 # Mathematics

Mathematics (from Greek: ) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis). It has no generally accepted definition.

Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.

Source: Mathematics (wikipedia.org)

#### Mandelbrot set

The Mandelbrot set (/ˈmændəlbrɒt/) is the set of complex numbers c{\displaystyle c} for which the function fc(z)=z2+c{\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated from z=0{\displaystyle z=0}, i.e.

#### Is zero an even number?

Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.

#### Loop (graph theory)

In graph theory, a loop (also called a self-loop or a "buckle") is an edge that connects a vertex to itself. A simple graph contains no loops. For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices.

#### The simple maths error that can lead to bankruptcy

As we head into 2021, Worklife is running our best, most insightful and most essential stories from 2020. Read our full list of the year’s top stories here. Fifteen years ago, the people of Italy experienced a strange kind of mass hysteria known as “53 fever”.

#### Noli turbare circulos meos!

According to Valerius Maximus, the phrase was uttered by the ancient Greek mathematician and astronomer Archimedes. When the Romans conquered the city of Syracuse after the siege of 214–212 BC, the Roman general Marcus Claudius Marcellus gave the order to retrieve Archimedes.

#### How modern mathematics emerged from a lost Islamic library

The House of Wisdom sounds a bit like make believe: no trace remains of this ancient library, destroyed in the 13th Century, so we cannot be sure exactly where it was located or what it looked like.

#### Euler's identity

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics.

#### Benford's law

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

#### Path-based strong component algorithm

In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep track of the current search path.

#### Strongly connected component

In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected.

#### Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges often called arcs.

#### Cycle (graph theory)

In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices.

#### Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines).

#### Tarjan's strongly connected components algorithm

Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph.

#### The violent attack that turned a man into a maths genius

BBC Future has brought you in-depth and rigorous stories to help you navigate the current pandemic, but we know that’s not all you want to read. So now we’re dedicating a series to help you escape.

#### From The MIT Press Reader

One of the key findings over the past decades is that our number faculty is deeply rooted in our biological ancestry, and not based on our ability to use language. Considering the multitude of situations in which we humans use numerical information, life without numbers is inconceivable.

#### The maths problem that could bring the world to a halt

It’s not easy to accurately predict what humans want and when they will want it. We’re demanding creatures, expecting the world to deliver speedy solutions to our increasingly complex and diverse modern-day problems.

#### The myth of being 'bad' at maths

Are you a parent who dreads having to help with maths homework? In a restaurant, do you hate having to calculate the tip on a bill? Does understanding your mortgage interest payments seem like an unsurmountable task? If so, you’re definitely not alone.

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