Practical Math
I read great article “Kill Math“ by Bret Victor which discusses shortcoming in current mathematics.
Apart from basic arithmetic calculations most people are not able to apply math into their day-to-day activities. This is because fundamentals of math which students learn are not visualized.
For example, What does solving 2nd degree equation mean ? Does it cover some 2 dimensional region in x-y axis. Or does a 1st degree equation represent a single line or a curve and 3rd degree equation represent a 3 dimensional region or curve. What are the parameters affecting the shape of the curve ?
Once we start practicing to visualize each algebraic equation geometrically, differentiation and integration of any order will also be easy to understand. So will be Sin, Cos functions which are wave curves.
Math is incremental in structure. Unless the basic mathematics is clear, higher math will remain difficult to understand. Also note that to solve the higher order math, something concrete like symbolic equation is necessary and not all equations can be visualized.
We require to look at representations other than symbols for equations so that it becomes more and more easily applicable in real universe.
This is what I take away from the article.
On lighter note , it is not easy to visualize dark matter colliding in outer space apart from equation as in the “big-bang theory episode 3-04” scene below
