It sometimes seems that the only real result of math education is to convince its worst students – and a substantial number of us mediocre ones – that numbers are magic. “Anything can be measured,” goes the myth; and, once a number is associated with something, it becomes much more real, much more defined. All problems are soluble once they have become mathematized – even TV pushes this philosophy on the dramatic series, Numbers.
This hocus-pocus has some startingly impressive roots. Psychologist Edward L. Thorndike – unskilled in basic algebra -- wrote: "Whatever exists at all exists in some amount. To know it thoroughly involves knowing its quantity as well as its quality." Heavy philosophy!
But what is the quantity of a chess game? Or of the relation "<>"? Do chess games or "<>" not exist? Do chess masters wait with bated breath for someone to mathematize a chess game so that they can “know it thoroughly?”
The harm done with this exaggeration is that it creates the expectation that when and only when a technical, measurable solution to a problem can be devised, can that problem be solved.
So it is that problems must be left to mathematical geniuses, since their solution is beyond the ken of most people who can only stumble through math counting on their fingers.
To examine these issues further, see Measurability and Educational Concerns