Mathematics: Master puzzler

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David Singmaster delights in the autobiography of Martin Gardner, whose Scientific American maths column enchanted tens of thousands.

Undiluted Hocus-Pocus: The Autobiography of Martin Gardner

Martin Gardner (with Persi Diaconis and James Randi) Princeton University Press: 2013. ISBN: 9780691159911

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For half a century, Martin Gardner (1914–2010) was an international scientific treasure. As the author of Scientific American's Mathematical Games column for 25 years, he introduced many thousands to the pleasures of mathematics. He enchanted tens of thousands more with more than 100 books spanning everything from pseudoscience and magic to Alice's Adventures in Wonderland. To anyone who knows Gardner's work, his self-proclaimed “rambling autobiography” — the posthumously published Undiluted Hocus-Pocus — comes as a delightful surprise.

Gardner reveals the roots of his unusual mix of expertise in his childhood in Tulsa, Oklahoma. His father — a freelance oil prospector with a background in geology — taught Gardner basic science such as why the Moon has phases, provided him with a small laboratory and taught him some magic tricks. Gardner learned to read by looking over his mother's shoulder as she read aloud L. Frank Baum's children's classic The Wonderful Wizard of Oz (1900). He subscribed to Science and Invention magazine and Amazing Stories, the first science-fiction magazine, launched in 1926. He performed his first magic trick at the age of eight, later following the famous US Tarbell Course in Magic.


Martin Gardner, pictured in 1995.

Gardner hated high school, except for mathematics and physics, noting that the “important history ... was the history of science”. Here, he writes, he penned “lots of mediocre poetry” and invented 'cherchez la femme', a flexagon-type puzzle — flat paper models folded different ways to reveal various images. In 1934, when Gardner was just 20, Hobbies magazine published his article on collecting mechanical puzzles — the first of its kind.

He had wanted to study physics, but instead read philosophy at the University of Chicago in Illinois. Its new president, Robert Hutchins, fomented an educational revolution by appointing Mortimer Adler to a chair in philosophy without consulting members of the department, most of whom resigned. Hutchins and Adler went on to promote the Great Books scheme — a curriculum focused on texts by scientific and literary luminaries from Archimedes to Virginia Woolf — and a highly flexible undergraduate programme. Gardner enjoyed the ferment as philosophers came and went, and recalls seeing Enrico Fermi cycling to the university's Stagg Field, where the great physicist was making the first atomic pile (an early reactor) in an underground squash court.

Gardner's complex of interests began to bear fruit in the 1950s, as he cut his writing teeth on journalism. He moved to New York to edit the quality children's monthly Humpty Dumpty for eight years. He published articles on maths and magic for Scripta Mathematica; these were gathered together for his first recreational mathematics book, Mathematics, Magic and Mystery, in 1956.

That same year, Gardner was shown a hexahexaflexagon, a puzzle made by folding a length of paper into a hexagonal Möbius strip; it was the work of four students at Princeton University (one of whom was Richard Feynman). Gardner thought Scientific American might like an article on it and the piece kick-started his much-loved column. In it, Gardner introduced or popularized a vast range of ideas, including polyominoes (the shapes formed by joining squares edge-to-edge); the Soma cube; the superellipse; M. C. Escher's iconic images, such as the Endless Staircase; Roger Penrose's tilings; and trapdoor ciphers and public-key cryptography, the basis of all financial transactions on the Internet. These pieces were eventually collected into 15 books.

Magic gripped Gardner throughout his life, and he may have written more on it than on mathematics. I feel that his years spent writing for children may partly account for the exceptional clarity and directness of his writing for adults. He became a leading expert on Lewis Carroll, with his Annotated Alice (Bramhall House, 1960) selling more than a million copies and explaining the mathematical, logical and literary associations in the book.

He also became a specialist on Baum, the prolific British writer G. K. Chesterton, and some minor poets. Gardner produced so much, on so many subjects, that it was rumoured that his name was the pseudonym of a writers' collective, such as the French mathematicians who published as Nicolas Bourbaki.

Debunking pseudoscience

Gardner received an immense amount of correspondence and apparently replied to all of it. Many students, encouraged by his friendly and prompt replies, became mathematicians.

Among scientists, Gardner is best known for his writing debunking pseudoscience. This began with 'The Hermit Scientist' in The Antioch Review of winter 1950–1951. In this, he described ideas such as psychiatrist Immanuel Velikovsky's catastrophist theories about ancient history as examples of pseudosciences created by persons working alone.

He expanded these ideas in books such as Fads and Fallacies in the Name of Science (Dover Publications, 1957) and Science: Good, Bad and Bogus (Prometheus, 1981). In 1976, Gardner helped to found the Committee for Scientific Investigation of Claims of the Paranormal (now the Committee for Skeptical Inquiry), which believes that it is “the duty of scientists to debunk bad science”. Amen.

Gardner's passion for writing and his warmth and humour shine forth on every page of this book, making it a memoir of a great human being — a 'rational man', as Isaac Asimov had it. Almost all of Gardner's books are still in print. They stand as a remarkable testament to the independent scientific life.

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