lol, yes, you discover how mathematicians think, but what they think is still an invention.
In the end, I agree that if we expand the definition of the universe beyond physical world to contain "everything" then yes, every invention is also a discovery.
Is there anything that any human thinks (other than straight-out mimicry) that is not an invention?
If I type:
squirgle florb snozbar
would you say that I have invented something? Because if the answer to that is yes, then I'll concede the point (and observe that "invention" is not a particularly interesting concept). But if the answer is no, then I challenge you to draw a distinction between what I just did and what mathematicians do in a principled way.
neither inventions nor discoveries have to be interesting.
>squirgle florb snozbar
yes, you invented something (i think you can even claim copyright on that). I agree that it is not very interesting. mathematicians usually/sometimes produce more interesing inventions.