> In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your understanding.
This is a great point and example of the problem with a one-size-fits-all strategy. For some books, exercises are an essential part of comprehension. For others, not so much.
> Math is not a spectator sport. Reading about math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that.
My experience is that by taking excellent notes and asking why, you engage with the material to a similar degree, if not a greater degree, than by doing exercises. (Once again, depending on the book, as you mentioned.)
> Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.
I would argue that's the point. Usually self-taught math is about self-growth. Getting new ideas, being exposed to new concepts, recognizing patterns. Being able to actually "do it" on-the-spot is beside the point (and is the quickest level of skill to evaporate once you stop focusing on that material, anyway.)
This is a great point and example of the problem with a one-size-fits-all strategy. For some books, exercises are an essential part of comprehension. For others, not so much.
> Math is not a spectator sport. Reading about math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that.
My experience is that by taking excellent notes and asking why, you engage with the material to a similar degree, if not a greater degree, than by doing exercises. (Once again, depending on the book, as you mentioned.)
> Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.
I would argue that's the point. Usually self-taught math is about self-growth. Getting new ideas, being exposed to new concepts, recognizing patterns. Being able to actually "do it" on-the-spot is beside the point (and is the quickest level of skill to evaporate once you stop focusing on that material, anyway.)