**Pure and Applied Mathematics**

*During the 20th century, mathematics became a very abstract discipline that lost its connection to concrete mathematical problems somewhat. *

*Despite a high level of abstract thinking, it often results in newly developed theories that are surprisingly useful for practical applications, for example, in the financial industries.*

**Mathematics – Pure Mathematics **

*The purpose of pure and abstract mathematics is to find solutions to mathematical problems for the sake of fundamental research into mathematics itself without any primary interest in practical applications.*

Pure mathematics may be difficult to understand but this may very well be the reason for its fascination. Ancient Greek mathematicians formed a distinction between pure and applied mathematics. For example they introduced the term logistics to describe basic arithmetic calculations to solve tangible problems, such as the organization of an army.

Logistics was therefore considered its own subject area separate from mathematics and perhaps less interesting to the Greek mathematicians. They were much more interested in abstract principles, and the close connection between philosophy and mathematics was certainly a contributing factor.

Modern numeric theory is based on this fundamental research which resulted in the development of various mathematical methods including the calculation of the greatest common factor and a proof of the existence of an infinite number of primes. After the fall of the Roman Empire, mathematics of the Middle Ages was mainly influenced by monasteries, for instance the development of a calendar, and by contact with Arabic cultures.

**Hilberts program **

Up to the 20th century the development of mathematics as a discipline was shaped by increased efforts into fundamental research and critical analysis. One of the central figures was the German mathematician David Hilbert (1862-1943) whose work and definitions of terms played an important role in determining the boundaries of mathematical knowledge. His legacy has been a great influence for mathematical sciences.

In 1900 he proposed a list of 23 mathematical problems that were yet to be solved. One of the problems included assumed the existence of a fully consistent axiom system, the ultimate mathematical formula of the universe or the theory of everything, from which other scientific insights could be derived. Only a few years later a mathematician called Kurt Gbdel (1906-1978) proved that such a system was impossible.

Gbdel’s incompleteness theorem states that as soon as objects are related to each other, a system is created that is either incomplete or contradictory. This is why mathematics also studies the limits of knowledge. Another one of Hilberts approaches concentrated on the structural relationships in mathematics, for example, between geometry and algebra, as every bridge between these two disciplines that could combine the previous results of each, would count toward an enormous rise in knowledge.

**FIELDS MEDAL**

The Fields Medal is the highest possible award for a mathematician (apart from the Abel Prize first awarded in 2003), as the Nobel Prize does not include a cate- gory specifically for mathematics.

Every four years the International Mathematical Union (IMU) awards two to four mathematicians during the International Congress of Mathematics. A recipients age cannot be more than 40 years at the time of their accomplishment.