The actual problem with learning "data science" is making inferences and conclusions which do not violate the laws of statistics . I've seen many submissions to Hacker News and Reddit's /r/dataisbeautiful subreddit where the author goes "look, the analysis supports my conclusion and the R^2 is high, therefore this is a good analysis!" without addressing the assumptions required for those results. Of course, not every…
The classic venn diagram of data science is still helpful: http://drewconway.com/zia/2013/3/26/the-data-science-venn-di... This article reads like a way to find yourself in the danger zone.
I think the key is to find the mathematics and statistics interesting because you want the [data] science to be meaningful. If that's a driving force, then you can learn math and statistics on your own (like the author did). Otherwise, yes--you will find yourself in the danger zone.