Combinatorial explosion in math

One of the key difficulties in math, compared to puzzle games, is the combinatorial explosion of ideas. A puzzle may have merely 20 moves you could make at each step, a branching factor of 20. But in math, a problem about analysis might use an insight from algebra which seems totally out of left field. When such "moves" are possible in math, that means the space of potential moves you could make when trying to solve a problem is vast. There is just not much brute force/type tetris type ways you can solve a problem unless it's a very simple problem like the ones where you just apply a definition.

See also

• Spaced proof review as a way to understand key insights in a proof -- one way to combat combinatorial explosion is to repeatedly try to prove a theorem