathematics itself.

But just because we don't talk about our feelings with each other doesn't mean we're not feeling them.


Dana Hunter said...

You've given me a thought.... I think it may be a very good idea to bring out the emotion more when discussing science and math. Emotions are excellent hooks, and I think if fewer people saw it as pure Vulcan logic done by passionless nerds, science and math both might get some of the appreciation they deserve.

This was a beautiful post. I am so plugging this!

Cujo359 said...

I've seen many impassioned arguments in my business, and have even been a part of a few. Whatever your line of work, if you put a lot of thought and effort into it, you're going to feel attached to it. To be otherwise would probably not only be inhuman, it would almost certainly be contradictory. We don't work hard for logical reasons. Emotion is what drives us.

LihuaEmilyP said...

I quite agree. This is a really marvelous article.

Unknown said...

great article! I found this really useful as I'm currently writing a Theory of Knowledge essay: 'there is no absolute distinction between true and false. Discuss this claim.' I was researching emotion in maths (as a way of knowing in an area of knowledge), to see if there is such thing, when I came across your article and found it very interesting. If you have any comments or suggestions concerning my essay don't be afraid to reply!!

Anonymous said...

Could I quote you in my TOK essay? If so, what should i call you? I found this post very interesting!! You make some very good points!

Anonymous said...

There is a real connection between emotions and mathematics!!.
I was diagnosticated with a emotional trastorn and I had to took a lot of psychiatric medicines. I noticed that something inusual happened when I studied maths, while I felt so depressed ... I just felt in complete peace and equilibrium. Now my medicine is studying mathematics

PD: sorry for my english, I'm learning

Anonymous said...

Math does leave can leave one with some rather strong emotions. After spending hours on a problem without knowing how to solve it can get rather frustrating. I'd say math is more a way of life as well as a discipline. You part way, with thoughts, and life, and attend to the many problems that need attention. Different emotions, and it really all becomes a meditation.