Both are right. Practically speaking your view is right, and is similar to one of hilberts quest to come up with a proof spitting machine. Just get a computer t

Both are right. Practically speaking your view is right, and is similar to one of hilberts quest to come up with a proof spitting machine. Just get a computer to enumerate through all proofs and we absorb the results. But you have to agree this is deeply dissatisfying intellectually. This is like if trigonometry was discovered with no relation to circles and triangles but just as a series of look up tables (like in a calculator) and we just know it works for certain scenarios and that's all there is to it.