Mathematical and experimental techniques employed in the natural sciences. Many empirical sciences, especially the social sciences, use mathematical tools borrowed from probability theory and statistics, together with such outgrowths of th...

Until the seventeenth century, mathematics in Japan was a subject known almost exclusively among the upper class. Like art, music, and poetry, it was primarily a leisure time activity with little practical application. That situation was c...

In mathematics, the sum of infinitely many numbers, whose relationship can typically be expressed as a formula or a function. An infinite series that results in a finite sum is said to converge (&see; convergence). One that does not, diver...

Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its terminology and concepts. These include the operations of union (∪), and inters...

Sexagesimal numeration is a numeral system in which all derived units are based on the number 60 and the powers of 60. The word sexagesimal is derived from the Latin word sexagesimus (sixty). Between 4000-3000 b.c. the Sumerians developed ...

Shiing-Shen Chern has specialized in differential geometry and he studied what are now known as the Chern characteristic classes in fibre spaces. This work has relevance in mathematics as well as mathematical physics. Chern also produced a...

The Sierpiski triangle (also know as the Sierpiski gasket or sieve) is a fractal first described by Sierpiski in 1915. To construct it, draw the outline of an equilateral triangle on white paper. In its middle draw a black upside down tria...

The sieve of Eratosthenes is a useful method for making a list of prime numbers. Let d and n be positive integers. We say that d divides n, or that d is a divisor of n, if the fraction n/d is an integer. For example, 4 divides 12 and 1 div...

Simon Jean Antoine Lhuilier is best remembered for making mathematical advances that were key in the subsequent development of , a branch of geometry. His textbooks on geometry and algebra were staples in the curricula of many European sch...

Simon Donaldson shocked the mathematical world during the 1980s with a series of papers on the structure of four-dimensional spaces. Researchers had produced a collection of results during the previous decade that outlined a general unders...

Sine is a trigonometric function derived from the Latin sinus meaning curve. In a right triangle the sine of an angle (sin) is defined as the length of the side of the triangle opposite the angle divided by the length of the hypotenuse. si...

Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equa...

Picture a rectangle divided into two right triangles by a diagonal. How is the area of the right triangle formed by the diagonal related to the area of the rectangle? The area of any rectangle is the product of its width and length. For ex...

The foundational work of Sophie Germain (1778-1831) on Fermat's Last Theorem, a problem unsolved in mathematics into the late 20th century, stood unmatched for over one hundred years. Though published by a mentor of hers, Adrien-Marie Lege...

Space, most generally, might be described as the boundless container of the universe. Its contents are all physical things that we know of, and more. To describe the contents of space, we use terms of distance, mass, force, motion, energy,...

Single entity that relates space and time in a four-dimensional structure, postulated by Albert Einstein in his theories of relativity. In the Newtonian universe it was supposed that there was no connection between space and time. Space wa...

Einstein's theory of relativity consists of two major portions: The special theory of relativity and the general theory of relativity. Special relativity deals with phenomena that become noticeable when traveling near the speed of light an...

A spiral is a curve formed by a point revolving around a fixed axis at an ever-increasing distance. It can be defined by a mathematical function which relates the distance of a point from its origin to the angle at which it is rotated. Som...

The number k is a square root of the number n if k2 = n. For example, 4 and -4 are the square roots of 16 since 4 x 4 = 16 and (-4) x (-4) = 16. The square root symbol is and for n greater than zero the symbol is understood to be a positi...

The Indian mathematician Srinivasa Ramanujan Aiyangar (1887-1920) is best known for his work on hypergeometric series and continued fractions. Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school ...

Stanislaw Lesniewski cofounded the Warsaw school of logic and served as one of its top representatives. Along with a student,, and colleague , he formed a triangle of expertise that made the University of Warsaw the world center for resear...

The concepts of extrema and critical points of functions is an extremely useful concept in mathematics, particularly the areas of calculus and differential equations. Extrema may be absolute, such as the maximum (or highest) value or the m...

Branch of mathematics dealing with gathering, analyzing, and making inferences from data. Originally associated with government data (e.g., census data), the subject now has applications in all the sciences. Statistical tools not only summ...

Stephen Wolfram shook up the scientific world from an early age, and has been recognized as a leading innovator in scientific computing since the first version of his computer program Mathematica was released in 1988. Stephen Wolfram was b...

Subrahmanyan Chandrasekhar (1910-1995) worked on the origins, structure, and dynamics of stars and earned a prominent place in the annals of science. The Nobel Prize-winning physicist's most celebrated work concerns the radiation of energy...