My interest in mathematics grew as I began to understand how deeply it was structuring the human society from the fundamental level. Mathematics has never been my strongest subject. Actually I even used to reject the idea that strict sets of logic could capture the essence of the world. But soon I came to realize that the focus should be on what we can express with the logic, not on what we can't. The power of mathematics lies in its capacity to explain complex problems in simpler forms. This compelling idea is dominant in science, even finance, and its importance is becoming stronger each moment as the technology of such fields advances. Many even foresee the humanities to be divided into two groups in the close future; those who understand mathematics underlying technology and those who don't. Although this gap has existed ever since, it will become a problem if it grows to be one of the main sources of power concentration and social inequality. But how does mathematics affect us in reality anyway? Why is it important that we understand it? There are historical events that show us such reasons.

 

In 1905, the world's most famous equation was introduced. Einstein's E=mc2, known as mass-energy equivalence, was to revolutionize the way we depict the universe. What did the equation imply? First, it meant that we could turn energy into matter. This idea promoted the development of particle colliders for probing subatomic particles. Particle colliders are devices that accelerate particles to extreme speeds, close to the speed of light, letting them crash into one another. At the moment of impact, massive energy is discharged and then transformed into new matter; new subatomic particles. Such experiments were crucial in discovering the fundamental building blocks of the universe upon which new theories were able to make sense. Secondly, the equation implied that reversely we could convert matter into energy. This idea gave insight into understanding and manipulating nuclear energy. Using the formula, estimating how much mass needed to create a certain amount of energy became possible. In the process of a nuclear fusion, particles at the beginning of the event weigh slightly more than the combined body at the end of the process. The reduced mass is converted into energy. Nuclear reactors use such principles to produce energy efficiently. Not only did the formula enable the development of nuclear physics, but it gave vast amounts of hints about the universe itself; the big bang theory, dark matter and energy, black holes etc.

 

These are the two general perspectives of the equation E=mc2. It is surprising to find out how one equation could be powerful enough to dramatically change the human society. Now let's look into a more controversial event that occurred recently.

 

On May 6, 2010, an unprecedented stock market crash took place in the United States, known as the Flash Crash. The Dow Jones Industrial Average experienced huge sudden drops within minutes without an explanation for the cause. Why did such an inexplicable event happen in the financial system? Research shows that the cause lies at the heart of the trading system itself; Algorithmic Trading.

 

Algorithmic Trading, the dominant trading system in the financial market of Wall Street, uses automated computer systems in which algorithms pre-programmed with instructions are initiated to execute the trading. The role of algorithms is to scan huge amounts of data for signs of potential profit. With the inception of such system, the market has now come to be operated by computers armed with complex mathematics, leaving no space for the human subjectivity and misjudgment to intervene. This has enabled the scale and speed of trading to be expanded and increased far beyond which would have been possible with only the capacity of the human intellect. At the same time, however, to regulate and control the interactions of algorithms, which endlessly do business according to continuously fluctuating market conditions, has become almost impossible. This is why chaotic events, such as the Flash Crash, can enter the market. Paul Wilmott, a researcher in quantitative finance, put this irony as "a combination of the sublime and the ridiculous. Sublime because it uses elegant mathematics, but ridiculous because you've got to use the thing."

 

It now seems true that mathematics is deeply affecting our lives from various aspects. However, whether it be science or finance, the issues boil down to one problem. It is not about mathematics itself but how we use it that is important. As seen above, mathematics is the foundation of technology. Technology is shaping the human society more than ever and will intensify its influence. Therefore the control of technology will become the essential source of power in the close future. However, unlike mathematics, technology is not always able to solve complicated problems with sets of simple assumptions. The invention of an atomic bomb did not bring peace but a new kind of anxiety and horror to the world. The abuse of automated decision making systems to loan as many mortgages as possible without managing risk by managers resulted in the Subprime Mortgage Crisis. Reality is about people, who do not work the way mathematics does. More is needed to comprehend the human society.

 

I believe that the assumptions we make about the role of technologies require just as much consideration as the mathematics used in developing technologies. Assumptions that sacrifice the unpredictable reality in preference of unrealistic but rational judgments are often the factors of the false usage of technology. Assumptions that insist that endless technological prosperity will naturally solve the problems of the humanities are often the causes of wasteful investments. Once new technology enters the society, things never become the same. It is our job to be awaken to the technologies changing our lives and make sure they don't get out of control. It is no question that understanding both assumptions and mathematics is a difficult task. But surely a minority of people at the center of technology are doing it and changing the world of the majority. I felt the need to understand how they were trying to control things. This is how I got interested in a subject that used to frustrate me the most. It seems to be worth a shot, though.

 

 

Da-Un Chung
(2013 Graduate; Seoul National University)