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The task proving some statement and the task of finding the shortest, or a "reasonably short" proof, are very different endeavours. The first is about certaint
by jusuhi 3y ago
The task proving some statement and the task of finding the shortest, or a "reasonably short" proof, are very different endeavours.
The first is about certainty that a statement is valid ("true"). The other is about simplifying the understanding of _why_ it is valid. Most of the time, you don't care much about the latter.
- zamadatix 3y agoIt would be nice to have an reproducible example of how the result was achieved though. Otherwise it's a compendium of results, not proofs.
- ivancho 3y agoWhat is your certainty that that statement is true? What if it was a calculation which takes decades on a supercomputer?
- jusuhi 3y agoAt current rates, whatever is done on a supercomputer today is done by a cheap pocket-size device just decades later. So, I'm not too worried about this case. One of the first famous examples of this is the four-coloring theorem. I don't know any serious mathematician who is not certain of that result.