American Author 1914–
One of the most well-known creators of mathematical puzzles is Martin Gardner. From 1957 to 1982, he wrote a column for Scientific American called "Mathematical Recreations." He presented intriguing problems, discussed the mathematics of various games, and demonstrated recreational aspects of mathematical discoveries. He always aimed to entertain and stimulate his readers, which ranged from high school students to college professors.
Born in 1914 in Tulsa, Oklahoma, Martin Gardner became fascinated with mathematics in high school when he took Pauline Baker's geometry course. She communicated a love for the subject that he readily absorbed. Gardner also had other academic interests. He graduated from the University of Chicago in 1936, with a major in philosophy, and did graduate work in the philosophy of science.
Most of Gardner's early writing had little to do with philosophy or mathematics. Before World War II, he worked as a reporter for the Tulsa Tribune. After serving in the U.S. Navy, he supported himself as a freelance writer, working for eight years as a contributing editor to Humpty Dumpty's Magazine. This ended in 1957 when, drawing on his interest in magic, he sold his first article to Scientific American.
Fascinated when a magician showed him a paper toy called a hexaflexagon, Gardner contacted the inventor, John Tukey, a mathematician at Princeton, and with Tukey's permission and help, he wrote an article about hexaflexagons and the mathematics behind them. Delighted, the Scientific American editors published it and asked for more. Martin Gardner scoured New York City for old books on recreational mathematics and found enough material to get the column going. Shortly thereafter, he began to draw material from recreational mathematics journals.
Gardner had a gift for simplifying ideas and communicating them wittily in a warm, playful spirit. His writing was so well received that mathematicians whose work had recreational aspects—Solomon Golomb, John Conway, Roger Penrose, and Frank Harary, among others—shared their discoveries with him. Through these contacts his columns became more sophisticated, and he enabled mathematicians to present their work to a much larger audience.
Central to his work was the belief that mathematics, whether formal or recreational, is enormously interesting and of vital importance to humankind. Mathematics is the solving of puzzles. Good puzzles, even if they appear to be of trivial importance, open the door to all sorts of useful interconnections, often leading to "better and better answers to puzzles posed by nature."
One of his most popular columns was on John Conway's Game of Life, a population simulation game. A few counters are placed on a large checkerboard. Counters are born or die according to these rules:
- a counter survives to the next round if it has two or three neighboring counters;
- a counter dies if it has four or more neighbors or one or zero neighbors; and
- each empty cell with exactly three neighbors will give birth to a new counter in the next round.
The game is fascinating because of the great variety of population behaviors that arise from different beginning arrangements of counters.
Another favorite article was on a method of encoding messages called trapdoor functions, which are functions whose inverses—the key to decoding the message—are computationally impossible to discover in thousands of years. Martin Gardner's article was the first to discuss the work of Ron Rivest, who combined trapdoor functions with prime number factorization, creating coding systems that could be used in the electronic transmission of information over the Internet.
The Works of Martin Gardner
Over the years Martin Gardner published challenging problems in his columns, the answers of which can be found in the books listed here:
Aha! Gotcha: Paradoxes to Puzzle and Delight.
Fractal Music, Hypercards, and More: Mathematical Recreations from Scientific American Magazine.
Hexaflexagons & Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games.
The Incredible Dr. Matrix.
Knotted Doughnuts and Other Mathematical Entertainments.
Mathematical Magic Show.
Mathematics, Magic, and Mystery.
My Best Mathematical and Logic Puzzles.
New Mathematical Diversions from Scientific American.
The Numerology of Dr. Matrix.
Penrose Tiles and Trapdoor Ciphers.
Riddles of the Sphinx and Other Mathematical Puzzle Tales.
The 2nd Scientific American Book of Mathematical Puzzles and Diversions.
Sixth Book of Mathematical Diversions from Scientific American.
Time Travel and Other Mathematical Bewilderments.
The Unexpected Hanging and Other Mathematical Diversions.
The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays.
Wheels, Life, and Other Mathematical Amusements.
