4
$\begingroup$

To start really getting somewhere with attacking hard problems in the wild, I would guess we need to have a cursory understanding of a wide variety of math topics, and how they link together.

How much do we really need to know to get somewhere, and in what order do we need to learn it? Where can we learn how the different topics in Maths link together?

For example, graph theory, number theory, calculus, trig, complex, ... We learn each topic but rarely discuss how they all weave together.

  • 0
    I wrote my book "proof patterns" to try and show the commonality in proof techniques across areas.2015-07-17

1 Answers 1

4

Of course, all mathematics is the same, it just takes a while to notice the similarity between some parts.

Two suggestions:

  • learn more math particular subareas and compare them with each other/seek out applications of one to the other yourself

  • learn category theory which is an overarching extrapolation of abstract properties of different areas of mathematics and is among other things geared towards showing similarities between diverse areas of mathematics.