Chebyshev has given his name to results in probabilityand analysis, one of the first Russian mathematicians by birth to be so recognized. His work reflected a great deal of mathematical sophistication, making connections between different ...

Pappus of Alexandria was a late Greek geometer whose theorems provided a foundation for modern projective geometry. Virtually nothing is known about his life. He wrote his major work, Synagoge, or the Mathematical Collection, as a guide to...

One of the five postulates, or axioms, of Euclid underpinning Euclidean geometry. It states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Unlike Euclid's other four postul...

Parametric equations are those that relate typical x and y values to another variable or arbitrarily chosen constant. Such equations are widely found in studies dealing with motion as a function of time. There are scalar and vector paramet...

Pascal's triangle is a well known set of numbers aligned in the shape of a pyramid. The numbers represent the binomial coefficients. Binomial coefficients represent the number of subsets of a given size. The numbers in Pascal's triangle ar...

Paul Bernays secured his reputation with a classic treatise on mathematical logic, the Foundations of Mathematics, and through his refinement and consolidation of set theory into the von Neumann-Bernays system. Bernays was a platonic mathe...

The English physicist Paul Adrien Maurice Dirac (1902-1984) formulated a most general type of quantum mechanics and a relativistic wave equation for the electron which led to the prediction of positive electrons, the first known forms of a...

The work of Guldin is covered in four separate volumes which he published during his life, they are entitled De Centro Gravitas. Volume one considers centres of gravity with particular reference to the centre of gravity of the Earth. The s...

In 1889, the Italian mathematician Giuseppe Peano (1858-1932) published the first set of axioms, or assumptions, upon which to build a rigorous system of arithmetic, number theory, and algebra. Peano was a professor and developer of advanc...

A magic hexagram is a hexagram such that each outer point and each crossing point is assigned a number so that different points are assigned different numbers. The sum of the numbers on any line is required to be the same for all lines. In...

Perfect number-a number that is the sum of its proper divisors (a proper divisor is a divisor smaller than the number itself). For example, 6 is perfect, since its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Twenty-eight is a perfe...

Mathematical perspective is the realistic representation of a three dimensional object on a two dimensional surface. In a perspective drawing, vertical lines in an image are drawn as vertical lines on the paper or canvas. Parallel horizont...

Math phobia, which is exhibited by many students, is the persistent, illogical, intense fear of not succeeding in math. It is the belief that one is unable to handle the difficulty associated with learning math. Many people incorrectly ass...

The French mathematician Pierre de Fermat (1601-1665) played an important part in the foundation and development of analytic geometry, the calculus of probabilities, and especially the theory of numbers. Pierre de Fermat was born on Aug. 1...

A mathematician, biologist, and astronomer, Pierre-Louis Moreau de Maupertuis was a strong proponent of Sir Isaac Newton's theory of gravitation, helped confirm Newton's theory on the exact shape of Earth, and formulated the principle of l...

The French mathematician Pierre Simon, Marquis de Laplace (1749-1827), made outstanding contributions to pure mathematics, probability theory, and dynamical astronomy. Pierre Simon Laplace was born on March 23, 1749, at Beaumont-en-Auge in...

Plato stands at the center of philosophical thought in the ancient world. He was the first person to approach philosophical issues systematically, but it was the genius with which he treated those issues that made his thought so influentia...

The Poincaré conjecture started out as a question asked by the founder of the subject of topology, Henri Poincaré, in 1904: Is a simply connected, compact, three-dimensional manifold necessarily a hypersphere? Poincaré...

In geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides). If none of th...

In algebra, an expression consisting of numbers and variables grouped according to certain patterns. Specifically, polynomials are sums of monomials of the form &math.a;&math.x;&math.n;, where &math.a; (the coefficient) can be any real num...

A power series expresses a function f(x) as an infinite sum (or "series") of terms involving powers of the variable x. Power series can be considered a natural extension of polynomials, which are finite sums of such terms. All of the impor...

The prime number theorem addresses the question of what proportion of integers are prime numbers. It was proved at the end of the 19th century by the French mathematician Jacques Hadamard and the Belgian mathematician Charles de la Vall&ea...

Branch of mathematics that deals with analysis of random events. Probability is the numerical assessment of likelihood on a scale from 0 (impossibility) to 1 (absolute certainty). Probability is usually expressed as the ratio between the n...

Proof by deduction is the primary method of proof used in classical mathematics. Deductive proof is the process of deriving conclusions from logical premises without resort to empirical evidence. A deductive mathematical system typically c...

In mathematics, a proposition is a statement which must be proved by a deductive argument in order to be considered true. Propositions are also called theorems. In general, mathematical propositions have the logical form "If p, then q" whe...