The math puzzles Gardner presented to the public were enjoyed by people of all ages, and offered a variety of problems for readers to solve. Some examples include:
A boy and a girl were talking. "I'm a boy," said the one with black hair. "I'm a girl," said the one with red hair. If at least one of them is lying, who has black hair? [From Wheels, Life, and Other Mathematical Amusements, 1983]
A cylindrical hole six inches long is drilled right through the center of a solid sphere as shown below. Determine the volume remaining in the sphere. [From Hexaflexagons & Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games, 1988]
Dissect an isosceles triangle ABC with a 120° angle into five triangles similar to ABC. [From Wheels, Life, and Other Mathematical Amusements, 1983]
A worm is at the end of a 1 kilometer rubber rope. It crawls forward for one second, covering 1 centimeter and then the length of the rope is increased by 1 kilometer. This process is continued indefinitely. When the rope is stretched it is pulled from both ends. Show that the worm can reach the end of the rope. [From Time Travel and Other Mathematical Bewilderments, 1988]
Consider the figure below. As you drink a soda, the center of gravity C drops, but when the can is empty, the center of gravity has risen back to its starting point. Assuming that the can is 8 inches high, weighs 1.5 ounces empty and 13.5 ounces full, determine the lowest point reached by the center of gravity C. [From Wheels, Life, and Other Mathematical Amusements, 1983]
The game of Sim: put six dots on a paper, forming the vertices of a regular hexagon. Each player in turn connects two of the dots; one player uses a blue color, the other a red color. The first player forced to form a triangle of his own color loses. What is the best strategy? [From Knotted Doughnuts and Other Mathematical Entertainments, 1987]
A paradox: a man who always keeps his promises tells his wife that "tomorrow for your birthday I will give you an unexpected gift. You have no way of guessing what it is. It is the gold bracelet we saw at the jewelry store." Will his wife be surprised or not? [From The Unexpected Hanging and Other Mathematical Diversions, 1991]
Gardner also created the mysterious Dr. Matrix as a foil for playing with numerology. Here, for example, is Dr. Matrix's proof that William Shakespeare helped translate the King James Bible: In Psalm 46, the 46th word from the beginning is SHAKE and the 46th word from the end is SPEAR. Furthermore, the King James Version was completed in 1610 when Shakespeare was 46 years old.
see also Puzzles, Number.
Frazier, Kendrick. "A Mind at Play: An Interview with Martin Gardner." Skeptical Inquirer 22, no. 2 (1998): 34.
Notes on Martin Gardner. The Recreational Math Pages. <http://www.citlink.net/citlink/d/dmn1/gardner.htm>.
Gardner, Martin (1924-)
Gardner, Martin (1924-)
Journalist and writer, born in Tulsa, Oklahoma, on October 21, 1914. Gardner graduated from the University of Chicago (B.A., 1936). His first job was as a reporter for the Tulsa Tribune. In the 1950s he moved to New York and in 1957 became associated with Scientific American, for which he has written a column on mathematical games for many years.
In 1952 Gardner wrote what has become the most famous and enduring of his many books, In the Name of Science (reprinted in 1957 as Fads and Fallacies in the Name of Science ), a skeptical book dealing with numerous scientific deadends, hoaxes, and religious groups that made scientific claims to support their beliefs. The volume has become a classic of debunking literature relative to the occult.
Gardner continued to turn out books, primarily on mathematics, over the years. Periodically he gathered his columns into what has turned into a series of books on mathematical games. In the 1980s he returned to the debunking role and turned out three new volumes: Science: Good, Bad, and Bogus (1981), The New Age: Notes of a Fringe-Watcher (1988), and How Not to Test a Psychic: Ten Years of Remarkable Experiments with Renowned Psychic Pavel Stepanek (1989). In this debunking role he has identified with the Committee for the Scientific Investigation of Claims of the Paranormal, of which he was an original member.
Gardner, Martin. How Not to Test a Psychic: Ten Years of Remarkable Experiments with Renowned Psychic Pavel Stepanek. Buffalo, N.Y.: Prometheus Books, 1989.
——. New Age Notes of a Fringe Watcher. Buffalo, N.Y.: Prometheus Books, 1988.
——. Science, God, Bad, and Bogus. Buffalo, N.Y.: Prometheus Books, 1981.