Archive for September 2011
Timothy Gowers just started a new series of blog posts for first-year mathematics students. While the blog posts will be centered around Cambridge’s courses I am pretty sure that the discussed topics and hints will be valuable to other students as well. In fact, what I find most impressive is the goal of the series: to teach people how to do mathematics! We all learned what mathematics is and results have been presented to us in a nice, cleaned-up fashion. However only very few of us were taught how to solve/approach problems – most of us learned it the hard way at some point. It is as if you go to a restaurant to get great food: this does not teach you how to cook yourself! In particular it does not teach you that the nice result is a product of quite a mess in the kitchen. When doing math, everybody will reach her or his limit sooner or later (as compared to math in school which was easy for many math students) and it is precisely this point in time, when students start to doubt their own potential. In fact some kind of a bias is bound to take place: every math problem that can be solved is “easy” and every problem that is not solved is a small personal crisis – “am I good enough”? As you did not see the mess in the kitchen, one might think that things come easy in a nice form or not at all. In the end there is no positive feedback available anymore, only negative feedback.
I am very much looking forward to this series and I am sure that Tim has some valuable insights to share!