Generally, evident truths do not require mathematical confirmation, but it is pleasant to run into strict proofs from time to time. Here is a recent example – reportedly, due to Rob Howard of Next Level Systems.
It is well known that “Knowledge is Power” and “Time is Money”. In the algebraic form,
K = P, T = M.
On the other hand, power is work per unit time, i.e.
P = W/T.
Eliminating P and T from this system of three equations, we readily get
M = W/K,
i.e. the more knowledge the less money (at given work), in good agreement with recent observations. Keep telling your students to study hard, my colleagues. —KKL