The idea of nothingness and emptiness has inspired and puzzled mathematicians, physicists, and even philosophers. What does empty space mean? If the space is empty, does it have any physical meaning or purpose? From the mathematical point ...

Addition is one of the four basic operations of arithmetic (the others being subtraction, multiplication, and division). In arithmetic, addition operates on the set of real numbers such that for any real numbers added together, another rea...

In the simplest sense, addition is a process of combining groups of things to form a new, larger group. Consider two baskets of apples: if apples are transferred from one basket into the other, a new bunch of apples is formed that is under...

The Belgian statistician and astronomer Lambert Adolphe Jacques Quételet (1796-1874) is considered the founder of modern statistics and demography. Adolphe Quételet was born in Ghent on Feb. 22, 1796. When he finished seconda...

Born into a well-to-do family, Adrien-Marie Legendre decided early in life to dedicate himself to the study of mathematics. He enrolled at the College Mazarin in Paris, France, concentrating on science and mathematics. Although independent...

Relatively few mathematical writings have survived from the time the rulers of Egypt built the pyramids. This is largely because writing at that time was done on laminated sheets of the papyrus plant, and such materials readily decompose u...

The German-born American physicist Albert Einstein (1879-1955) revolutionized the science of physics. He is best known for his theory of relativity. In the history of the exact sciences, only a handful of men--men like Nicolaus Copernicus ...

The German painter and graphic artist Albrecht Dürer (1471-1528) introduced the achievements of the Italian Renaissance into northern European art. His prints diffused his new style, a fusion of the German realistic tradition with the...

Aleksandr Yakovlevich Khinchin (or Khintchine) is best known as a mathematician in the fields of number theory and probability theory. He is responsible for Khinchin's constant and the Khinchin Levy constant (sometimes referred to as the L...

Ergodic theory, Alexandra Bellow's field of specialization, deals with the long term averages of the successive values of a function on a set when the set is mapped into itself, and whether these averages equal (converge to) a reasonable f...

A child prodigy, Alexis Claude Clairaut studied calculus at age 10, wrote mathematical papers at 13, and published a mathematical work on the gauche curve at age 18. Clairaut surpassed even Isaac Newton in his analysis of the effects of gr...

The Polish-American mathematician and logician Alfred Tarski (1902-1983) is regarded as the cofounder of metamathematics and one of the founders of the discipline of semantics. Alfred Tarski was born in Warsaw on Jan. 14, 1902. He taught a...

Set algebra is fundamental to all of modern mathematics. Indeed, sets form the very foundation of mathematics. The algebra of sets consists of the operations union, intersection, and complement. Suppose S and T are sets. The union of S and...

The term algebra comes from the Arabic al-jabr, meaning to combine. Al-Jabr refers to the mathematician's process of combining like terms to solve an equation. Historical references to algebra date back to Greek history, spanning the years...

The Arab astronomer Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was the author of about a half dozen astronomical works, including a book entitled Al-jabr w'al muqabala (written in 830 AD) that gave the name al-jabr to the branch of mathemat...

Alternating series—an infinite series whose terms alternate sign, i.e. whose terms are alternately positive and negative. Examples are the series 1 - 1 + 1 - 1 + 1 ... and the series 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... , which is c...

Two numbers are said to be amicable (i.e., friendly) if each one of them is equal to the sum of the proper divisors of the others, i.e., whole numbers less than the given numbers that divide the given number with no remainder. For example,...

The Greek philosopher Anaxagoras (ca. 500-ca. 428 BC) was the first to formulate a molecular theory of matter and to regard the physical universe as subject to the rule of rationality or reason. Anaxagoras was born on the Ionian coast of A...

In 1993 Princeton University professor Andrew J. Wiles (born 1953) announced that he had solved one of the most legendary challenges in mathematics. Fermat's Last Theorem was an elegantly simple problem in need of a proof, and it had confo...

Born into an upper class family in Ryazan, Russia, Markov suffered from poor health throughout his childhood, but he exhibited keen intelligence and had a talent for mathematics that attracted the attention of his high school teachers. He ...

Louis François Antoine Arbogast made a threefold contribution to mathematics. He is primarily known as a mathematics historian who organized Marin Mersenne's papers, as well as letters and miscellany of other scientists. Arbogast wa...

Computers not only operate on principles of mathematics, but are very useful in the often complex and time-consuming tasks mathematicians and scientists are required to perform. The operations and seemingly limitless abilities of computers...

Ideally, every function would be easy to deal with in all mathematical situations, abstract and applied. Unfortunately, this is not always the case. It sometimes becomes convenient to have an approximation to the function, usually a polyno...

In the third century B.C., Archimedes of Syracuse created a special spiral-shaped curve by pulling the legs of a compass apart while turning it. By performing both actions at a steady rate, he found that the resulting spiral moved outward ...

Archytas of Tarentumwas a Greek mathematician of the Pythagorean school who formulated the harmonic mean and was the first to integrate mathematics and mechanics. He also developed an ingenious geometric solution for the ancient Greek prob...