Vladimir I. Arnol'd is a former Soviet mathematician who made important contributions to the field of nonlinear dynamics (e.g., Kolmogorov-Arnold-Moser theorem, Kolmogorov was Arnol'd's supervisor) when he was still very young (early 20s). He also made an important contribution to the fluid dynamics by extending Lyapunov stability theorems from classic/particle mechanics to fluid mechanics. The so-called Arnol'd invariants are powerful tools for studying the nonlinear stability of fluid motion (or nonlinear saturation of linearly unstable flows). The followings are what he said about questions of multiple choice that often appear in TOEFL and GRE types of exams:

"......The United States has a different danger. No Russian professor is able to solve correctly the problem they give in the Graduate Record Examination, the official entrance examination for graduate studies: find the closest pair to (angle, degree) among the pairs: (time, hour), (area, square inch), and (milk, quart). Every American immediately solves it correctly. The official explanation for the correct response (area, square inch) is: one degree is the minimal measure of angle, one square inch is the minimal measure of area, while an hour contains minutes and a quart contains two pints. I always wondered how it is possible for so many Americans to overcome such difficulties and become great mathematicians. One physicist in New York who solved the problem successfully told me that he had the correct model of the degree of stupidity of the authors of such problems........"

(2003.07.02)