>The apparent distinction arises from our separation of physical and mental processes.
You make the distinction based on (physical or mental) processes involved in the discovery/invention. I wouldn't care so much about how the discovery/invention came to be and look more into what the discovery/invention is about.
Usually, you can discover things which are present in the real world.
Mathematicians are rarely interested in the real world. They invent things which are true (or false) regardless of the physical world.
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.
You make the distinction based on (physical or mental) processes involved in the discovery/invention. I wouldn't care so much about how the discovery/invention came to be and look more into what the discovery/invention is about.
Usually, you can discover things which are present in the real world. Mathematicians are rarely interested in the real world. They invent things which are true (or false) regardless of the physical world.