Application of mathematics was restricted to physical sciences, but only till the last century or so. In the last 90 years, math has seen a greater advent in Economics. An increasing proportion of research papers published had use of advanced mathematical techniques to arrive at results. More so, the display of these results is in mathematical or symbolic language, rather than in the literary form. Where there is nothing wrong with the use of math to arrive at results, as it helps quantify certain effects or changes, or give at least an estimated value to it, at best, math is not the easiest and simplest language to communicate in. Not everyone understands or follow math entirely as they do English or a dialect, nor is it as easy to quickly learn it.
Economics has seen an increasing use of mathematical, statistical and econometric models, to measure change. This surely has helped to expand boundaries of the science. Economics has now become more and more interdisciplinary. For example, Brownian motion, a concept in physics to explain the random motion of particles suspended in a fluid, is used to measure movement of high frequency data in time series analysis. Production functions and utility functions are given different forms, using simple arithmetic operations, or square roots or exponentials, so as to arrive at an optimum price and quantity. Matrix algebra are used in the calculation of national income. And the list goes on.
My contention; is it possible to even capture most aspects of human behaviour mathematically? Let us begin with microeconomics, which deals with smaller economic units. Humans are complex animals. Multiple considerations go into the making of any decision, big or small. When your microeconomic agent is a factory, each visible output is a culmination of several invisible decisions taken by multiple humans. This multiplies drastically at a macroeconomic level. It combines millions of small invisible decisions into a few equations. There is active generalisation of reasons when there is clearly no need to do so. Hence, the regression ‘line’ is impractical for real uses when it actually never a line or a smooth curve. Reality lies in the fluctuations and the bulges and the troughs.
I recently came across an article stating that Buchanan, a Nobel laureate had colluded with capitalists to formulate the public choice theory. This was the very theory that helped him bag the revered Prize. This is one of the many cases of such elite behaviour of economists that might or might not have come out in public. What mathematical economics does is, it segregates those who know how to use it, and very much to their advantage, from those who do not. This gives the former undue advantage to manipulate the latter, just as Buchanan did. This reminds me of a very Indian sociological phenomenon. Historically, Brahmins were custodians of scriptures and any other text of wisdom as they were the only learned section of the society who could understand them. This gave them enough reason to practice elite behaviour to close doors unto other classes of the society. This also gave them an enviable position where people belonging to other classes wanted to enjoy that power. They thus followed Brahmin practices in several rituals like marriage, or prayer. Thank goodness, sociology is safe from math, at least for now. Or they would probably fit regression lines and find the root cause to origins of caste discrimination if they like to!
One could argue, on these grounds, that people who do not know math, should learn math so as to understand it, and challenge wrong doing, completely removing any chance of manipulation. I do not believe so. It has always been, and will always be, in the hands of a few to maintain the sanity of a profession and they shall do it without others recognising it. I would rather advocate lesser use of math in economics.
Think about the ones who advocate policy and ones who make it, and the differences in their intellectual capabilities. Not everyone who does not know math is not bright or diligent. But what if they are wrongly influenced because they fail to ask the right questions, or they are plain intimidated by all the math. It is easier to read, “Inflation is going up because demand of Onions is higher than supply”, for example, than to read, “beta is statistically significant at 0.35, with an R-squared of 0.9”. Financial and Development economists rule the world for now. And this is where they are taking the boat. Only time will tell if it reaches the coast safely.