[Myrmornis]

It depends whether you want to work more as an engineer / data analyst, or more as a "ML researcher". For the latter, then, yes, as everyone says below, you need to be totally comfortable with multivariable calculus, linear algebra, probability and statistics, numerical optimization etc. But many jobs are more practical in nature, in which the main case essential skill is, being able to run a bunch of different models with different parameter values and collect and interpret the results, efficiently and reproducibly, and be able to talk about them and make recommendations for the way forwards. In those jobs you're not actually going to need to be able to derive updates for backpropagation, even though it's certainly satisfying to understand it.

[mindcrime]

Yep. We have to keep in mind the distinction between "applied ML" and "ML research" (while realizing that this is a continuum, not a binary distinction). Not everybody is doing cutting edge original research... some people really can just get by with downloading DL4J, reading a few tutorials, and then applying a basic network to their problem, and create some value in the process.

I think cars are a good analogy. In the early days of automobiles, you needed to be something just short of a mechanical engineer to keep one going for any length of time, and it was routine to need to carry around tools and spare parts to perform significant repairs. You really needed to know a pretty good bit about how the car worked to use it effectively. But over time cars developed better abstractions and became more dependable and it became possible to operate a car without caring one lick about how it works, beyond know that it needs gas (or electricity!) and taking it in for the occasional tuneup /tire change / alignment / etc.

I wouldn't say we're at the point yet where ML afford one the opportunity to be completely divorced from caring about the underlying details, but I think we are at a point where you can legitimately get useful stuff done without needing to be able to, say, derive the equations for backprop by hand.