that&#x27;s debatable, once you appreciate the point about having a reason to do something.<p>calculation itself really only exists with purpose.  it&#x27;s a thing to do if you have a reason to do it.  of course, these kinds of things too seem more &quot;discovered&quot; than &quot;invented&quot;, but it&#x27;s a very different kind of discovery than &quot;the earth revolves around the sun&quot;.  the earth revolves around the son, as far as we can figure these days, whether any agent&#x2F;subjectivity&#x2F;etc intends anything or not.<p>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 &quot;inventing&quot; strategies in mathematics.  and of course, a lot depends on your ontology of mathematics in the first place.  if you&#x27;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 &quot;number&quot; still exist without mathematics as a tool, you may not, but you&#x27;d probably see all mathematics existing as active work, not pre-existing objective Truth.<p>of course, most people think of math as an always-there abstract object (roughly).  maybe they&#x27;re right.  even so, there must be some force in the &quot;i use it as a tool&quot; and &quot;it just revolves around the sun no matter what anyone--god or man or beast--wants&quot; distinction.