>As someone who only ever encounters math as a tool rather than a a great passion or source of intellectual stimulation, it makes me really happy to see this sa

>As someone who only ever encounters math as a tool rather than a a great passion or source of intellectual stimulation, it makes me really happy to see this said out loud. From the perspective of a mathematician, I'd like to see textbooks strike a happy medium between page after page of explanation and absolute terseness. When I'm taking an intermediate level course, I know that the math I encounter may rarely be useful on its own. It should be sufficient to say "you won't even think about this until you take analysis!" I think the biggest mistake universities make is to offer one type of math instruction. I still remember taking a linear algebra class that had mathematics majors, engineers, and secondary education majors(!) all in the same class! The professor taught it in a way that I very much appreciated -- a large focus on theory and concepts, and much less focus on application & concrete problems. Of course, I and the math majors loved this, while the education majors & engineers detested it. It might've been more difficult, but I believe that everyone would've benefited from instruction that was tailored to what people would need & could appreciate -- the engineers could learn applications of linear algebra, the secondary education majors could learn how to teach linear algebra, and the mathematicians could learn the theory behind linear algebra. Instead, we had one class that a subset was guaranteed to hate.