What do L. Ron Hubbard, H.G. Wells, G.K. Chesterton, Lord Dunsany, Alice in Wonderland, M.C. Escher, John H. Conway, Roger Penrose and Oprah Winfrey have in common? The same thing as Isaac Asimov, Vladimir Nabokov, and Salvador Dali. And the vase illusion shown, which was designed by Atlanta-based magician and illusion artist Victoria Skye.
They're all connected in meaningful ways to Martin Gardner, the best friend mathematics ever had. His wonderful posthumous memoirs Undiluted Hocus-Pocus: The Autobiography of Martin Gardner (Princeton University Press) just appeared. Gardner had a long and productive publishing career, spanned 80 years (from 1930 to 2010) and spawning over 100 books. As Stanford statistician and magician Persi Diaconis says in the foreword to those memoirs, "Pick up anything he wrote. You'll smile and learn something." It's Gardner's profile that frames the vase image above. He continues to have a profile on Twitter today, as followers of @WWMGT (What Would Martin Gardner Tweet?) can attest.
Gardner was particularly well-known for posing puzzles in the recreational mathematics realm. Here's one of his which I first encountered in my teenaged years: the configuration of pennies on the left below is to be transformed into one on the right with the fewest number of moves, where "each move consists in sliding a penny [flat on the surface], without disturbing any of the other pennies, to a new position in which it touches two others." How many moves are required?
I was very fortunate get to know Martin in the last decade of his life, and he was a delightful, generous and modest man, who often had a mischievous gleam in his eye, and always displayed an insatiable curiosity about the universe. He could sit for hours chatting about philosophy, magic, physics, poetry, and the meaning of life. Gardner was not, as many have assumed, an atheist, though he had a low opinion of organized religion in any form. He considered himself to be a mysterian. He wasn't much impressed with his own fame either, preferring to remain in the shadows and keep on reading and writing about the things that fascinated him, right up to the end.
Thanks to Martin, and the highly influential monthly "Mathematical Games" column he wrote for Scientific American for a quarter of a century, many people were turned on to fun and sometimes esoteric topics which often had deep ramifications, such as origami, Conway's Game of Life, fractals, RSA cryptography and Penrose tiles. It's been said that he had a million readers there at his peak.
The first list above is of people who really got Gardner's attention over the decades, and inspired him to write passionately and eloquently about some aspect of them. First and foremost Gardner was a debunker of bad and fake science. His book Fads and Fallacies in the Name of Science from the early 1950s became the bible for skepticism, and lead to his key role in the founding of what's now The Committee for Skeptical Inquiry. L. Ron Hubbard's dianetics was just one of many fads he demolished there, over six decades ago. The last thing he published in his lifetime was an article called "Oprah Winfrey: Bright (but Gullible) Billionaire" in the spring of 2000.
The second list reflects just a fraction of the influence that Gardner had on the rest of the world, some of which is discussed in his new memoirs. Dali sought him out in NYC in the 1970s, being a huge fan of the "Mathematical Games" column. The surrealist artist was intrigued by Martin's writings on the 4-dimensional cube, or tesseract---which had been a prominent feature of his own 1954 painting Crucifixion (Corpus Hypercubus)---and the first time they met for lunch, Dali had with him a copy of Gardner's book The Ambidextrous Universe (1964).
Gardner's close friend Asimov started writing annotated versions of his favorite books modeled after the former's best seller, The Annotated Alice (1960). Here's Martin with the Mad Hatter sculpture in Central Park, New York, from this period (photo by George Cserna).
M.C. Escher was an early fan of the Alice tome, and after some correspondence between the two men, Gardner's piece on the then-unknown Dutch artist's amazing work led to his memorable flying birds image gracing the cover of Scientific American in 1961. (With hindsight, that fit right in with the more liberated mindset of the 1960s that was about to arrive.)
Then there's NPR's Car Talk. The Tappit brothers were big Gardner fans too, and often used (uncredited) some of the brainteasers he helped to popularize as their show-opening "puzzlers". Martin even made it (by name) onto their 2CD 25th Anniversary set. (The bothers may have felt bad about having mistakenly announced on the radio in the 1990s that Martin had died; that saga is revisited on the June 5, 2010 Car Talk podcast.)
Every October sees thousands of people all over the planet celebrate Gardner's astonishing legacy via do-it-yourself Celebration of Mind events to honor his birthday (October 21st this year would have been his 99th). There are terrific resources available for lovers of illusions, magic, hexaflexagons, mobius strips and more, who want to organize their own event, big or small. (Put please register at that site so that there's a good record of how many events are held!)
Given that Gardner wrote 300 columns for Scientific American, there's no shortage of great brainteasers either. In addition to the sliding pennies one already mentioned above, there's the old classic about the Monkey and the Coconuts; or the conundrum of the cork plug that fits round, square and triangular holes. I remember reading those three gems in my first Gardner book, purchased during my first year at university in Ireland. My copy of that paperback survived long enough for Martin to sign it for me, and it has a graphic cover which also made a big impression: it shows how to slice a doughnut into 13 pieces with just 3 straight cuts:
On one of my last visits to see Martin, in a retirement community in Norman, Oklahoma, he predictably drank a can of Dr. Pepper mid-afternoon. I waited until it was 3/4 gone, and he'd wandered away, then easily balanced the can on its edge as Spanish magician Fernando Blasco had shown me how do to.
When Martin turned back and spotted what I'd done, he was thrilled: it was a stunt he hadn't seen before. As was typical in such situations, he quickly made notes so that he could include it in a future book, perhaps one of the many he wrote for children. As his memoirs reveal, he was a young child himself when he discovered a love that was to last a lifetime: magic. Over the decades, he became particularly enamored with mathematical card tricks, about which he wrote extensively.
We leave you with a question in the Gardner spirit. Which of the triangles below is larger? The first has sides 5, 5, 6, the second, 5, 5, 8.
In our experience, knowing too much mathematics can get in the way of nailing this one! Let's just say that the solution hinges on a simple observation.
"Card Colm" Mulcahy is professor of mathematics at Spelman College, Atlanta, GA, currently visiting American University, in Washington, D.C. He's author of "Mathematical Card Tricks" (AK Peters/CRC Press) and is on Twitter at @CardColm.