The Accidental Mathematician

The mysterious effectiveness of trivial pursuits


This is probably not worth posting about, but I’m curious to see if anyone will respond.

I usually take notes while reading a math book or article. There may be obvious utilitarian reasons to do so, for instance I may want to reorganize a proof in order to understand it better, fill in some gaps, work out the details of the omitted calculations, and generally rewrite selected parts more to my liking. No, I didn’t really expect that you’d be surprised to hear any of that.

What’s more interesting is that I also seem to benefit from the physical process of writing out my notes in longhand, the old-fashioned way. This summer I spent some time reading a paper that, in addition to proving a significant result, is a perfect example of how I’d like all math papers to be written. Aside from a couple of minor calculations that I wanted to work out in detail, there was no need to add, clarify or reorganize anything whatsoever. Even so, I still found that copying bits and pieces of the paper by hand helped me understand it better, as if the motor activity fired up some part of my brain that would otherwise remain disengaged.

It was not the first time I noticed this, and I don’t think that this is just me, either. I even have a vague recollection of reading a popular science article that said something to that effect. (That was a long time ago and I can’t find it now.) It works in other settings, too. You might expect that taking notes during a lecture would divide my attention and leave me less able to focus on the subject matter, but actually it’s quite the opposite. This is of course assuming that I can follow the lecture, at least in principle; some topics are too far out of my reach, and some lectures can’t be saved. But I digress.

Now, here’s where I have a question, especially to the readers under the age of 30 or so. I’m told that handwriting is out of fashion these days, all but replaced by typing and texting. This article reports that the younger generation in China loses the ability to write Chinese characters by hand because they don’t have much use for handwriting except to sign the back of their credit cards. Over here, I suppose it helps that we have a somewhat less complicated alphabet, but it’s still true that there are fewer and fewer reasons to write anything in longhand. Even signatures might become obsolete eventually, replaced by PINs, passwords and biometric technologies.

This isn’t going to be a “kids these days” rant. I’m not particularly eager to go back to the days when “cutting” and “pasting” meant using scissors and glue, respectively. I don’t really miss the logarithmic tables, either, in case you were interested. Nor would I want to type all of my papers the way I typed my Master’s thesis, on a borrowed mechanical typewriter with no word-processing capabilities and no math symbols. Those had to be filled in by hand, in the spaces you’d have to leave between the typed letters and numbers. For corrections, I used the white-out fluid that a colleague had brought from a trip abroad. Also? The wired kids these days might not even know the literal meaning of the expression “carbon copy”, or they might look at old issues of scientific journals and wonder about the instruction for authors to submit the “original copy” of the manuscript. I could explain it all to them in more detail than they’d ever want.

But I said I had a question. It’s this: if you didn’t grow up doing a lot of handwriting, if it’s typing and texting but not longhand that feels natural, do you still take handwritten notes when you read a math paper, for reasons similar to those I described? If not, is there something else that you do instead? Taking notes in TeX, for example, does not do it for me. Obviously I use TeX to write papers and exchange notes with collaborators, but typing in TeX distracts me from thinking about the mathematics involved, whereas writing in longhand helps me focus on it. Does anyone here see it differently?