I'm currently studying maths at XYZ university. I'm currently a maths student. My view is that 'a student of' is perhaps a little old-fashioned. And that you don't really need the word 'currently', unless you want to emphasise this is your current situation and you expect it will change at some point. But it gets a little confusing with, for example... I'm an English student. This can mean I am from England (English), or that I am studying English.

Well, I think it's pretty much the same. I'm a student at Oxford University. I am a student of mathematics. "Currently" emphasizes that you are being a student at present time. I hope that helps!

Basically these two expressions say the same thing, but with using the word "currently" sometimes it may mean there was an earlier discussion and now you are trying to state what's happening at thr moment. I hope this helps

правильно: Can I say that? и I'm currently the student...