>I'M REALLY THINKING ABOUT THE WAY I SHOULD APPROACH
>MATHS.I'M IN THE FIRST CLASS OF HIGH SCHOOL AND OUR TEACHER
>GIVES US EXERCISES OF A "SPECIAL" WAY OF THINKING AND SHOWS
>AN OTHER PHILOSOPHY OF MATHS.I TAKE THIS AS CHALLENGE-MATHS
>ARE CHALLENGE THEMSELVES- AND I GET KEEN ON THEM.THAT WAS
>THE REASON OF SEEING MANY SITES ABOUT MATHS AND MORE AND
>MORE AND...EXERCISES AND GETTING BORING WITH THE OTHER
>LESSONS.HOEVER,I FEEL "OBLIGED" TO SOLVE ANY OF HIS
>EXECISES.I think it must be a nice feeling. This may be akin to being driven. It's an internal spring that pushes people to do thinks. And this is the best way to approach maths, viz., by doing. I would say that it does not exactly matter why you do that. But this is the only way tp acquire appreciation of maths.
>OTHERWISE I FEEL THAT I'M NOT WORTH THE HIGHEST
>GRADE I WAS GIVEN-THAT'S LESS IMPORTANT-
>AND THAT I CAN'T REACH HIS DEMANDS.I'M ALSO AFRAID THAT I
>LOOSE THE ESSENCE;THE SCHOOL DEMANDS.I REALLY APPRECIATE THE
>WAY OF HIS TEACHING BYT I FEEL I HAVE BECOME SLAVE OF MY
>FAVOURITE LESSON WHEN I HAVE TO FIND SUCH QUADRILATERALS OF
>MY QUESTION IN ONE DAY.WHAT'S YOUR OPINION ABOUT THAT?
Much has been written about how mathematicians find their proofs. In school it is assumed that the process is logical, even algorithmic. While indeed there are problem solving strategies, mathematicians often share a notion that solutions come to them unexpectedly after a period of intense concentration on a problem.
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