Fair enough. I tried in my youth to solve every problem I came across. There were many I couldn't solve. It took a while before I developed the wisdom and discipline not to solve every problem no matter how long it took. By a while I mean decades. I sacrificed the possibility of family life, have stopped talking to my uncomprehending stepfather, and have kept my social interactions to an absolute minimum to pursue my consuming interest. (I mention this as a point of pride.) I find myself continually astonished by the ingenuity of solutions I probably could never have imagined after years of work. Perhaps, after a lifetime of effort that must be continually maintained, I have attained the level an entering freshman at Harvard. At this stage, I may be reduced at best to connoisseurship of some aspects of mathematics.
Now for some reflections on attitudes. Mathematicians sometimes act as if they believe that expertise in mathematics transfers to expertise in mathematics education. Suppose you are a sensitive student, lacking in confidence. You open Korner's beautiful book on Fourier Analysis, and the first thing you are greeted with is "This book is meant neither as a drill book for the successful student nor as a lifebelt for the unsuccessful student." Korner does not mention other references suitable for the successful and the unsuccessful student. You take this comment to mean that Korner would let the unsuccessful student drown. There is no implication, but this is the psychological import, the implicature. Why mention the unsuccessful student at all? Why not say who the book is for, without planting this gratuitous image in the reader's mind? It would take some time to return to this book, to get past the wonder at a mind capable of such an incidental, dismissive, off-handed acknowledgement of "the unsuccessful student."
You could say this is "overthinking." Such remarks, microagressions as they are termed today, "perpetrated against those due to gender, sexual orientation, and ability status", are sometimes revealed in the asides of mathematical authors [1].
And now if only mathematics educators would evaluate their students on the state of their confusion!
Now for some reflections on attitudes. Mathematicians sometimes act as if they believe that expertise in mathematics transfers to expertise in mathematics education. Suppose you are a sensitive student, lacking in confidence. You open Korner's beautiful book on Fourier Analysis, and the first thing you are greeted with is "This book is meant neither as a drill book for the successful student nor as a lifebelt for the unsuccessful student." Korner does not mention other references suitable for the successful and the unsuccessful student. You take this comment to mean that Korner would let the unsuccessful student drown. There is no implication, but this is the psychological import, the implicature. Why mention the unsuccessful student at all? Why not say who the book is for, without planting this gratuitous image in the reader's mind? It would take some time to return to this book, to get past the wonder at a mind capable of such an incidental, dismissive, off-handed acknowledgement of "the unsuccessful student."
You could say this is "overthinking." Such remarks, microagressions as they are termed today, "perpetrated against those due to gender, sexual orientation, and ability status", are sometimes revealed in the asides of mathematical authors [1].
And now if only mathematics educators would evaluate their students on the state of their confusion!
[1] http://en.wikipedia.org/wiki/Microaggression