What are the differences between invention and discovery? Ever since my post Propositions as Types I’ve been trying to determine what they are. Some say that mathematics and logic are completely human inventions and they have no correspondence to the natural world. Others say that mathematics already exists in some “Platonic” realm just waiting for our discovery. Similar to convergent evolution, the parallel invention or discovery of similar notions in mathematics lends credence to the idea that there is something “out there” just waiting for us to find it, although one could also argue that it’s merely the cultural climate along with some innate functioning of the brain. For example there is the parallel development of calculus by Newton and Leibniz. The notion of effective computability in the “Propositions as Types” paradigm also has several concurrent developments.
Modern science is based on mathematics so as one goes so goes the other. Physicist Eugene Wigner wrote a famous article on the “Unreasonable effectiveness of mathematics in the natural sciences” which has inspired a host of similarly titled articles about the “unreasonable effectiveness” of one thing for another. But the key point is that we really don’t understand the origins of mathematical thinking, or why it is so useful in helping us understand the natural world. Its value and utility seems, in fact, unreasonable.
But let’s return to the differences between invention and discovery. If something is invented, it means that it is new, freshly created. If something is discovered, it means that it already exists and it’s just waiting for us to find it. Thus the difference is between the natural and artificial, or between what exists and what didn’t exist before humans created it. Some believe the natural world itself is socially constructed, so in some sense it didn’t exist before humans saw it, or will disappear when humans stop perceiving it. This is about is arrogant as believing that the world didn’t exist before a person was born or after they die; a solipsistic view if ever there was one.
Once something is discovered, one can learn about it. Once something is invented, one can make it. Thus learning and making are tied to discovering and inventing, respectively. Inventing and discovering are required for making and learning. Of course one can also learn about an invention or how something is made, or one can learn facts about a discovery.
This fourfold of inventing, discovering, learning, and making is also related to other fourfolds. The Four Hats of Creativity seem to utilize each of these special actions for each livelihood: inventing (or creating) for the artist, discovery for the scientist, and making for the engineer (but less well learning for the designer). In addition, the Psychological Types of Jung appear to emphasize a type for each special action: intuition for invention, sensation for discovering, and cognition for learning (but less clear emotion for making).
Please compare this with a related analysis on the methods of active learning at the Tetrast (link below), where the key faculties are struggle for invention, practice for discovery, value for making, and discipline for learning.
References:
https://en.wikipedia.org/wiki/Convergent_evolution
https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
http://tetrast2.blogspot.com/2013/04/methods-of-learning.html
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Equivalent eXchange 
Interesting post!
I’ve found this subject a tough one for me. “Invention” and “discovery” aren’t quite symmetrical to each other; one can discover an _individual_ thing (e.g., an island) or a _kind_ of thing (e.g., a species), but one invents only a _kind_ of thing. One is said to invent an individual thing only in the sense of making a fictional individual thing (e.g., Prince Hamlet). We sometimes use the word “fabrication” in something like that sense, but “fabrication” can also mean making an artificial physical object (_fábrica_ in Spanish means “factory”). When one uses “fabrication” in a sense other than that of “faking,” it refers to making not a new kind, but a new individual (possibly but not necessarily an individual of a new kind). “Creation,” used in not too strong a sense, might be a better word than “invention” for the making both of new individuals and of new kinds.
I usually put _creation_ in a tetrachotomy of creation, preservation, destruction, and (existential) suppression. The idea of discovery doesn’t even appear there, yet creation (or invention) and discovery obviously belong together in some sort of classification (fourfold or otherwise).
One might try splicing together halves of two tetrachotomies in order to get:
creation, preservation, discovery, confirmation,
where preservation is considered a kind of existential confirmation or “firming up” of creation. Confirmation per se seems like what I think you meant by “learning,” i.e., not just discovery but the consilience and build-up of knowledge. Still, I’d consider my spliced-together fourfold above not a good fourfold, but maybe a step towards one.
There is a fourfold of the creative problem-solving process due to Helmholtz and Poincaré:
Saturation, incubation, illumination, verification.
http://tetrast4.blogspot.com/2008/12/helmholtz.html
Saturation is the struggle to get handles on a problem, and I figure it may be considered to involve attempts at creative explanatory hypotheses. Incubation is when one continues to work, often with decreasing consciousness, on the problem. Illumination is a lot like discovery – it’s the “eureka” moment; but the solution that it finds tends to be rather creative, it’s not like the discovery of some random island.
Anyway, my understanding of these things remains misty.