Becoming a data scientist using only StackExchange sites - what questions should I look at? If I had a maths degree with a little foundation in statistics, what would be the top $100$ questions/posts on CrossValidated or MathStackExchange or MathsOverflow or Stack Overflow that I would have to study in order to become a data scientist?
And if not possible, could you give me an idea of the steps (skills, knowledge, courses) that I would need for different career paths? For example research data scientist, data scientist in a start up, machine learning scientist, etc?
 A: First, it is hard to define what is data scientist. Different people have different definitions. See this question:  What is a data scientist?
Then, you may want to think what kind of job you want to do: more on building statistical model? Or more on making software (engineering work) tuning on clusters to processing huge amount of data. In addition, what field are you interested in? e.g., Health care, education? An interesting diagram can be found here. Where "hacking skills" and "subject expertise" are also extremely important. 
I personally do not think Kaggle Competition can be counted for "science". And blindly using pre-developed packages to make "accurate predictions" and climb on ladder board is meaningful work.
Steps to follow is really depending on your objective (dream job). Working in a big company as a research (data) scientist vs. working in a start-up that taking care of everything from server/cloud maintenance to talking to customer would be totally different. 
If you want to become a research scientist in AI / machine learning, read top conference papers in the filed (Such as AAAI, NIPS, ICML, ICDM) get try to get a Ph.D. in machine learning / statistics / operations research. (We have an interesting question here Why do Statistics, Machine learning and Operations research stand out as separate entities) 
If you want to become a data scientist in a start up company, staring with MOOC courses may be better. In most of those courses, they emphasize how to use it in real world instead of the theoretical background behind statistical methods. In addition, trying to learning how to use could, e.g., AWS and learn how to programming (e.g., in python / java). Finally, the communication skill is also very important.
To conclude: think more on the career path you want to have in the future. How much time you want to spend on reading paper and deriving math.  How much time you want to spend to debug the code and configure the server. Which field / subject expertise are you thinking you want to get into. Then search related questions and answers to read.
