Do they use a similar terminology in mathematics when talking about proofs? Software solutions don't seem that much different in regards to solving specific problems.
"Invent" comes from Latin and simply means "find". If you think about it, no matter what language, there is no fine line. An invention is just a discovery, but we typically use the word to describe a very specific discovery.
The English language often has multiple synonyms with a difference in connotation. Discover and invent may be synonyms (although many would disagree), but everybody would agree at least the connotation is different.
My hypothesis above was that there may be languages where that connotation does not exist.
Well I always thought there was a fine line: an invention must be brought into existance witj intelligent design (probably by a human), and a discovery exists naturally.
All matter is information, and all information is functional. Therefore perception is the lazy evaluation of the universe, and discovery is the fountain of invention.
Not sure if it was rhetorical, but to answer your actual question: Mathematicians often say they "discovered" or "found" a proof. I've never heard one say they "invented" a proof, although they might talk about "building" a formalism or framework.
