218 Gardner, Martin

probability, player Rcan be guaranteed an expected

profit of , regardless of what

player Cdoes. Similarly, following a mixed strategy,

player Cshould select column 1 with probability 5/9 so

as to minimize her expected loss.

In 1928 von Neumann proved the famous “mini-

max theorem”:

If each player adopts her best mixed strategy

in a zero-sum two-person game, then one

player’s expected gain will equal the other’s

expected loss.

The shared expected outcome of such a game is called

the “value” of the game.

Games that are not zero-sum games are called vari-

able-sum games. The

PRISONER

’

S DILEMMA

and

CHIC

-

KEN

are examples of such partial-conflict games. In

them, one searches for dominant strategies, hoping to

encounter an equilibrium for the game.

In recent decades the theory of games has success-

fully been extended to n-person variable-sum games

and to games with a continuous range of possible

actions and strategies. Game theory is now a standard

course offered in university economics departments.

See also

FAIR DIVISION

.

Gardner, Martin (1914– ) American Recreational

mathematics Born on October 21, 1914, in Tulsa,

Oklahoma, freelance writer Martin Gardner is regarded

today as solely responsible for cultivating and nurturing

interest in 20th-century recreational mathematics. With

numerous articles and more than 65 books to his credit,

Gardner has achieved worldwide fame as a writer who

can make the complex issues of science and mathemat-

ics accessible and meaningful to the general audience.

Although not a mathematician, Gardner is often cred-

ited with having done more to promote and prompt the

general pursuit of mathematics than any scholar in the

field.

Gardner graduated from the University of Chicago

with a bachelor’s degree in philosophy in 1936. After

serving in the U.S. Navy for four years, Gardner

returned to Chicago and began a career as a freelance

writer, at first editing and writing short works of fiction.

In 1958 Gardner accepted the position of mathematical-

games columnist for Scientific American, despite never

having taken a mathematics course in college. His first

piece explaining the mathematics of a Soma cube, a

cube dissection puzzle named after a fictitious addictive

drug, illustrated his natural ability to discuss and clarify

complex issues with ease. This initial piece garnered him

national attention, and Gardner remained a columnist

for the publication for 25 years. His articles were

extremely influential and have since been collected and

republished (multiple times) as books.

Well-versed in the practices of illusion and magic,

Gardner has also published works on magic, the math-

ematics of magic, as well as texts that discuss, and

debunk, the claims and practices of pseudoscience. He

has written two novels, The Flight of Peter Fromm

(1994) and Visitors from Oz (1998), and some works

on the topics of philosophy and literature. His best-sell-

ing work is The Annotated Alice—Alice’s Adventures

in Wonderland and through the Looking Glass (1965).

Gardner currently lives in Hendersonville, North

Carolina, and continues his work as a freelance writer.

Despite a lack of formal training in mathematics, Gard-

ner has made some original mathematical discoveries,

of a recreational flavor, that have been published in

scholarly periodicals.

Gauss, Carl Friedrich (1777–1855) German Num-

ber theory, Geometry, Algebra, Analysis, Statistics,

Physics, Astronomy Born on April 30, 1777, in

Brunswick, Duchy of Brunswick (now Germany), Carl

Friedrich Gauss is recognized today as the greatest pure

mathematician and physicist of his time. His contribu-

tions to both fields were enormous. At the age of 18,

he invented the

LEAST SQUARES METHOD

and made the

new discovery that a 17-sided regular polygon can be

constructed with straightedge and compass alone, sig-

naling that he had accomplished great advances in the

theory of

CONSTRUCTIBLE

numbers. In 1801 he pub-

lished his masterpiece Disquisitiones arithmeticae

(Arithmetical investigations) in which he proved the

FUNDAMENTAL THEOREM OF ARITHMETIC

, the

FUNDA

-

MENTAL THEOREM OF ALGEBRA

, and introduced the

theory of

MODULAR ARITHMETIC

. In later work, he pro-

posed general solutions to the problem of determining

planetary motion, developed theories of statistics that

led to the discovery of the Gaussian

DISTRIBUTION

, and

studied potential theory and electricity and magnetism