No, if there's any computations happening, that's engineers and physicists, especially if there are approximations happening.
A mathematician looks at the recurrence formula and generalises it (e.g. f(n) = a f(n-1) + b f(n-2) or f(n) = f(n-1)*f(n-2) (solve this one, hint: xkcd) or ...) and investigates its properties. The actual values of the numbers are not of much interest.
And a^n can only be computed in constant time if one uses exp(n log(a)), and (I think) that the scale of the numbers can have a large impact on the accuracy of the result, and so for large n, one needs more operations within both exp and log to give the same (relative) accuracy.
A mathematician looks at the recurrence formula and generalises it (e.g. f(n) = a f(n-1) + b f(n-2) or f(n) = f(n-1)*f(n-2) (solve this one, hint: xkcd) or ...) and investigates its properties. The actual values of the numbers are not of much interest.
And a^n can only be computed in constant time if one uses exp(n log(a)), and (I think) that the scale of the numbers can have a large impact on the accuracy of the result, and so for large n, one needs more operations within both exp and log to give the same (relative) accuracy.