On Overwhelming Numerical Evidence in the Settling of Kinney’s Waiting-Time Conjecture
Eugene F. Schuster · SIAM Journal on Scientific and Statistical Computing · 1985
The computer is often used as an exploratory tool in problem solving. This exploratory analysis is very important in gaining insight into problems and theorems and often leads to new conjectures. Heuristic reasoning may then lead from the conjecture to a formal theorem whose validity leads itself to further numerical investigation. When these numerical investigations present overwhelming numerical evidence that the proposed theorem is true, the researcher sets upon a search for a mathematical proof. This note reports experience in this regard in the settling of Kinney’s waiting time conjecture on the asymptotic logarithmic form of the expected value of the maximum of independent identically distributed geometrics. The lesson learned is that overwhelming numerical evidence is not enough.