[jusuhi]

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]

It 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]

What is your certainty that that statement is true? What if it was a calculation which takes decades on a supercomputer?

[jusuhi]

At 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.