I was reading the article "Quantum physics sheds light on Riemann hypothesis" from Bristol University (http://www.bristol.ac.uk/maths/research/highlights/riemann-hypothesis/) and stopped here:
From a conference in 1996 in Seattle, aimed at fostering collaboration between physicists and number theorists, came early evidence of correlation between the arrangement of the Riemann zeroes and the energy levels of quantum chaotic systems. If this were true it would prove the Riemann hypothesis.
I think this would not prove the Riemann hypothesis, since mathematics is a formal science, as opposed to natural sciences, and is independent of our universe. It can only go the other way around, i.e., mathematics implies that something in our universe is true (not our universe implies something in mathematics is true).
Still, I'd like to ask whether the mathematical community agrees or disagrees with the above article.
There are two possible interpretations.
One interpretation is that a correspondence between the zeroes of the Riemann zeta function and the energy levels of certain quantum systems may suggest a new theoretical approach that leads to a logical proof (or disproof) of the Riemann hypothesis. This is possible, but the proof/disproof would still lie within the field of mathematics, even if the method was suggested by physical considerations.
A second interpretation is that the experimental measurement of the energy levels of certain quantum systems could add to the weight of heuristic evidence for (or against) the Riemann hypothesis. This is very unlikely, since the hypothesis has already been verified by numerical calculations for at least the first $10^{13}$ zeroes of the Riemann zeta function (and for some ranges of values beyond that). I cannot see how any physical experiment could match either the volume or the precision of those existing numerical results.
A key sentence in the press-release style summary that you linked to is this:
If we don't (yet) understand the approach then it isn't (yet) mathematics.