Understanding The Development of Mathematics From The History of The Basel Problem
by Jaewoo Lee
Abstract – In the field of mathematics, development is still ongoing nowadays. People are constantly finding new theories or formulas to develop the knowledge of mathematics. Currently, there are numerous amounts of mathematical questions that are not yet solved. The Basel Problem used to be one of such questions that many prestigious mathematicians had struggled. Leonhard Euler is the first mathematicians who managed to solve the problem. In the method he used, he mainly used the concept of integrals and trigonometry. In the process of historical development inside mathematics, previous knowledge is always used to explore new knowledge. In fact, Euler only used past knowledge to solve the Basel problem. By analyzing how Euler approached the Basel Problem, I will find out how reliant mathematics is on already discovered concepts. Nowadays, the Basel Problem is applied in other topics. One of the millennium prize problems, the Riemann Hypothesis, is not yet solved, but the solution of the Basel problem can be used as a hint. This represents the mechanism of history in mathematics, that past knowledge is being applying to new knowledge to explore the unsolved pathway.