Why Thinking Geometrically and Graphically is Such a Powerful Way to Do Math
I am currently teaching my favorite course: “The Economics of Risk and Time.” I love the challenge of making math that could have been very difficult easier. To do that, I use geometry, graphs and diagrams as much as possible. I not only find trying to use pictures helpful for myself, I recommend it to my students when they are working on problems.
Why are pictures (geometry, graphs and diagrams) so helpful in doing math—at least for those who have developed their skill in using pictures to do math? I think brain science and evolutionary psychology together give a good answer. Because our ancestors a few million years back lived in the trees, there was a great survival advantage to visual processing to see a branch to catch and to see fruit to grab. As a consequence, those of us who remain inherited genes for a large visual processing region in our brains. If you can bring that visual processing region to bear on math problems, you will be bringing a lot more brain-power to bear. That will make you smarter at math.
For me, a big side-benefit of taking a geometric and pictorial approach to math is the enjoyment I get from the images in my head as I consider the math. It is remarkably similar to the enjoyment I get from looking at great visual art, which is a big deal for me, as you can tell from half of my tweets being retweets of great art.
I have links to many other posts on math in my post “Gabriela D'Souza on Failure in Learning Math”