We agree that if you want actually to be able to do the math then you need to do the exercises.
Do we agree that if you don't do the exercises then you probably won't actually be able to do the math?
You are discussing learning about the math, and not eventually being able to do it, because you say that you don't care about becoming a mathematician, therefore you don't need to do the math. Fair enough.
But my reading is that that's not what this thread is about. This thread, and the original submission, is about learning how to do the math.
> i do not see the exercises as essential for anyone other than practicing mathematicians.
I think you're wrong. Knowing how to actually do the math has proven useful to many people for whom it is a tool in their craft/job/employment. Learning Linear Algebra properly, being able to actually do it rather than just talk about it, can be enormously useful in Machine Learning.
>> That, to me, implies learning to do, not learning about.
> here's a fantastic explanation of the topological proof of Abel-Ruffini ... would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?
Understanding a single proof implies very little about one's ability to actually do the math. I've met many people who are math enthusiasts and who have watched hundreds of math videos. They say they understand all of what they've seen, and yet they are unable to do the simplest proofs, or the most elementary calculations.
My experience of people's abilities is that if they haven't done the exercises, they usually can't actually do the math.
But you complain about the length of my replies, so I'll stop. I think I've made my position clear, and I think I understand what you're saying, even if I don't agree with it.