For starters: 1. All math and CS prerequisites to an intro computational complexity course. 2. An intro computational complexity course. 3. All math and CS p

For starters: 1. All math and CS prerequisites to an intro computational complexity course. 2. An intro computational complexity course. 3. All math and CS prerequisites to an advanced, graduate-level computational complexity course. Let’s say by this point you have worked through two linear algebra courses, three calculus courses, one or two discrete mathematics courses, some graph theory, some combinatorics, some logic, and a couple of algorithms courses. 4. The advanced, graduate-level computational complexity course. Hopefully you work on probabilistic computation and, in particular, quantum computation. 5. Now read and understand the relevant papers advancing the field (not just this one problem) for the last two decades. That one paper from 1990 about reducing the permanent to the determinant? You should know about that. 6. Finally, to reach the temple you must walk the path littered with the bodies of would-be explorers before you. Read the papers of failed proofs, starting with the easily refutable ones. The most sophisticated failed proofs have errors so subtle that they are useful for the research community in their own right as an exercise in peer review. As a rule, a grad student near their PhD in this area should know of everything Aaronson mentioned here: https://www.scottaaronson.com/talks/pvsnp.ppt https://www.scottaaronson.com/talks/pvsnp.ppt. None of that should be unfamiliar or unknown. A postdoc and beyond should actively have ideas percolating on how to chip away at some small aspect of a lesser problem featured therein. Here’s the reality: at almost every stage of a researcher’s career, “taking a stab at” a famous outstanding problem is the wrong way forward. Usually a problem is still outstanding because it actually needs a new theory - this is the practical utility in solving theoretical problems in the first place. Therefore the best bet for solving this problem is actually to chip away at it over a long period of time. Think hacking through a rainforest to reach a goldmine, not managing to somehow parachute to the goldmine directly when it’s hidden beneath the trees.