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eli_sennesh comments on The most important meta-skill - Less Wrong
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In my experience, in math/science prerequisites often can (and should) be ignored, and learned as you actually need them. People who thoroughly follow all the prerequisites often end up bogged down in numerous science fields which have actually weak connection to what they wanted to learn initially, and then get demotivated and drop out of their endeavor. This is a common failure mode.
Like, you need probability theory to do machine learning, but some you are unlikely to encounter some parts of it, and also there are parts of ML which require very little of it. It totally makes sense to start with them.
Can I give a counterexample? I think that way of learning things might help if you only need to apply the higher-level skills as you learned them, but if you need to develop or research those fields yourself, I've found you really do need the background.
As in, I have been bitten on the ass by my own choice not to double-major in mathematics in undergrad, thus resulting in my having to start climbing the towers of continuous probability and statistics/ML, abstract algebra, logic, real analysis, category theory, and topology in and after my MSc.
There's a big difference between the fundamentals, and the low-level practical applications. I think the latter is what estimator is referring to. You can't really make a breakthrough or do real research without a firm grasp of the fundamentals. But you definitely can make a breakthrough in, say, physics, without knowing the exact tensile strength of wood vs. steel. And yet, that type of "Applied Physics" was a pre-requisite at my school for the more advanced fields of physics that I was actually interested in.
Oh. Really? Dang.
You're right; you have to learn solid background for research. But still, it often makes sense to learn in the reversed order.