1 less than 2, 1 less than 3, 1 less than 4, 1 less than 5, 2 greater than 1, 2 greater than 3, 2 less than 4, 2 less than 5, 3 greater than 1, 3 greater than 2, 3 less than 4.

Mathematics (hanyu pinyin: shùXué；; ; Greek: μ α θ η μ α κ; English: Mathematics comes from the ancient Greek word μ θ η μ α (má th?ma), which means learning, learning and science. Ancient Greek scholars regarded it as the starting point of philosophy and the "foundation of learning".

In addition, there is a narrow and technical meaning-"mathematical research". Even in its etymology, its adjective meaning related to learning will be used to refer to mathematics.

Its plural form in English and as the plural form of mathématiques in French +es can be traced back to the Latin neutral plural (Mathematica), which is Cicero's plural from Greek τ α α θ ι α τ κ? (Tamatika)

In ancient China, mathematics was called arithmetic, also called arithmetic, and finally changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).

Mathematics originated from early human production activities. The ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. Judging from mathematics itself, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but we should fully affirm their contribution to mathematics.

Mathematics is applied in many different fields, including science, engineering, medicine and economics. The application of mathematics in these fields is generally called applied mathematics, which sometimes arouses new mathematical discoveries and promotes the development of new mathematical disciplines.

Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many jobs begin with learning pure mathematics, they may find suitable applications in the future.

Mathematical space

The study of space originates from Euclidean geometry, while trigonometry combines space with numbers, including the famous Pythagorean theorem, trigonometric function and so on. Now the research on space is extended to high-dimensional geometry, non-Euclidean geometry and topology.

Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold.

Algebraic geometry has the description of geometric objects such as polynomial equation solution set, which combines the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.