calculus is a way to count what it can't be counted. it's beautiful! in the case of dfferential calculus, it boils down to dividing 0/0. really. integral calculus is about mutiplying ∞ x 0. that's it really.
at the core of it is the problem of limits. how deal with things when they approach zero, or infinite. i'd suggest before you look at calculus, look at limits, and read up on infinitesimals..
anyway that mathematician is just another version of zeno's paradox (aka achilles and the turtle), which is one of our earliest ideas about limits-- where things approach when they can't really get there. calculus starts from that.
in differential calculus for example you want to measure the slope of a function.
but what when it's not a straight line? what if it's a curve? in each point of this curve the slope is different, yes? how do you measure the slope at each point?
to make a long story short-- in order to measure the slope (aka rate of change) at a curve, you take a tiny triangle that gets close to the curve. well that's not close enough to so make the triangle smaller. and smaller. and smaller. until the height and the length of your base approach zero. but you can't divide 0/0 yes?
anyway, if you think about it-- the derivative (gradient) of a function is also a function. and the relationship between a function and its derivative can be really a thing of beauty.
