The Greek astronomer Aristarchus of Samos (ca. 310-230 BC) hypothesized that the earth revolves yearly about the sun and daily rotates about its own axis. He attempted to determine the relative sizes and distances of the sun, moon, and ear...

Branch of mathematics that deals with the properties of numbers and ways of combining them through addition, subtraction, multiplication, and division. Initially it dealt only with the counting numbers, but its definition has broadened to ...

A sequence of numbers is said to be arithmetic if the difference between any two successive terms is the same. For example the sequence 1,3,5,7,9,... is arithmetic because the difference between any two consecutive terms is 2. This differe...

In a time and place where people believed certain distant stars, called "asuras," possessed malevolent powers capable of inflicting harm on Earth, Aryabhata the Elder took the first steps towards separating scientific explication from folk...

In mathematics, a line or curve that acts as the limit of another line or curve. For example, a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the cu...

August Crelle was an engineer and amateur mathematician who founded one of the first European mathematical journals, Journal für die reine und angewandte Mathematik, also known as Crelle's Journal. Born in 1780 in Eichwerder, Germany ...

Augustus De Morgan entered the English mathematical scene during a period of inactivity and by the time of his death it had regained the stature it had since the time of Isaac Newton. Although De Morgan did not devote himself wholeheartedl...

In mathematics or logic, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful (e.g., “Nothing can both be and not be at the same time and in the same respect”). The term is of...

A Banach space is a vector space over the field of real numbers, or over the field of complex numbers, together with a norm. And in a Banach space the metric topology determine by the norm is complete. Thus the assertion that a certain obj...

A theologist by trade and a strong influence in the Calvinist government of his time, Bartholomeo Pitiscus also essentially coined the term "trigonometry." The term comes from the title of his book Trigonometria, which consists of three pa...

The Polish-born French-American mathematician Benoit B. Mandelbrot (born 1924) is the inventor of fractals. Fractal geometry has been described as one of the major developments of 20th-century mathematics. He calls himself "a physicist als...

The German mathematician Georg Friedrich Bernard Riemann (1826-1866) was one of the founders of algebraic geometry. His concept of geometric space cleared the way for the general theory of relativity. On Sept. 17, 1826, Georg Riemann was b...

Bessel functions are solutions to Bessel's differential equation. The Bessel differential equation follows the form x2y'' + xy' + (x2 - n2)y = 0, where the prime notation is indicative of a derivative of y with respect to x. This equation ...

The binary number system, also called the base-2 number system, is a method of representing numbers that counts by using combinations of only two numerals: zero (0) and one (1). Computers use the binary number system to manipulate and stor...

The French scientist and philosopher Blaise Pascal (1623-1662) was a precocious and influential mathematical writer, a master of the French language, and a great religious philosopher. Blaise Pascal was born at Clermont-Ferrand on June 19,...

Bonaventura Cavalieri refined early Greek work on the concept of indivisibles. His work served as a stepping stone to the concept of infinitesimals and was the foundation of Isaac Newton's development of the calculus. Cavalieri was born in...

Brahmagupta was an Indian astronomer and mathematician. He was the head of the astronomical observatory at Ujjain (his probable birthplace). His main, but not sole, achievements in the field of mathematics were the introduction of zero and...

The ball, Bn, is the subset of Rn (this is n-dimensional real space) equal to the set of all real n-tuples (x1,..,xn) such that the square root of (x12 + ... + xn2) is less than or equal to one. Brouwer's fixed point theorem states that if...

Although the abacus, the first tool of calculation, has existed since ancient times, advanced calculating machines did not appear until the early 1600s. Scientists and mathematicians were determined to simplify complex astronomical and nav...

Field of mathematics that analyzes aspects of change in processes or systems that can be modeled by functions. Through its two primary tools—the derivative and the integral—it allows precise calculation of rates of change and o...

any system for dividing time over extended periods, such as days, months, or years, and arranging such divisions in a definite order. A calendar is convenient for regulating civil life and religious observances and for historical and scien...

Cantor set—an infinite set of numbers between 0 and 1, defined by an inductive process. To define this set, start with the closed interval [0,1]. Remove the middle third--the open interval (1/3,2/3). (That is, remove all the points b...

Bernhard Bolzano defined cardinality in his book Paradoxes of the Infinite (1851). The cardinality of a set is, roughly speaking, its size. Precisely, the cardinality of X is said to be less than or equal to that of Y if there is a functio...

As the impact of the American and French Revolutions was felt across Europe, a social atmosphere arose that encouraged ground breaking work in mathematics. Karl Gustav Jacob Jacobi, who attracted early attention from luminaries such as Adr...

Casper Wesselmade a significant contribution to mathematics, but his legacy is to be a footnote in histories of other great mathematicians. Karl Friedrich Gauss and Jean Robert Argand are most often given credit for expressing complex numb...