that's debatable, once you appreciate the point about having a reason to do something.
calculation itself really only exists with purpose. it's a thing to do if you have a reason to do it. of course, these kinds of things too seem more "discovered" than "invented", but it's a very different kind of discovery than "the earth revolves around the sun". the earth revolves around the son, as far as we can figure these days, whether any agent/subjectivity/etc intends anything or not.
however, no full-blooded calculation will ever occur anywhere in the universe unless someone needs to figure something out. in other words, intention is implicit with calculation (and truth-functional representation, by the by). as such, you could make a case for an argument for "inventing" strategies in mathematics. and of course, a lot depends on your ontology of mathematics in the first place. if you're a wittgensteinian about numbers, and you think any of what i said above is at all compelling, you may be inclined to believe that mathematics itself is an invention. you may admit of some more nuanced way that entities like "number" still exist without mathematics as a tool, you may not, but you'd probably see all mathematics existing as active work, not pre-existing objective Truth.
of course, most people think of math as an always-there abstract object (roughly). maybe they're right. even so, there must be some force in the "i use it as a tool" and "it just revolves around the sun no matter what anyone--god or man or beast--wants" distinction.