Pretty sure in the USA you can patent mathematics if it is an integral part of the realisation of a physical system.* There is a book "Math you Can't Use" that discusses this.

* not a legal definition, IANAL.

I would think you could only patent a particular usage of it.

> Pretty sure in the USA you can patent mathematics if it is an integral part of the realisation of a physical system.

Yes, that's true. In that example, you're not patenting mathematics, you're patenting a specific application, which can be patented. In my reading I see that mathematics per se is an abstract intellectual concept, thus not patentable (reference: https://ghbintellect.com/can-you-patent-a-formula/).

There is plenty of case law in modern times where the distinction between an abstract mathematical idea, and an application of that idea, were the issues under discussion.

An obligatory XKCD reference: https://xkcd.com/435/

And IANAL also.