Residency isn't independent study, it's pretty tightly directed by the hierarchy.
And I'd hire a math major with limited software experience over a boot camp or self-taught person that only knows code any day. In fact, I'd take a math major over most people with MS in CompSci. They know how to learn very difficult stuff, and didn't do it in an environment that is mostly people wanting to be highly paid, but mostly people that have a love of complicated but beautiful abstract structures (hence less weird resume lying and so on; also, tends to be a bit of a salary arbitrage opportunity). (Hiring for experienced people is of course a different problem.)
Of course, trying for a professor job in the US is very likely to a difficult career path; I'm taking some math classes just for fun and the professors are usually grading our papers at insane hours, 3 am and then office hours at 9 am). I could not have done that much work and been a good parent.
But academia is great training. One of the best project managers I've worked with had a PhD in Anglo-Saxon english; her dissertation was on masculinity in the court of the Anglo-Saxon king (or something, I've not worked with her in a long time); surprisingly relevant to trying to get the mostly male dev teams to coordinate to finish projects when she didin't have the feudal power of the technical managers, just the soft power of the travelling minstral.
And I'd hire a math major with limited software experience over a boot camp or self-taught person that only knows code any day. In fact, I'd take a math major over most people with MS in CompSci. They know how to learn very difficult stuff, and didn't do it in an environment that is mostly people wanting to be highly paid, but mostly people that have a love of complicated but beautiful abstract structures (hence less weird resume lying and so on; also, tends to be a bit of a salary arbitrage opportunity). (Hiring for experienced people is of course a different problem.)
Of course, trying for a professor job in the US is very likely to a difficult career path; I'm taking some math classes just for fun and the professors are usually grading our papers at insane hours, 3 am and then office hours at 9 am). I could not have done that much work and been a good parent.
But academia is great training. One of the best project managers I've worked with had a PhD in Anglo-Saxon english; her dissertation was on masculinity in the court of the Anglo-Saxon king (or something, I've not worked with her in a long time); surprisingly relevant to trying to get the mostly male dev teams to coordinate to finish projects when she didin't have the feudal power of the technical managers, just the soft power of the travelling minstral.