How to become self taught quant?

Start by understanding the financial system as a whole. Decide where you want to specialize. You also need to understand, options, futures, bonds, stocks and the different derivative products. Together with that, investigate the different tools that are used by the industry.

Ultimately, understanding statistics at high level will be your primary goal but you need to be very comfortable with math. I would say that at the minimum you need an equal to a minor in math at a university -many in the field have a PhD in math.

Look at the different job postings and determine, from that, what the industry is requiring for an entry level job in the field you want. Look for other people in the field that you can be friends with to give you a nudge in the right direction.

Also, set a grand goal and define a project that you can't accomplish without learning the different specialties in the industry. I would say that the hardest part is to continue to educate yourself without giving up once the material gets hard. Defining a project where you need to learn something to complete it will help you a lot towards finishing.

You’re going to need math—especially calculus, probability, differential equations, and stochastic calculus. AI, machine learning, and data science skills would also help. Perhaps getting some data science experience can boost your chances. Try some of the online trading algorithm testing/competition sites. Look for kaggle completions dealing with trading/securities. Network like a boss on LinkedIn, etc. Maybe make some financial software like an options calculator to showcase your skills and fundamental understanding of some pricing mechanisms. Get involved with FINOS Fintech Open Source Foundation (https://www.finos.org/) oh and network there too!