Mathematics Throughout Human History

The area of mathematics that humanity has developed the longest is likely number theory. Number theory has continuously evolved from the one-to-one correspondence used in primitive times to count objects, to modern cryptography. Number theory, the system of numbers, is literally the study of the properties of integers. At first glance, it might seem unlikely that there are any hidden secrets within integers like 1, 2, 3, and so on. Even if there were, they may appear to have little practical use. The main areas of research in number theory can be broadly divided into two categories: the study of prime numbers and the study of integer solutions to equations.

Many results from number theory have been applied not only in other areas of mathematics but also in various fields outside of mathematics. In particular, some of the research findings related to cryptographic systems using number theory are considered so valuable that they are classified as military secrets. Just based on this fact, the historical significance and academic importance of number theory cannot be overstated.
Historically, cryptography has primarily been used for military purposes. Records suggest that even Julius Caesar exchanged encrypted letters with his generals, meaning the history of cryptography dates back at least 2,000 years. Cryptography began to develop significantly with the invention of the telegraph and the impact of World War I. Then, during World War II, highly sophisticated cryptographic systems were created. It is said that one of the key factors in the Allied victory was their success in decrypting German and Japanese codes. After the world wars, the advancement of computers and communication technologies rapidly increased the use of non-military cryptography.