Sharing In
The
Triumph

Academic Writing
Tim Lu
07.10.2014
Among numerous subjects in myriads of fields, mathematics and philosophy, demanding impeccably logical thinking, share a great deal of features. All of the deans of ancient mathematics, Pythagoras; of Renaissance, Gottfried Leibniz; of modern, Bertrand Russell, were also major philosophers. Meanwhile, the ultimate ambitions of both subjects are closely linked—to give an explanation of everything by finding the general rules and patterns governing the entire universe. Nevertheless, it is reasonable to deduce that almost no one is able to state the subtle connection between these two fields. Try wandering in the most densely populated spot in New York City, Times Square, and asking someone from the crowd. Therefore, it is a good idea to show how they can blend into each other.
Theory, as the word is used by scientists, is the highest expression of the quintessential ideas. In mathematics, some influential theories eventually boil down to philosophical ideas after their natures have been extracted and refined, and vice versa, even though the creators of such theories do not intentionally start thinking with ideas from the other discipline. For instance, the Nash Equilibrium, the great idea from John F.Nash, also a milestone in the development of game theory, has changed the foundations of economics. However, if we meticulously deconstruct this theory until we find its intrinsic nature, a philosophical idea will emerge at its core. The principal idea of the Nash Equilibrium can be interpreted as “To avoid the worst instead of to get the best,” a thought that existed in eastern philosophy—staying in the middle. Such a coincidence is indeed more than a coincidence, demonstrating how philosophy and mathematics “get along with each other”. However, the Nash Equilibrium is not the only example, as shown by some other shared concepts such as infinity, fairness, set, and function. Moreover, game theory can explain much of ethics, a basic branch of philosophy.
Ethics, a major topic of philosophy, can be analyzed as the result of game playing which existed since the age of the earliest human societies. Any male members in a matrilineal tribe were working under a pervasive rule that no matter how much prey they got by the end of the day, they had to submit the prey to the head of tribe who would assign the portions equally to every member of the tribe, including the hunters. In a sense, such a rule is now recognized as the ethical norm that every individual was supposed to obey. Moving our focus to the process of how the rule was formed, we capture the hidden traces of mathematics (our game theory, again). If a man decided not to conform to such a common rule, he would be able to keep all of his prey, which would be indeed much more beneficial to him than to obey the rule, especially on a day when he got a large amount of food. On the other hand, the rule sometimes helped him survive when he could not hunt much food. Otherwise, hunger was waiting for him. In a word, he was playing a game with rules, and the transformation from a pure rule to a commonly accepted norm comes when a set of people playing the same game finally choose the rule because they believe it is profitable. That means an ethical ideal emerges from the pattern described by a prevalent branch of math, game theory.
In a nutshell, philosophical ideas may be secretly hidden behind mathematics, and mathematical concepts sometimes are in the disguise of philosophy, as seen from their final purpose, theory and also practice. Philosophy and mathematics are two of the most glorious triumphs of human thought.