Comment author:[deleted]
12 October 2010 12:55:47PM
21 points
[-]
The most impressive quality I've seen in mathematicians (including students) is the capacity to call themselves "confused" until they actually understand completely.
Most of us, myself included, are tempted to say we "understand" as soon as we possibly can, to avoid being shamed. People who successfully learn mathematics admit they are "confused" until they understand what's in the textbook. People who successfully create mathematics have such a finely tuned sense of "confusion" that it may not be until they have created new foundations and concepts that they feel they understand.
Even among mathematicians who project more of a CEO-type, confident persona, it seems that the professors say "I don't understand" more than the students.
It isn't humility, exactly, it's a skill. The ability to continue feeling that something is unclear long after everyone else has decided that everything is wrapped up. You don't have to have a low opinion of your own abilities to have this skill. You just have to have a tolerance for doubt much higher than that of most humans, who like to decide "yes" or "no" as quickly as possible, and simply don't care that much whether they're wrong or right.
I know this, because it's a weakness of mine. I'm probably more tolerant of doubt and sensitive to confusion than the average person, but I am not as good at being confused as a good mathematician.
Comment author:minhyongkim
17 October 2010 01:22:41AM
3 points
[-]
Although I agree on the whole, it might be worth recalling that 'I don't understand' can be agressive criticism in addition to being humility or a skill. Among many examples of this aspect, I rather like the passage on Kant in Russell's history of western philosophy, where he writes something like: 'I confess to never having understood what is meant by categories.'
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The most impressive quality I've seen in mathematicians (including students) is the capacity to call themselves "confused" until they actually understand completely.
Most of us, myself included, are tempted to say we "understand" as soon as we possibly can, to avoid being shamed. People who successfully learn mathematics admit they are "confused" until they understand what's in the textbook. People who successfully create mathematics have such a finely tuned sense of "confusion" that it may not be until they have created new foundations and concepts that they feel they understand.
Even among mathematicians who project more of a CEO-type, confident persona, it seems that the professors say "I don't understand" more than the students.
It isn't humility, exactly, it's a skill. The ability to continue feeling that something is unclear long after everyone else has decided that everything is wrapped up. You don't have to have a low opinion of your own abilities to have this skill. You just have to have a tolerance for doubt much higher than that of most humans, who like to decide "yes" or "no" as quickly as possible, and simply don't care that much whether they're wrong or right.
I know this, because it's a weakness of mine. I'm probably more tolerant of doubt and sensitive to confusion than the average person, but I am not as good at being confused as a good mathematician.
Although I agree on the whole, it might be worth recalling that 'I don't understand' can be agressive criticism in addition to being humility or a skill. Among many examples of this aspect, I rather like the passage on Kant in Russell's history of western philosophy, where he writes something like: 'I confess to never having understood what is meant by categories.'