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If you are right then calling them "proofs" is misleading. The results aren't proven, just made convincing. So I guess they are "arguments" -- only detailed e

If you are right then calling them "proofs" is misleading. The results aren't proven, just made convincing. So I guess they are "arguments" -- only detailed enough to convince others who already know enough about the entities being discussed. Automated proofs by contrast really are proofs but as many of these comments show are not arguments. So maybe the problem to be solved is to appropriately connect mathematical arguments (what mathematicians call proofs) to proofs, while recognizing that they are actually two entirely separate families -- as different as plants and animals.

thanatropism 8y ago
Again, the goal is not to convince, but to understand. Thus the ubiquitous "proof is left as an exercise for the reader". To extent that mathematics is a science, the whole point is to understand. Of course, people time and again have succumbed to the feeling that (e.g.) numbers are divine, but there's nothing mathematical about that. --- It's not like it has been established as a mathematical theorem based on simpler ontological facts that capital-T truth exists. And everything in our daily experience points out to the contrary. That fact that computers and programming languages have evolved from XOR and NAND semiconductors says a lot about the power of a particular branch of mathematics; it says nothing about the nature of mathematics. That idea is like claiming that the existence of probability theory implies that mathematics is about reasoning with uncertainties.