
A Harvard scholar argues that mathematical models can provide solutions to current economic challenges, explaining that the economic meltdown of 2008 was based on a misunderstanding of scientific models rather than on the models themselves.
Ed Thorp is still alive and has written some interesting biographies. Check out A Man for All Markets if you are interested. The Physics of Wall Street is also a good overview of quantitative financial analysis.
I think the best resource for anyone starting out investing would be "A Random Walk Down Wall Street" (Burton Malkiel), and maybe "The Intelligent Investor" (Benjamin Graham), even if you don't intend to be a traditional value investor. I think these books (I'll admit I haven't read all of The Intelligent Investor) set your expectations. I also listen to Masters in Business, Odd Lots, and P&L podcasts by Bloomberg (P&L is more short-term, while MiB and Odd Lots are more generally applicable). Both of those books might be floating around the internet.
I also really enjoyed "The Physics of Wall Street" (James Weatherfall). It's a look into how financial mathematics got started and how it has grown and been increasingly applied in modern finance.
If you're interested in options and other derivatives (I find derivatives to be the most interesting, and least arbitrary, financial product), I'd start with John Hull's "Options, Futures, and Other Derivatives", which is a textbook at maybe the sophomore or junior level. I hear the PDF is freely circulated online. I think understanding how options and futures work is essential for understanding finance. A slightly more technical text, "Dynamic Hedging" (Nassim Nicholas Taleb) is also good (and maybe also available online somewhere...). It is less philosophical and polemic than his other books, but doesn't resist calling you an idiot either, as is Taleb's style.
You might also find work on non-ergodicity (Ole Peters), the Kelly criterion, universal portfolios (Thomas Cover, 1991), and Ed Thorpe (a mathematician who derived a precursor to the famous Black-Scholes model) of interest (Ed Thorpe is an incredibly interesting person in his own right). If you find yourself wanting to get into technical analysis, I'd recommend "Evidence-Based Technical Analysis" by David Arons (a spoiler: the evidence is not good). If you're interested in ML applied to trading, I keep seeing references to Advances in Financial Machine Learning (Marcos Lopez de Prado), although I haven't actually read it.
Regarding other financial products, CME has a large number of resources available for understanding futures trading, although futures are generally too high value for regular traders to use safely (the highly liquid /ES contract controls ~$130,000 exposed to the S&P500 and allows one to take about 22x margin, or even as high as 250x for intraday trading). Similarly, there are some nice introductions to the forex market, but again I'd caution you to stay away. And as much as I'd similarly caution you about blindly following their advice (and in general about being a "volatility seller"[1,2] -- see Taleb's book), TastyTrade produces a ton of videos on options trading (particularly retail options trading), which include the mechanics of options trading and how their trading platform works (which is similar to TD's platform -- the CEO/Founder, Sosnoff, was involved in the development of it when he was at TD). You can download TD's ThinkorSwim and paper trade options, or just "preview" their application with delayed prices and see how options work.
Finally, rather than r/wallstreetbets (which is now 99% low quality memes and loss porn), I'd recommend checking out r/options and r/thewallstreet, which are more professional forums, and potentially forums such as EliteTrader and Nuclear Phynance as well.
[0] https://www.bloomberg.com/news/audio/2018-12-07/why-part-of-...
[1] https://www.bloomberg.com/news/articles/2018-11-29/broker-se...
[2] https://www.bloomberg.com/news/articles/2018-02-06/credit-su...
The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall https://www.goodreads.com/book/show/13356644-the-physics-of-...
Faster Than Thought: A Symposium on Digital Computing Machines (1953) by B. V. Bowden. http://www.computinghistory.org.uk/det/10719/Faster-Than-Tho...
Thing is, my background is in physics, so I'm more interested in what physicists call "sociology": how institutions are put together, what the incentive structures are, how individual personalities affect outcomes, etc., and I found Weatherall's descriptions of such things lacking. His analysis tends towards hagiography of individual scientists, with less attention for context. This intensely biographical approach to the history of science is a common-enough failing in books that focus on the science, not the history---it reminded me a bit of those boxes about the lives of prominent scientists that dot some introductory textbooks---but it's still frustrating.
I actually found Roger Lowenstein's /When Genius Failed/ much more illuminating---he gives more attention to institutions, incentives, and personalities, and how they interact.
Edit: missing word, style
The Physics of Wall Street: A Brief History of Predicting the Unpredictable
Automate This
The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It
Dark Pools: High-Speed Traders, A.I. Bandits, and the Threat to the Global Financial System
Hedge Fund Market Wizards