I think this is a good question actually, and highly topical; I'm not sure if there is an answer however. A recent article stirred a deal of controversy (see here) by suggesting that data science was easy to learn online. One notable thing about most of the case studies mentioned in that article however is that they come from actuarial or mathematical backgrounds.

This is an interesting point, because it indicates that while online courses like Coursera, Stanford and edX are helpful in teaching the specific computer science skills required, it is likely that some mathematical background is essential to understand what the models you're applying are doing. On the other hand, an equally strong argument could be made that these guys were all analytically minded to start with, and this is both why they work in quantitative disciplines as well as why they picked up machine learning easily and won competitions.

I think fundamentally that there is a levels of analysis problem going on here. While mathematical skills are sometimes helpful in understanding the probabilistic roots of the algorithms you're applying, there's an equal argument to be made that good software engineering skills can add just as much by allowing you to do high level analysis and put together parts of algorithms to accomplish your goal even if you don't entirely understand why they are doing that. Generally, data science (and machine learning by association) is an exciting field precisely because of this breadth - you can be a database guy and use brute force to solve problems, or a mathematician who uses simulation, or a computer scientist who leverages well engineered code to put together different algorithms and approaches in an optimal way.

All approaches that add to the prediction are good, so I'd say that learning some mathematics may be a good idea to give you the best chance of success in the field. If you want some good starting points, MIT has a great linear algebra course, with some nice computational applications, that I found easy to understand. They also have other courses on stochastic processes and multivariable calculus that may also be of interest in building up your knowledge.

I think this is a good question actually, and highly topical; I'm not sure if there is an answer however. A recent article stirred a deal of controversy (see here) by suggesting that data science was easy to learn online. One notable thing about most of the case studies mentioned in that article however is that they come from actuarial or mathematical backgrounds.

This is an interesting point, because it indicates that while online courses like Coursera, Stanford and edX are helpful in teaching the specific computer science skills required, it is likely that some mathematical background is essential to understand what the models you're applying are doing. On the other hand, an equally strong argument could be made that these guys were all analytically minded to start with, and this is both why they work in quantitative disciplines as well as why they picked up machine learning easily and won competitions.

I think fundamentally that there is a levels of analysis problem going on here. While mathematical skills are sometimes helpful in understanding the probabilistic roots of the algorithms you're applying, there's an equal argument to be made that good software engineering skills can add just as much by allowing you to do high level analysis and put together parts of algorithms to accomplish your goal even if you don't entirely understand why they are doing that. Generally, data science (and machine learning by association) is an exciting field precisely because of this breadth - you can be a database guy and use brute force to solve problems, or a mathematician who uses simulation, or a computer scientist who leverages well engineered code to put together different algorithms and approaches in an optimal way.

All approaches that add to the prediction are good, so I'd say that learning some mathematics may be a good idea to give you the best chance of success in the field. If you want some good starting points, MIT has a great linear algebra course , with some nice computational applications, that I found easy to understand. They also have other courses on stochastic processes and multivariable calculus that may also be of interest in building up your knowledge.