Mathematics

The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning...

• abacus

  calculating device, probably of Babylonian origin, that was long important in commerce. It is the ancestor of the modern calculating machine and computer. The earliest “abacus” likely was a board or slab on which a Babylonian spread sand so he could...

• Abel, Niels Henrik

  Norwegian mathematician, a pioneer in the development of several branches of modern mathematics. Abel’s father was a poor Lutheran minister who moved his family to the parish of Gjerstad, near the town of Risør in southeast Norway, soon after Niels Henrik...

• Abel’s test

  in analysis (a branch of mathematics), a test for determining if an infinite series converges to some finite value. The test is named for the Norwegian mathematician Niels Henrik Abel (1802–29). Starting with any known convergent series, say Σ  a n (i.e.,...

• Abraham bar Hiyya

  Spanish Jewish philosopher, astronomer, astrologer, and mathematician whose writings were among the first scientific and philosophical works to be written in Hebrew. He is sometimes known as Savasorda, a corruption of an Arabic term indicating that he...

• absolute value

  Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number a is positive or zero, its absolute...

• Abūʾl-Wafāʾ

  a distinguished Muslim astronomer and mathematician, who made important contributions to the development of trigonometry. Abūʾl-Wafāʾ worked in a private observatory in Baghdad, where he made observations to determine, among other astronomical parameters,...

• Adams, John Couch

  British mathematician and astronomer, one of two people who independently discovered the planet Neptune. On July 3, 1841, Adams had entered in his journal: “Formed a design in the beginning of this week of investigating, as soon as possible after taking...

• Aepinus, Franz Maria Ulrich Theodor Hoch

  physicist who discovered (1756) pyroelectricity in the mineral tourmaline and published (1759) the first mathematical theory of electric and magnetic phenomena. Aepinus studied medicine and briefly taught mathematics at the University of Rostock, where...

• Agnesi, Maria Gaetana

  Italian mathematician and philosopher, considered to be the first woman in the Western world to have achieved a reputation in mathematics. Agnesi was the eldest child of a wealthy silk merchant who provided her with the best tutors available. She was...

• Ahlfors, Lars Valerian

  Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981. Ahlfors received his Ph.D. from the University of Helsinki in 1932. He held an appointment there...

• Aiken, Howard Hathaway

  mathematician who invented the Harvard Mark I, forerunner of the modern electronic digital computer. Aiken did engineering work while he attended the University of Wisconsin, Madison. After completing his doctorate at Harvard University in 1939, he remained...

• al-Ḥanafī, ʿAlam al-Dīn

  Egyptian mathematician, astronomer, and engineer. He wrote a treatise on Euclid’s postulates, built water mills and fortifications on the Orontes River, and constructed the second-oldest existing Arabic celestial globe.

• albedo

  fraction of light that is reflected by a body or surface. It is commonly used in astronomy to describe the reflective properties of planets, satellites, and asteroids. Albedo is usually differentiated into two general types: normal albedo and bond albedo....

• Aleksandrov, Pavel Sergeevich

  Russian mathematician who made important contributions to topology. In 1897 Aleksandrov moved with his family to Smolensk, where his father had accepted a position as a surgeon with the Smolensk State Hospital. His early education was supplied by his...

• Alembert, Jean Le Rond d’

  French mathematician, philosopher, and writer, who achieved fame as a mathematician and scientist before acquiring a considerable reputation as a contributor to and editor of the famous Encyclopédie. Early life The illegitimate son of a famous hostess,...

• Alexander, James W., II

  American mathematician and a founder of the branch of mathematics originally known as analysis situs, now called topology. The son of John White Alexander, an American painter who created murals for the Library of Congress, James studied mathematics...

• algebra

  branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. The notion that there exists such a distinct subdiscipline of mathematics, as well as the term algebra to denote...

• algebra, elementary

  branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business....

• algebra, linear

  mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations. Unlike other parts of mathematics that are frequently invigorated by new ideas and unsolved problems, linear algebra is very...

• algebra, modern

  branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers, complex numbers, matrices, and vector spaces), rather than rules and procedures for manipulating their individual elements. During the second...