What Do You Think about Mathematics?

I find that at school the children like the teachers and not the subjects. A short time ago I delivered a lecture to would-be students of an engineering college. There were about five hundred in all. I asked them who liked mathematics and got two hundred raised hands. Then I asked them who were particularly fond of their math teacher, and again I got 150 to 200 positive responses. But when I asked them how many liked mathematics but did not like their mathematics teacher, I got four hands out of 200 lovers of mathematics!
Most of the students who finish grade school and high school, and even college with a short course in higher mathematics ordinarily forget almost all the details and even the mathematical methods they studied. They find it hard to recall even isolated fragments and they dont often know what use it has been to them (It ought to be very interesting to make a check of all the sciences and find out what a person remembers 5,10 and 15 years after leaving school. What has been of use and what is totally useless or even harmful. Very interesting! What they usually remember are poor marks, funny or dramatic incidents and, finally, some of the theorems that caused them a headache or two. Generally they adhere to one of two contrary points of view.
The first—rather with haughty disdain—goes something like this: "Mathematics is a dull and truely boring science where all you do is count; oh, its like book-keeping. Where does anyone find use for problems in pouring water from one pool into another? Time spent on things like that could be used more profitably. Why seek a complicated method for determining the third side of triangle via the other two sides and the angle between them? First, its simpler to use a protractor for the angle and then measure the other side with a ruler, and second, thats another instance of something that is never needed in life." And so on in the same vein.
The other viewpoint is one of awe. "Mathematics? Oh, good heavens, thats very difficult, thats complicated, thats way out beyond the reach of the ordinary person. Only talents and men of genius can understand what mathematics is all about. Mathematicians pose fantastic problems and even find solutions to them."
But both camps firmly believe that mathematics consists of algebra, geometry and trigonometry, and also something called higher mathematics, which is pictured as a conglomeration of such intricate formulas as to be a complete mystery to both parties. Arithmetic doesnt seem to be connected with mathematics; it has something to do with childhood and is as common as the alphabet, penmanship and babies illnesses.