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Mathematics is defined as the science of numbers and their operations which can be seen as a group of abstract concepts (pure mathematics) or as applied to other subjects such as engineering and physics (applied mathematics). Pure mathematics is divided into different subsets: algebra, calculus and analysis, geometry and topology, combinatorics, logic, and number theory. As well as this, applied mathematics is segmented into different areas: dynamical systems and differential equation, mathematical physics, computation, information theory and signal processing, probability and statistics, and game theory. Since the 17th century, the discipline has become indispensable to other disciplines such as physical sciences and technology, and in modern time mathematics has become vital also to calculate quantitative aspects of the life sciences.
Depending on cultures, mathematics has been used for different needs such as commerce and agriculture, developing far beyond basic counting. The discipline has been a great help for many societies which thanks to mathematics have maintained these activities and had the opportunity to build their success.
All the mathematical systems include a combination of axioms and theorems which can be deduced from the axioms.
Most of mathematics has been developed since the 15th century and over the years, new developments in the discipline have been concentrated in Europe and North America. Nevertheless, this does not mean that improvements elsewhere have not been important. Indeed, to understand the history of the subject in Europe, people must know the history of maths related to the ancient Mesopotamia and Egypt, as well as the influence the Islamic civilisation had on the subject from the 9th to the 15th century.
Science is the discipline that allows people to get to know facts related to the natural world through the observation, study, experience and practice of phenomena. Nevertheless, the discipline is more than gathering knowledge as it is a deep understanding of how the world work and the development of something that is useful, practical and realistic.
The discipline has ancient root as the empirical investigation of the natural world is associated with Aristoteles and Thales, as well as the scientific method has been used since the middle age.
Modern science has developed in the early modern period, in particular during the European scientific revolution (16th-17th century), and from the 18th to the 20th century, the discipline has been seen as a progressive accumulation of knowledge, where new theories have replaced false belief.
People who study science are known as scientists. However, the world scientist has been introduced only in the 19th century. Before, people who were interested in the subject were called natural philosophers.
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