
1. Technical analysis - trend following, etc. I personally was unconvinced but some people swear by it.
2. Fundamentals/value investing. Read the intelligent investor and security analysis. Very sound IMO.
3. Arbitrage - read "Beat the Market" by Ed Thorp. Also very sound IMO.
Since Thorp, Casinos have made it harder to beat them (e.g. larger decks), but they still tease the possibility you can beat them to entice people to try (and lose).
Edward Thorp later went on to write Beat the Market, where he tried to apply similar probability principles to the stock market. He independently invented the options formula, before Black-Scholes (which the latter won a Nobel Prize).
On who Simons hired: IIRC there is an interview with Simons where he explains that he hired good mathematicians, etc. who had published interesting work or some such. In particular, he required no MBA or business degrees, experience with accounting, reading corporate annual reports, SEC filings, or business.
So, my guess would be that at least for the early years of Simons's work, such people would not be very welcome in the rest of Wall Street and usually not considered the "best" or even good at all.
Point: That he hired "the best" has to do with what criteria one is using for goodness!
By the way, in this thread there is mention of Thorpe! So, yes, his Beat the Market had in the back that some argument was from "measure theory". So, before my Ph.D., I was working carefully through Royden, Real Analysis! I was getting through the two exercises on upper and lower semi-continuity when I went to grad school. Right away I took the 700 level course in analysis (measure theory and functional analysis) and probability. The prof was a star student of E. Cinlar, long head of Operations Research and Financial Engineering at Princeton. Got to meet him once! So, that background should be of interest on Wall Street? After some good efforts, not as far as I could tell although then I didn't yet know of Simons.
It is true that the year I got my Ph.D. near DC, the ORSA (Operations Research Society of America) conference was there and I submitted a resume. I was 110% busy taking care of my (later fatally) sick wife so didn't go but some friends said that on some bulletin board I had lots of requests from Wall Street! Gee!
At one time I interviewed at Morgan Stanley and mentioned my paper on multi-variate, distribution-free anomaly detection. A computer systems management guy was a little interested. Another guy wanted me to give him an outline of the paper; I did and mentioned that I'd like to work on applied math of trading -- his reaction seemed to be that neither he nor Morgan Stanley nor anyone on Wall Street would be interested in any such thing!
Later a Bertsekas student from MIT gave me the rumor that Simons also liked hiring Russian mathematical physicists!
Point: It seems to me from a distance that Wall Street has been slow to hire people like Simons did.
On what Simons did: There's an old comment that a good casserole is like a good marriage -- only the people who made it really know what is in it. My guess is that this remark applies also to Simons! In particular I doubt that we should regard him as a quant much like the rest of Wall Street.
Bluntly, I suspect that there's no telling what the heck Simons did: E.g., there's no law that he had to have much contact with the Markowitz work, the Sharpe work, the CAPM (capital asset pricing model), econometrics, classic time series analysis, the Thorpe work, the Black-Scholes work, the Martingale convergence theorem, the Doob decomposition, controlled Markov processes, stochastic differential equations, the Brownian motion solution to the Dirichlet problem -- he could have been doing things totally different!
Heck, quite generally it's beyond super tough to be on the outside trying to know what's going on inside: E.g., I got interested in cooking, once took my wife to André Soltner's Lutèce, but never got a clue about how he did it! E.g., I made some progress with violin but never figured out how Heifetz did it! E.g., I made some progress in physics but never figured out how Einstein did it! E.g., I made some progress in math but really have no idea how Simons did it. It's a Robert Frost one?? -- "We dance round and round and suppose while the secret sits in the middle and knows."??
My approach to making money is not to try to get hired on Wall Street, out on Long Island, or near the commodity pits in Chicago or Kansas City but just to do my startup. There I don't have to know all the ways people got rich in business -- it's enough for me to find just ONE way!
I don't have to know how all the cooking, music, physics, or math of the past was done -- it's enough for me to do some math for the problem I'm trying to solve.
I don't have to know every computer operating system, programming language, memory management or concurrency algorithm -- it's enough for me to know enough computing to get the code running for my startup.
Since I'm able to be a sole, solo founder, I don't have to convince people on Wall Street or Silicon Valley that I might make them money -- I just need to convince myself and then actually DO it!
And if I'm successful, my crucial core original applied math secret sauce should remain secret!
Point: I don't believe I can figure out how Simons did it!