Earlier quoted context omitted.
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…
>You are discussing learning about the math You keep repeating this but you're evading the question about abel-ruffini and the question about whether reading a history book is "learning about history" as opposed to learning history. You're making a weird distinction. People learn in different ways. Some by doing exercises and some by just playing with the objects. I wonder how you think actual research mathematicians…
> You're making a weird distinction.
As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math, and headed a team doing research in technology, this is a distinction that I can clearly see. My inability to explain it to you is regrettable.
> People learn in different ways.
Yes they do.
> Some by doing exercises and some by just playing with the objects.
Doing the exercises is playing with the objects to try to answer specific questions. Good exercises are carefully constructed to help the reader learn how those objects work in an efficient manner.
> I wonder how you think actual research mathematicians learn new math from papers that don't include exercises lol.
In my experience research mathematicians learn now math from papers by, in essence, constructing their own exercises based on what they're reading. In general it takes significant experience and training to be able to do that.
Clearly you don't think one needs to do the exercises subsequently to be able to do the math. Good for you.
I disagree.