The stereotype of math is of a white-haired professor writing equations on a blackboard. Usually the professor doesn’t care about real life or applications. But math is a really broad field.
In the above map, different theoretical or ‘pure’ concepts have their mirror with different applications. How many have you seen in your field?
My mathematical map
Here I indicated the maths I’ve used so far by purple check marks. Most are on the applied side. I’m planning to dip a little further into engineering, optimization, and probability. On the theory side, I haven’t done as much. I’m very interested to move into chaos theory, category theory, more matrix work, and number theory in general. Hopefully this time next year I’ll have accomplished most of these mathematical goals!