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Notes -
Do you think that mathematical theorems are discovered or invented? I have a segue I want to make from this question (it involves a book that was popular w few years ago), but first I'd like to hear your opinions on that.
I would say invented, because any arguments about them being "discovered" or "already out there waiting to be found", while mostly true, apply equally to literal inventions. Was the telephone discovered or invented? Well, kind of both. The laws of physics always allowed sound waves to convert into electric signals and travel across wires to be converted back into sound waves. Someone just had to figure that out.
You can make a strong argument that invention is a subset of discovery. You can make a strong argument that mathematical theorems are a form of discovery. You can't really make arguments that they aren't inventions except by sneaking in a hidden assumption that these are mutually exclusive, when actually they're not.
I would say "discovery" is unearthing the physical laws governing our universe, and "invention" is designing tools which apply those laws practically. It's the difference between science and engineering.
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