And that is just the first half of the quote. It goes on:

Also, mathematics may predict things which don't exist, or are impossible in nature.

As a former experimental physicist I can't help but notice how true this is. ;)

Physicists deal with impossible things every day - light is a particle And a wave, far-away objects can be receeding faster than the speed of light.

How are they impossible if they are happening?

In the macroscopic world, they make no sense.

Somebody said "the Universe isn't just stranger than you imagine; its stranger than you Can imagine"

Mathematics will always be inadequate to describe mathematics, let alone the universe, as there will always be a need for new axioms.

That's mathematically proven, so it must be true.

It also depends to some extent on whether you count interpretations as "within" mathematics. For example, Stephen Hawking's latest book clearly draws on a lot of mathematical models of the universe, but its main arguments are non-mathematized, philosophical ones. Arguably they're arguments over how to interpret the existing mathematical models (though some stray further from math than others), but the arguments themselves appear to live outside what you'd normally call mathematics.

Interpretations of quantum mechanics fall into a similar camp. There is the actual formal theory of quantum mechanics, which is clearly mathematics; but something like the Copenhagen Interpretation is also attempting to "describe" the universe, but is forced to do it extra-mathematically, by attaching interpretations (which can't be mathematically proven) to the formal results.

I suppose it also depends on what one means by "describe": does quantum mechanics fully "describe" the universe, or is it quantum mechanics plus an interpretation which describes the universe?

Everything that is provably correct becomes mathematics. Of course physical laws are never provably correct.

So mathematics is not even adequate to describe the universe? “Adequate” doesn’t imply ”perfect“ for me.

The meaning of the sentence hinges on the word 'describe'. I took it to mean a complete description.

You're right though, it could mean a description of any complexity, something Mathematics is well capable of.