I am studying at the department of mathematics and I really want to be a good mathematician. That is why I want to know what mathematics is. Different people say about it:

• Pure mathematics is like a ghost, everybody tells about it but nobody has seen it.
• Mathematics is a queen and a maid of sciences.
• Mathematics as a whole is in fact one large equation for the other sciences.
• Mathematics is like a game or an art.

However, what is mathematics? The word "mathematics" means "the science of sciences". Many years ago mathematics arose. People needed closing, footing, later they needed changing too. That is why people needed the calculus. People needed houses, fields. That is why people needed geometry. As soon as man began to count, using his fingers, mathematics arose. Neanderthals made the earliest mathematical discoveries: the number and the circle. First steps of mathematics as a science were done in Babylonia, Egypt and Greece. The outstanding mathematician Fales (Фалес) is called "the father of mathematics", because he entered proofs in the mathematics theory.

But what is mathematics in the modern sense of the term? Mathematics is a science, in which practical results arise from abstract ideas and concepts. Mathematics it is not only arithmetic which is the science of numbers and computation. Mathematics is not only algebra which is the language of symbols, operations and relations. It is not only geometry which is the study of shapes, sizes and spaces. It is not only statistics which is the science of interpreting data and graphs. It is not only calculus, which is the study of change, limits and infinity. Mathematics is all these and even more.

The language of math is a language of abstract symbols. Abstract symbols and concepts are the foundation of mathematics. Foundation of each branch of math is the system of axioms.

But math isn't a closed science. Some people think that it is more just to call mathematics an art or a game, since mathematics, unlike the sciences, but like an art or a game, is the free creation of human mind. For example, music was one of basic branches of mathematics in Pythagorean School; but mathematics was a branch of physics in 18^th century. Many geniuses in mathematics were also talented in other fields. For example, mathematician O.Hayam (Хайям) was a poet, the French mathematician P.Fermat (Ферма) was a lawyer, the well-known mathematician A.Durer (Дюрер) was an artist, famous mathematicians Descartes (Декарт), Newton (Ньютон), Bernoulli (Бернулли) were physicists, mathematician C.Dodgson (Доджсон) was a famous writer Lewis Carroll (Льюис Кэрролл). All these mathematicians entered mathematical methods in their profession or hobby. Now math is actual in the economy: mathematicians J.Nash (Нэш) and Kontorovich (Конторович) got Nobel premium in the economy, but they solved only mathematical problems.

Mathematics is very interesting and very beautiful science. Mathematics is not only numbers and facts. Mathematics is the collection of beautiful ideas and their tangles. Ideas in mathematical theory like the colours in a pointing, words in a poem or sounds in music must fit together in a harmonious way. That is why every mathematician must be a poet and an artist at heart.

In the end I would add, that I like mathematics because it is a way of thinking and a way of reasoning as well as a way of creating beauty.