Mathematics
| This is an AoPSWiki Word of the Week for February 4-11 |
Mathematics is the science of numbers, and the study of relationships that exist between them. It generally also is considered to contain geometry and topology as a subset, as they are related to 
and 
in general.
Contents
Overview
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 the base ten number system. |
Modern mathematics is normally built around base 10, with ten digits. (
) Modern mathematics is separated into two categories: discrete mathematics and non-discrete.
Non-Discrete Mathematics
Non-discrete mathematics is study of mathematics that is generally applicable to the "real world", such as algebra, Euclidean geometry, statistics, and other such topics. (Note that the real world is actually only approximately Euclidean if one studies large areas of it, infinitesimal areas actually are non-Euclidean) There is some controversy over what varieties of algebra are non-discrete, but it is generally agreed that elementary and superior algebra are non-discrete, while abstract algebra and intermediate topics such as field and graph theory and Diophantine equations are discrete.
Discrete Mathematics
Combinatorics, number theory, and some of the algebraic fields mentioned above are examples of discrete mathematics. Topics of discrete mathematics are generally not directly applicable to the "real world", and if they are, it is only in an abstract fashion.
History of Mathematics
Mathematics was noted by the earliest humans. Over time, as humans evolved, the complexity of mathematics also evolved. There was an astounding discovery on how the numbers correlated with each other, as well as in nature, so well, as they created the concept of numbers. As a great 19th century thinker said,
"God created the integers. All the rest is the work of man." (Leopold Kronecker)
