Is there any branch of Mathematics which has no applications in any other field or in real world?

Many fields of mathematics are not currently used in other fields and real world society. Crossing the ivory tower, the thing studying becomes very difficult and may not be related to other things.

However, this does not preclude anyone finally finding the possibilities associated with it. Prior to the 20th century, number theory was considered an interesting "wasteful" mathematics. It has created a huge security industry

Andrew Wells, of course, may say, "There is this relationship between this esoteric field and (difficult-to-understand field)" (Andrew Wells uses algebraic geometry, many of the number theory The technique proves Fermat's last theorem [Source: Wikipedia]

Regarding the relevance problem, Bronfenbrenner wrote that any mathematical model requires what he calls the "applicability theorem" to indicate the conditions under which it is actually available in the real world. "As it relates to the real world, the applicability theorem is very likely, but that is absolutely uncertain." If Lisa Randall is right, physicists usually know when Newton's theory is valid I will. Contrary to this, economists often do not know when their theories will be effective. What is the number of companies that apply "complete competition" theory? What kind of assumptions need to be made to closely link workers' wages and productivity, and are these assumptions actually realized?

Until the middle of the 20th century number theory was considered to be the purest field of mathematics and it was not applied directly to the real world. The advent of digital computers and digital communication suggests that number theory provides unexpected answers to real world problems. At the same time, advances in computer technology have enabled numberists to make major progress in decomposing large amounts of data, determining prime numbers, testing predictions, and solving numerical problems that were previously impossible.

Today, the term "applied mathematics" is used in a broader sense. It includes not only the classical areas mentioned above, but also other fields that are becoming increasingly important in applications. Even digital theory in mathematical theory is important in applications (such as encryption) as part of pure mathematics, but they are generally not considered part of applied mathematics itself. The term "applicable mathematics" is sometimes used to distinguish traditional applied mathematics developed in physics from many mathematical fields applied to today's real world problems.