Learning about history is not the same as then being able to do research in history, nor being able to apply the principles learned from it in context. So no, reading a history book is learning about history, not necessarily being able to "do history".

> 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.