Originally Posted by

**Reid**
Was not a fan of that really. I feel like his complaints of any substance aren't new, and otherwise much of it seems pointless.

For instance:

No it isn't. Math is not part of physics, nor could it be, nor does that make sense. I get he's being kinda rhetorical with this, but it's still wrong. Math is separate because it does other things from physics. That's why we put a qualitative difference on it.

He should say *applied math is better than pure math*, because I believe that's what's meant, and is also wrong.

Uh-huh

That's exactly what books like Stewart do, and then everyone complains about how it's not rigorous enough.

It's a constant cycle. Math is difficult, so everyone tries to blame the pedagogy for being at fault. So you always have complaints like this. Basically every undergrad loves having really strong opinions on how things "should" be done. Not that it's a bad thing, but people need a bit more perspective before prescribing overhauls to the education system.

But things like this is where he goes wrong. I agree many topics in math appear unmotivated when you approach them from a vacuum. But good teachers don't do that, and moreover he seems wrong to want to place all motivation in physics. We can understand the motivation for developing abstract algebra out of studying number fields, where factoring becomes harder to do. We don't need strict real-world applications for that.

I don't think it's really the case that a bunch of people mistake mathematical models for reality itself. If anything the complaint here is a philosophical one, anyway.

I don't even get the complaint here. It seems he's mad for the sake of being mad.

That's because that's what math does you idiot. That's not a fault of math, that's why it's math, and that's why it's not physics. This entire complaint is a waste of breath. If you want to do physics, you can go do physics, don't tell people in number theory that what they're doing is pointless because they haven't found a use for the twin prime conjecture in quantum physics.

So, what he's saying here is inaccurately accurate. What he said is a proper geometric interpretation of the determinant. But it also fails to capture the multilinear form properties, and how it relates to the wedge product and other stuff that's *really useful in physics*. The complaint here is a pedagogical one: yes, in intro linear algebra courses, this sort of intuition should exist, and I'm on board, but to try and dismiss the mathematical rigor behind appropriate definitions because it's not easy to intuit is just ego.

Same with this:

Yes, the Cauchy axiomatic based approach to group theory is something of a misleading one, and betrays the history of why group theory was invented. But let's read at what he says:

Literally what he said he is just a restatement of the group axioms in terms of transformations. That's not "totally different", and he's saying something in a poor and roundabout way: what makes groups important isn't the group itself, but how the group *acts* on another object. But every algebra course I've ever taken paused to talk about this. So his complaint isn't coherent, it's really not, he's just finding more things to rant about.

Plus, for the typical undergrad, to go through the volume of material necessary to follow the historical rise of group theory is far much more work than a few weeks of trust that the axioms lead to important results.

And again, every differential topology book I've ever seen discusses this openly. John Milnor's lectures make this very clear. Literally all discussion I've ever seen about smooth manifolds says this, then lays out the axioms. It's just simply not true the portrait he's painting of math pedagogy.

Yeah, that's not the situation.

I'll be fair: he does hint at *some* truths, personally I believe undergrad curriculum could be better motivated, and spend more time on examples and concrete stuff. Sure, but he's putting the cart before the horse on a bunch of topics, and fails to see the sense of learning abstract materials before jumping in to examples.