In CS it’s obvious how to contribute to the field, arguably this is due to the requirements being relatively low. How does one progress in mathematics or physics to the point of contributing?<p>Khan academy->Freshman text books-> post grad text books->???
MIT OCW physics--start with 'For the love of physics' then don't mention that video series again because it will get you cancelled. Then you can take MIT's quantum course. From there, PIRSA has a bunch of video courses available that will prepare you for theoretical physics. You'll need calc 1-2(3), linear algebra, differential equations, discrete math, real and complex analysis, and mathematical physics, which may include the discrete math and complex analysis as my coursework did. You'll need to read Alice in Wonderland and Through the looking glass, at least for cultural references. Most of what you need will be between PIRSA and MIT OCW. Khan Academy can help if you're not getting calc, but with CS you probably already have calc 1-diff eq and linear algebra.
I think learning it all on your own is not efficient even for a genius. At the very least (assuming you are a genius) you should do a double major in Electrical Engineering and Mechanical Engineering and a minor in philosophy at a mid- or top-tier university. EE and ME are the practical expression of the foundation of classical physics. Einstein's early work was related to integrating these two fields. In short (I am a bit sketchy on the exact details since it has been a while), before Einstein there was an odd inconsistency in Maxwell's equations whereby the results differed if the magnets were moving or the coils were moving in generating electricity. Since all motion is relative, at least mathematically, it should not matter which was moving. Einstein's revolution amounted to modifying the concepts of space and time (using Lorentz transformations) to make that inconsistency go away BUT it is possible that that is not the only possible solution to the puzzle. Once you get your BS degrees you should get your PhD in physics at a mid-tier school or no one will listen to you.<p>The reason you need to minor in philosophy is to understand the history of the field going all the way back to the Greeks. Most importantly, you need to clearly define a theory of concepts and apply it to fundamental concepts such as existence, consciousness, free will, space and time. Current physics (and math, btw) are vitiated by inconsistent fundamental concepts. In fact, Einstein's concept of spacetime is a denial of consciousness (an axiom) and a deadend. The fundamental concepts in physics should be lightspace and gravitytime to avoid this error. You won't learn much in modern philosophy courses in regard to these issues but you need to understand the history and read Ayn Rand's Philosophy:Who_Needs_It, Introduction_To_Objectivist_Epistemology and the title essay of her anthology For_The_New_Intellectual.
You could start with Road to Reality [1]<p>- [1] <a href="https://en.wikipedia.org/wiki/The_Road_to_Reality" rel="nofollow">https://en.wikipedia.org/wiki/The_Road_to_Reality</a>