It's totally cultural. The culture comes with some costs, and some benefits.
In physics, there are so many times where we present the same mathematical ideas in a manner that's way more ergonomic for the minds we're talking to-- other physicists.
Inexperienced mathematicians tend to see these presentations and are kind of gobsmacked, "why did no-one tell me it was that simple and concrete?" Experienced mathematicians tend to see these presentations and cringe, "don't they understand it's not that simple and concrete? For instance, look at this pathological example here that contradicts everything they just said."
The slick presentations are great if you're a physicist or anyone just wanting to use the ideas. And they're great if you're an inexperienced mathematician trying to get your bearings as fast as possible. But once you're a research mathematician, trying to build new ideas, too many slick presentations of ideas just creates groupthink. You want as many people to generate their own mental pictures as possible.
That said, few people studying mathematics go on to be research mathematicians. The mathematics culture should be much, much friendlier to people whose endgame is not being a math prof. Apathy toward those whose ambitions lie outside the ivory tower is a problem endemic to most academic subcultures.
Finally, when reading anything generated by academia, remember most of it is crap. Academics are fired if they don't make enough noise. This is truer than you think, even taking into account metrics like "impact". You can make a lot of "impact" just by making enough noise. And you generally can't make "impact" on a short timescale without making enough noise. Once your name shows up enough in a field, you'll get known as "a name", and start being cited in that field. Even when your work is drivel. If your name only shows up a couple of time in a field-- unless your work incredibly well written and you get a good dose of luck-- it'll take years before it gets uncovered and appreciated, if it ever does.
Think of how much more attention you pay to what someone like maxxxxxxxx says here. Sure. He's good. But he's also familiar. It's primarily his familiarity, more than his quality, that makes you feel like he's one of "names" in this little subfield of the internet called hacker news.
Yes, I think you are right. I offer a free Linear Algebra book that appears on the first page of a Google search. The book's approach is to give a lot of explanation and motivation, so I often get emails from folks about this topic. From students often the mails say something like, "I couldn't understand my prof but by using your book as a supplement .." while from the prof I get (much less often) "way too chatty."
So I agree that a lot of it is a question of culture and taste.
On my first day in grad school a prof who I admire a great deal told me what he liked best about Differential Equations is that you don't have to say how you found the answer. You just state the answer and verify it satisfies the equation. I think that's the taste of people who enter the field.
(I also think that is the taste of the moderators of MO, which is why questions like this have been closed over time.)
> what he liked best about Differential Equations is that you don't have to say how you found the answer. You just state the answer and verify it satisfies the equation.
Man, that is kind of magical from a productivity prospective.* The vast majority of my time is spent explaining why the answer I give is sensible and reasonable.
*The small cost of this approach is that all insight that led to him finding the solution will die with him.
Don't be. The first thing I did when reading your above comment was to do the Google search. I should have scrolled down!
I'm browsing through this, and it's clear to me this is a textbook. In that it easily looks like it could be the textbook of record for college courses. This is an enormous amount of work. Am I correct in assuming it grew out of your lectures notes? What lead you to make this a freely available textbook, instead of going the "normal" route of going through a publisher and getting royalties?
Yes, it is a text. As the linked-to page says, it has been used in hundreds of classes at many schools as well as by thousands of individuals for independent study.
> Am I correct in assuming it grew out of your lectures notes?
No, really I wrote it intentionally not organically. I used Strang's book in a course a couple of times and while that is a very fine book, the students I had in front of me had trouble with it (and anyway I wanted to cover a somewhat different set of topics). I looked around some more but basically I couldn't find a text that fit.
> What lead you to make this a freely available textbook, instead of going the "normal" route of going through a publisher and getting royalties?
I wrote it using LaTeX, on Linux, using emacs. It seemed natural.
I do get some money, from Amazon sales, because it would be stupid to not round the price up. (But in general, everyone tells you that unless you write a very popular text for a very big audience, you are not going to see much money. You need to get your pleasure from the creative accomplishment.)
In physics, there are so many times where we present the same mathematical ideas in a manner that's way more ergonomic for the minds we're talking to-- other physicists.
Inexperienced mathematicians tend to see these presentations and are kind of gobsmacked, "why did no-one tell me it was that simple and concrete?" Experienced mathematicians tend to see these presentations and cringe, "don't they understand it's not that simple and concrete? For instance, look at this pathological example here that contradicts everything they just said."
The slick presentations are great if you're a physicist or anyone just wanting to use the ideas. And they're great if you're an inexperienced mathematician trying to get your bearings as fast as possible. But once you're a research mathematician, trying to build new ideas, too many slick presentations of ideas just creates groupthink. You want as many people to generate their own mental pictures as possible.
That said, few people studying mathematics go on to be research mathematicians. The mathematics culture should be much, much friendlier to people whose endgame is not being a math prof. Apathy toward those whose ambitions lie outside the ivory tower is a problem endemic to most academic subcultures.
Finally, when reading anything generated by academia, remember most of it is crap. Academics are fired if they don't make enough noise. This is truer than you think, even taking into account metrics like "impact". You can make a lot of "impact" just by making enough noise. And you generally can't make "impact" on a short timescale without making enough noise. Once your name shows up enough in a field, you'll get known as "a name", and start being cited in that field. Even when your work is drivel. If your name only shows up a couple of time in a field-- unless your work incredibly well written and you get a good dose of luck-- it'll take years before it gets uncovered and appreciated, if it ever does.
Think of how much more attention you pay to what someone like maxxxxxxxx says here. Sure. He's good. But he's also familiar. It's primarily his familiarity, more than his quality, that makes you feel like he's one of "names" in this little subfield of the internet called hacker news.