>>11681727>all math and science boils down to memorizing at most 10 stepsDon't know about science in general, but here are my 10 steps for maths:
1. If it seems too complicated, use approximations by linearising it or otherwise a simpler structure (all of calculus/differential geometry rests on this principle, localization in algebraic geometry and number theory, triangulation in geometry singular homology etc.)
2. If your object is too small/incomplete, complete it yourself by adding what is needed. (the construction of real numbers, complex numbers, p-adic numbers, and a lot of topological objects rests on this principle)
3. Draw a diagram. Many diagrams if needed (seems obvious until it's not. Tremendously helpful)
4. Look for symmetry (foundation of group theory, Galois theory, a lot of number theory as well as most other subjects)
5. Reverse the arrows (cohomology)
6. Look for antisymmetry/alternating objects (most differential geometry is based on them)
7. Try to associate algebraic objects to geometric objects and vice versa.
8. Study the spheres. If you think you understand spheres, you need to study them more. Never stop studying spheres.
9. Study complex analysis. It's related to everything else.
10. If the problem is too hard, try to reduce it to the finite case somehow (finite fields, a lot of things in algebraic geometry)
