There is a serious lacking in the undergraduate ability to engage in conceptual work involving mathematical logic. After getting disappointing results in two recent quizzes on quantitative material, I am faced with a quandary – should I just not proceed further and spend a few classes instructing everyone on all the high-school mathematics that they should know and just plain forgot? Or is it too far down the road for this now?
The problem lies not in an absence of prior mathematics instruction. It lies in the approach to mathematics. Math tends to be taught as a set of rules and is usually taught by example, and not from first principles. This is like teaching a tourist the most popular phrases in a language before a trip, leaving only a rudimentary knowledge of the language. Such knowledge is not enough to “speak” and “reason” with, yet is enough to “get by” with.
Unless mathematics and logic become first languages for students, subjects like Finance will always remain out of reach. No math facility implies no finance fluency. Doing finance is speaking math.
I believe there are positive externalities too. Analytic thinking develops well with subjects like math. This is an invaluable skill even with non-quant subjects like strategy and policy. Math immersion brings conceptual clarity across the board.
Paul Graham goes so far as to emphasize that the only way to keep all life and academic options open over the long run is to make math a priority. Given he choice he suggests always choosing to major in math over economics. Doing math allows one to later do economics as well, but never vice versa. For a superb essay on these matters, see
Its never too late to go after mathematical training. I know many friends who came to math late in academic life (myself included). Initial progress is slow, but then the pace quickens. Its a subject where some immersion is required before everything begins to fall in place. There is a reasonable period of waiting, and then mathematical maturity begins to arrive. Its a great feeling.
Long run, the problem needs to be stemmed at the high school stage. It is here that the abhorrence of math develops. The subject is presented in a dull, dry manner. It is taught in a rule-based way, and very little appreciation for the physical nature of mathematics is conveyed to the student. By the time the student arrives in college, any positive inclination (barring those always serious students) to the subject is stolen away.
An additional problem is that no societal incentives exist that would attract students to math in the U.S. Mathematicians are looked down upon, they are badly paid, and even ostracized by big-talking bullshitters. In the corporate sector, the math-skilled are relegated to factories, back-offices and research shops and glory goes to the marketing people. On Wall Street, quants are often abused by traders, most of whom have confused their stock portfolios in the bull market with their IQs.
My students need to see that the finance profession of the future will belong to the math-skilled. Just take a look at the composition of people in hedge funds – most have PhDs in quantitative disciplines. As it is often said – “The Geek shall inherit the Earth” !!