Group theory as the basis of unifications
From the beginning, the fundamental questions in the focus of mathematics, more specifically geometry and algebra, have been the problems that could be discussed identically and therefore computed with similar procedures. The group theory, originating from Évariste Galois, became the starting point for a systematisation process which established the order of operations with strict consistency, and the practical use of this theoretical outcome laid the groundwork for all computer technology procedures and operations dealing with systems.
Group theory determines the system of conditions for such algebraic operations which characterise a given mathematical-geometrical concept group as a rule and which therefore can be carried out there. These operations are much like basic arithmetic operations, such as addition and the other derived operations, and include some elementary number theory definitions, such as those relating to units and inverses. In algebra and geometry the operations defined this way are extended to higher order operations generalised from them, thus to higher number of dimensions generalised from two- and three-dimensional shapes and to matrix procedures complying with the multidimensional approach, ranging from real numbers to quaternions and procedures performed with symbolic operations. The theories of modern physics relating to the micro and macro world are specifically enabled by these computational group mechanisms and their high level generalisations, whether used for the purposes of elementary particle physics or the aerospace industry.
The group theory was further developed by two prominent mathematicians in collaboration: Sophus Lie in algebra and Felix Klein in geometry. This duality is constantly present in the story of systems theory.