A lot of the history of mathematics is summed up in the last paragraph of this very interesting article. "The fact that the cap set problem finally yielded to such a simple technique is humbling, Ellenberg said. 'It makes you wonder what else is actually easy.'" Mathematical progress comes about by some mathematician noticing a pattern that makes solving a formerly difficult problem more easy than solving it used to be. (For this purpose, innovations like place-value decimal numeral notation fit the preceding statement.) Of course the hard thing is being the first human being to figure out the easy way to solve the problem, and then to embed that understanding in a technique that other problem-solvers can learn. But the increasingly rapid collaboration among mathematicians these days (mentioned in a comment posted earlier) speeds the uptake of new techniques and makes more likely that new understanding will rapidly spread among mathematical problem-solvers.