I'm puzzled.

Yes, the periods of pendulums that are to hand can be observed. But it is the accumulation of such observations that enables a predictive theory to be formed. That theory enables a formula to be constructed that will yield an estimate of the period of a pendulum given its length.

I would have said that this involved mathematics - isn't the substitution of a value into a formula mathematics?

(And the theory is also backed up by an applied mathematical theory of pendulums, although this is not required in standard cases.)