ebw said:
Sorry, but this is my area, and no one I know states the Riemann Hypothesis as fact. Mathematicians by training have pretty rigorous standards for what they are willing to call a fact. However, being creatures of abstraction not bound to the real world, we are still happy to write speculative papers built on the premise of RH, which are clearly labeled as being conditional and not factual results. A slightly better example from math would be the Axiom of Choice. Again, you won't find a mathematician who claims it as fact, but entire areas of mathematics would be unusable without this assumption (the effect is large enough that you wouldn't routinely call out the use of AC unless you were addressing a wider audience). Even still, operating in this way is pretty credibly justified by Gödel's and Cohen's consistency results (we essentially know that AC will never be proven or disproven in the future, not without taking down some more fundamental axioms). |
Oh, yeah, I'm not saying the papers state is as fact. I just mean a lot of work has been built on assuming it is true that would disappear if it's proven false.
Is it possible to quantify (even informally) how likely RH is to be false? Or AC?
