## amicable numbers

Overview page. Subjects: Mathematics.

A pair of numbers with the property that each is equal to the sum of the positive divisors of the other. (For the purposes of this definition, a number is not included as one of its own...

## Blaise Pascal

Overview page. Subjects: Literature.

(1623–1662) French mathematician, physicist, and religious philosopher

Pascal was the son of a respected mathematician and a local administrator in Clermont-Ferrand, France. Early...

## Carl Gustav Jacob Jacobi

Overview page. Subjects: Mathematics.

(1804–51)

German mathematician responsible for notable developments in the theory of elliptic functions, a class of functions defined by, as it were, inverting certain integrals....

## dice problems

Overview page. Subjects: Probability and Statistics.

Probability problems concerning the outcomes of rolling dice. A problem considered at length by Fermat and Pascal concerned the number of times that one must throw a pair of dice before...

## Marin Mersenne

Overview page. Subjects: Arts and Humanities.

(1588–1648)

A key figure of the French 17th century, Mersenne studied, like Descartes, at La Flèche, and subsequently taught in Nevers and Paris. Mersenne was a correspondent of...

## number theory

Overview page. Subjects: Mathematics.

The area of mathematics concerning the study of the arithmetic properties of integers and related number systems such as prime numbers. Representations of numbers as sums of squares etc....

## Pell's equation

Overview page. Subjects: Mathematics.

The Diophantine equation *x*
^{2}=*ny*
^{2}+1, where *n* is a positive integer that is not a perfect square. Methods of solving such an equation have been sought from as long...

## Peter Gustav Lejeune Dirichlet

Overview page. Subjects: Probability and Statistics.

(1805–59)

German mathematician who was professor at the University of Berlin before succeeding Gauss at the University of Göttingen. He proved that in any arithmetic series *a*, *a*+*d*, *null...*

## probability

Overview page. Subjects: Science and Mathematics.

A numerical value given to the expectation that a particular event will occur. Although in scientific usage it is normally reckoned on a scale of 0 (for impossibility) to 1 (certainty), in...

## problem of points

Overview page. Subjects: Probability and Statistics.

This problem was the subject of the correspondence between Fermat and Pascal that underpins the modern treatment of probability. The problem is as follows.

Two gamblers are playing...