I think it's a bit more subtle than that.

If you consider that exponential functions are inescapable in financial mathematics and modeling human economies, it could be argued certain constants like 'e' and 'pi' count as esoteric constants of economics -- however I understand what you mean. They are dragged in almost through the universality of mathematics itself, and we can express many functions using these constants without them having any explanatory nature.

I'm still not certain such constants don't exist for econ -- constants which describe limiting behaviour in graph theory (human relationships, barter, etc) exist and so may naturally be considered "constants of finance/economics".

But yes, the whole modern Keynesian / mathematical econ black box where they pretend the theories about inflation and the variables in them are akin to proven physical Theories (theories with the capital 'T' in science), it's not intellectually sound.