[ColinWright]

The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said:

> if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them

There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it about "being exposed", it's learning how to do the math.

And for that you need to do the exercises. You don't need to do all of them, you don't need to be completionist about it, but if you don't do the exercises, if you don't actually do the math then you won't actually be able to do the math.

Specifically, you said (quoting again):

> if you're ... just interested in learning ...

There's a difference between learning about and learning to do. If you meant just "learning about" then you are at odds with the entire thread. True, in that case you don't need to do the exercises, but I don't think that's what people are talking about here. I think people are talking about being able to do the math.

And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

Otherwise it's fairy floss, and not steak.

My apologies if all this seems overkill, but there's a real danger of talking past each other and being in violent agreement, and I wanted to state explicitly and clearly what I mean, and why I thought you said something different.

[throwlaplace]

> you won't actually be able to do the math

but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books).

>And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

no i didn't. that's precisely why i used the word "exposed".

>violent agreement

we don't agree but i'm not being violent. but my responses are short and yours are long.

i do not see the exercises as essential for anyone other than practicing mathematicians. i have read a great many serious math books (i just recently finished Tu's Manifolds book and am now reading Oksendal's SDEs). i read them without doing absolutely any exercises but following the rest of the guidelines in the post i responded to. the experience is gratifying because i learn about new objects and new ways of thinking about objects i've already learned about. that's absolutely the only thing that matters to me.

but let me ask you something

>That, to me, implies learning to do, not learning about.

here's a fantastic explanation of the topological proof of Abel-Ruffini

https://www.youtube.com/watch?v=zeRXVL6qPk4

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?

[ColinWright]

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.

[throwlaplace]

>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 learn new math from papers that don't include exercises lol.

You edited your response.

>I've met many people who are math enthusiasts and who have watched hundreds of math videos

There's a difference between watching numberphile or whatever and essentially watching a lecture on a proof. Very few people are watching/consuming rigorous expositions. I think that's the difference not the lack of exercise.

[ColinWright]

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.

[throwlaplace]

>As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math

Me too so now what? I don't think your credentials give you any real authority but just make you look like you're gatekeeping.

>Doing the exercises is playing with the objects to try to answer specific questions.

Great so then we're in agreement: playing with the object is doing the exercise.

The funny thing is that at one time I actually did all of the exercises in volume 1 of apóstol's calculus. You know what effect on me it had? I was so bored I didn't read volume 2. And today I'd still need to look up the trig substitutions to do a vexing integral.

[ColinWright]

> I don't think your credentials give you any real authority ...

It wasn't intended to, it was to provide a context for my opinion.

So let me state my opinion as clearly as I can, and then I'll leave it.

* Math is a "contact sport" ... you have to engage with it;

* Reading books is not, of itself, engaging with the math;

* Watching math videos is not, of itself, engaging with the math;

* Well designed exercises are a valuable resource;

* If you can easily do an exercise, skip ahead;

* If you can't do an exercise, persist (for a time);

* Ignoring the exercises is ignoring a resource;

* For the vast majority of people, doing the exercises is an efficient way to engage with the material;

* To say "ignore the exercises" is, for the vast majority of people, an invitation to not bother engaging with the subject;

* Doing all the exercises is probably a waste. Doing none of them is an invitation to end up with a superficial overview of the subject, and no real understanding.