A type of unproductivity

There is a certain very special type of unproductivity that I have experienced only in math.  You are working on something and you feel almost certain your strategy is not going to work.  In fact, it is more likely than not that your strategy is not even a new strategy, but a variant on something you’ve already tried unsuccessfully — or maybe not even actually a variant, but just a rephrasing you’ve fooled yourself into thinking is a variant.  So you are not sure whether you are actually working on something at all.  In fact, you doubt it.

And yet you keep going!  Because what if it works?


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2 thoughts on “A type of unproductivity

  1. I think banging one’s head against a problem is a thoroughly under-rated aspect of theoretical problem-solving. Special Relativity was genius, but General Relativity took another decade and is, by any metric, far more difficult, and stands as a much more important, if lesser know, achievement.

  2. Sean says:

    Maybe not so unproductive, according to Wiles (https://plus.maths.org/content/andrew-wiles-what-does-if-feel-do-maths):

    “I really think it’s bad to have too good a memory if you want to be a mathematician. You need a slightly bad memory because you need to forget the way you approached [a problem] the previous time because it’s a bit like evolution, DNA. You need to make a little mistake in the way you did it before so that you do something slightly different and then that’s what actually enables you to get round [the problem].

    So if you remembered all the failed attempts before, you wouldn’t try them again. But because I have a slightly bad memory I’ll probably try essentially the same thing again and then I realise I was just missing this one little thing I needed to do.”

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