The physical constants: relationship to mathematics?

[CuriousLearner]

Do we have any examples of physical constants appearing in topics that are focused more on abstract mathematics? For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics? Could they do so if we modified their values by some sort of scalar multiple? I mean for classes of constants that may be related to a particular phenomenon such as mass ratios with respect to the electron of the fermions.

 

[fresh_42]

Do $1, \frac{h}{ħ} \, , \, i$ or $e$ count? Or eigenvalues of matrices? If not, what makes you think randomly fixed numbers (due to the definition of units) could appear in math?

 

[mfb]

For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics?

No, unless you count values like 2, pi or similar things.
Such a connection would be amazing, because currently there is no known way to calculate dimensionless physical constants - if the same numbers appear in mathematics somewhere it would indicate some connection between that part of mathematics and the physical constant.

 

[FactChecker]

Certainly there are many constants ( e, π, Fibinachi numbers, the Golden Ratio, etc. ) that are important in purely mathematical issues and also important in physics. However, I don't think they would be called "physics constants" because their use is more general.

 

[chiro]

Hey CuriousLearner.

The physical constants are (naturally) in terms of physical units and the relation is between constants that have physical significance - which often involve changes in quantities that have a visual characteristic (i.e. involve geometry in some capacity meaning it involves distance and angle).

Mathematics can be organized in a geometric way but it doesn't need to be.

Also - quantities in mathematics that are able to use arbitrary mappings are dimension-less (example - you can't say find e^x of a unit x since it will change the units).