As you should all be aware by now, I am into careful definition. I believe that without careful definition, communication is impossible.

So: my definition of math!

Mathematics is is the science of constructing internally self consistent logical systems and documenting all their various extentions and conclusions.

What makes math so important is that we assume the universe is internally self consistent. Any time we can map any part of our knowledge into mathematics we suddenly have a wealth of deductions avaliable to us which, under the normal human abilities, could never have been achieved.

Under my definition, any logical construct is "Mathematics" and everyone who wants to think should learn all the math they can! To refuse is to insist that irrational thought serves some purpose other than intertainment.