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The Wikipedia entry on Physical Constants says:

With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory.

Can you give an example of the dimensionless physical constants derived from theory which this excerpt refers to? They don't have to be related to quantum chemistry, any such instance will do.

My motivation for asking this question is that I was reading the Wikipedia entry on the fine structure constant $\alpha$ and how for many physicists it is a secret obsession to derive the value of $\alpha$ from theory. Feynman speculates that this constant could have some relation to transcendental numbers such as $\pi$ or $e$. So I wonder if there are some dimensionless constants derived from theory which have values like that. If so, this might confirm that the universe is truly mathematical in nature, and this would be an incredible discovery in my opinion.

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  • $\begingroup$ Some particular examples related to atomic physics (if not chemistry) might be the values, for various chemical elements, of the Landé g-factor. $\endgroup$ – user12262 Feb 22 '15 at 23:05
  • $\begingroup$ The question (v5) seems like a list question. $\endgroup$ – Qmechanic Feb 23 '15 at 8:12
  • $\begingroup$ The list is quite limited I believe. $\endgroup$ – Joshua Benabou Feb 23 '15 at 9:01

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