T.K.O. Mathematics

          There are plenty types of martial art – boxing, taekwondo, sumo, judo, aikido, kung fu and solving math problems. Hold on a second, mathematics? Even though they might come from different fields, math and martial arts are more similar than differing. Picking up a fight is a good analogy to solving problems. (Proof? We, at least once, were “knocked out” by a math problem on an exam. Don’t tell me that you never had that experience!)

            In boxing, both amateur and professional, there are plenty of rules and settings – size of the ring, referee, using only fists, time per round etc. If a boxer violates a rule, he/she might get a point stripped off or even disqualified. In order to box, a boxer needs to have appropriate equipment. A paradigm of problem solving nowadays is similar to a rigorous boxing fight. Every step has to be beautiful, strict and perfect. Addition or multiplication must be exact, no room for estimation.

            However, not every fight in this world is staged in an arena. Actually, there are more “street fighting” than official boxing match. In street fighting, no rule applies – dirty tricks are even acceptable. It doesn’t matter how the strikes were conducted. Final result is the most important goal – not the beauty of a kick or the style of fighting.

            Sanjoy Mahajan, a professor at Massachusetts Institute of Technology, broke a paradigm of problem solving by introducing the “street fighting mathematics.” In some situations, the top priority is the final answer, not the pathway. Frequently, life attacks you with rough questions. Most of the time, an exact answer is not required to survive; a rough answer will do the trick. Thus, if you confront with problems in unofficial situation, you are free to make some rough assumptions and estimations. The answer might not be 100% correct but, with reasonable assumptions, it should turn out to be in the same order of magnitude. For example, a student solves a problem and discovers the Earth’s radius to be 2000 km. Even though the right answer ranges from 6353 km to 6384 km, the student’s answer is good enough for street-fighting mathematics.

            For practicing, there are couples of question for street-fighting mathematics in Ay20 first set. (The link is http://www.astro.caltech.edu/~jrv/Ay20/ws/ws_collab_sfmath.pdf) But don’t forget, even though it is a convenient way to solve a complicated problem, street-fighting mathematics is casual. In official exams, e.g. Caltech finals, it is fine to use street-fighting trick to figure out a problem roughly but not entirely. Otherwise, you would get a T.K.O. from a professor, if not an F.