1) When you have a hypothesis, you conduct an experiment.
2) When your experiment yields results that match your hypothesis, you consider that evidence.
3) When you have sufficient evidence, you upgrade your hypothesis to a theorem.
According to the Wikipedia article, we've got at least two probes that are producing results in line with our hypotheses. The bar for wikipedia is "sourced", not proven theorem with scientific rigor. In this case, we're in some nebulous area between 2 and 3. I think that meets the bar for an encyclopedia, which is intended to serve as a summary for these types of things.
Hit the sources and the transitive closure of references for more details.
Especially the four colour theorem - the first mathematical theorem to be proved with software. That said, I believe this discussion pertains to the hypothesis -> theory "upgrade", not to theorems.
The point I was hinting at was that some theorems can be proven by a sufficient body of evidence rather than requiring logical deduction - the four colour theorem being a good example as it was proven by 'brute force' rather than analytically.
Doesn't a logical proof count as evidence? To my mind, these two methods are demonstrating the same thing: considering all the possible inputs, we can show [using logic|by testing them all] that the output meets our criteria.
To my mind, in this context, the difference between maths and physics is that maths is exhaustive while in physics we don't usually have exhaustive evidence so we have to work with what we've got.
Interesting question - to me, the distinction is that 'evidence' of the validity of something is expected output(s) given known input(s), whereas 'proof' (at least in the mathematical sense) is a logical transformation that is applied to make it obvious that the theorem must be true. I'm not sure you could call a proof 'evidence' because it's not an output of the theorem - it is the theorem.
I'm less certain than I was before I read your post, though - so I stand to be corrected :-)
2) When your experiment yields results that match your hypothesis, you consider that evidence.
3) When you have sufficient evidence, you upgrade your hypothesis to a theorem.
According to the Wikipedia article, we've got at least two probes that are producing results in line with our hypotheses. The bar for wikipedia is "sourced", not proven theorem with scientific rigor. In this case, we're in some nebulous area between 2 and 3. I think that meets the bar for an encyclopedia, which is intended to serve as a summary for these types of things.
Hit the sources and the transitive closure of references for more details.