Uh, yeah something has to be made of matter in order for it to be classified as a discovery. You have to be able to prove to others what it is, and that it exsists or can exist, not just in your mind, but in reality.
This is simply untrue, unless you're using some arbitrary definition of the word "discovery."
A discovery is the act of learning about something that was there even though you did not know about it. That's where it differs from invention: the television did not exist before we made it. It was not waiting for us. It was possible for it to have never existed.
The method of calculating the area of a triangle, on the other hand, is immutable. There has never been any other way to make that calculation. There was no other option for us. If you say we invented it, tell me how:
how did we somehow CAUSE a circle's radius, multipled by Pi and doubled, to equal its circumference?
If Math were not a discovery, why would so many people completely cut off from one another all define it the same way, with different names being the only variables?
And what I said was, "any thought or idea
brought into reality is an invention." Like mathmatics.
Yes, but it's the names that are the invention. That's what I'm saying. The concepts are not. We could rename the letters "one," "two," and "three" and Math would carry on as usual. We can not, however, rework the principles of Math.