# Mathematics

Area of knowledge that includes such topics as numbers , formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

- Mathematics171 related topics

## Complex number

[[File:A plus bi.svg|thumb|upright=1.15|right|A complex number can be visually represented as a pair of numbers

[[File:A plus bi.svg|thumb|upright=1.15|right|A complex number can be visually represented as a pair of numbers

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit, and satisfying the equation

## Science

Systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

Systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes.

## Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories.

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories.

The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.

## Philosophy

Systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.

Systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.

Before the modern age, the term was used in a very wide sense, which included the individual sciences, like physics or mathematics, as its sub-disciplines, but the contemporary usage is more narrow.

## Euclid

Not to be confused with Euclid of Megara.

Not to be confused with Euclid of Megara.

His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.

## Leonhard Euler

Leonhard Euler (, ; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

## Number

Mathematical object used to count, measure, and label.

Mathematical object used to count, measure, and label.

In mathematics, the notion of a number has been extended over the centuries to include 0, negative numbers, rational numbers such as one half and pi, and complex numbers which extend the real numbers with a [[imaginary unit|square root of

## Physics

Natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

Natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

Over much of the past two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the Scientific Revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right.

## Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively.

## Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.