Martin Gardner stands by every word he ever wrote: the six shelves consist
entirely of his own publications, dating back to 1931.
Winning Ways (Academic Press, 1982), by Elwyn R. Berlekamp, John
H. Conway & Richard K. Guy, is dedicated to "Martin Gardner, who has
brought more mathematics to more millions than anyone else." It's been
half a century since Martin Gardner's magic spell was first cast over the
general public, thanks to two landmark events in the world of publishing:
the appearance of his Mathematics, Magic and Mystery (Dover 1956),
the first book for non-magicians to treat mathematical cards tricks in
depth, and the launching of his long-running monthly "Mathematical Games"
articles in Scientific American. (One could argue that the latter
turned out to be, among other things, the original Card Column!)
This month, for our lucky thirteenth Card Colm, we take a break from
our usual format and celebrate Martin Gardner's ninety-second birthday by
sharing his recent musings on the origins of these classy and influential
Along the way, the conversation turns to the highly eccentric and equally
innovative mid-twentieth century magician and mathematical card trick
inventor Bob Hummer, and the longevity of Gardner's own writing career,
which has seen him publish an average of one book a year, on subjects as
diverse as recreational mathematics, physics, pseudoscience, philosophy,
religion and Alice in Wonderland, for three-quarters of a century.
He also reveals details of some of his current projects—including
completely updating the fifteen books spawned by the Scientific
Remember to keep a deck of cards handy: we wrap up with a recent refinement
of an old spelling routine of his.
An Interview with Martin Gardner
It's 2006, so it's fifty years since Mathematics, Magic and Mystery
appeared. I wondered if we could wind the clock back a little bit and if
you can tell us how that book came about.
When I was living in New York, I use to go to a gathering of mathematicians at
Yeshiva University, and it was a gathering that was run by a fellow named
Jekuthiel Ginsburg who edited Scripta Mathematica, a magazine devoted
to history of mathematics. He found out that I was interested in mathematical
magic and asked me to do a series of articles, for Scripta. So I did a
series of pieces, one on card tricks and one on dice tricks and on miscellaneous
objects and so on, and I put those together and that became a book. That is
how it became about and Dover published it and I was paid a total of $500 for
it. No royalties, but later it got translated into French and German and
fortunately for me and unfortunately for Dover, they forgot to put into the
clause anything about foreign sales. So I got all the royalties on foreign
sales and made far more on the German edition then I did on the English one.
That is how that came about.
It has been in print ever since, hasn't it?
MG: It has been in print ever since, right.
How long did it take to write it then?
MG: Oh, I don't remember. Not so long though.
So the Scripta appearances had appeared over a period of a couple of years?
MG: I think they ran in a single year, in different issues. The magazine came out I think quarterly and I think it is still going. Scripta Mathematica.
You included creations of many famous magicians. Did you know them all personally?
Blink and you might miss it: his famous Wink Change (published January
1971 in the Hierophant, No. 5).
Well, I think I knew most of them. I knew Bob Hummer for example and I included
quite a number of his card tricks. Bob Hummer was certainly the most eccentric
person I ever knew, I can talk for several hours about Bob Hummer stories. He
enjoyed being poor and he was very very poor. I visited him once and he was
staying at some cheap hotel in New
York. He was trying to explain a card trick to me by dealing the cards on the
bed and the bed was crawling with cockroaches, and I remember Hummer just
knocking them off with his hands on the floor and then going back to the card
trick, paying absolutely no attention to them. His father by the way was an
official with the Salvation Army, so I don't know if that had any influence on
him or not. He enjoyed the role of being a very poor magician and he earned
his living doing what they called busking, going to bars and doing magic for tips
and he would take off his hat and pass his hat afterwards. I remember he told me
on one occasion he was performing in a bar and one of the customers in the bar
didn't like magic and when he was passing the hat the customer spit in the hat.
Hummer said he paid no attention to it and he just took the money out of the hat
and put the hat back on his head and walked out (chuckle).
Hummer had a shock of hair that hung down past his forehead and he was a
cigarette smoker and as a gag he would light a cigarette and then he would set
his hair on fire, and then he would tap it out like this (smacks his head with
his hand). He enjoyed very peculiar stunts like that (chuckle). Then another
story about Hummer was he walked into Joe Berg's magic shop one day in Chicago
and he had on ragged clothes—pants and jacket—and he took his jacket
and spread it on the floor and walked across it as he entered the magic shop and
then he picked up the jacket again and put it back on. He was really an eccentric
character. I use to get letters from him that was written on the labels of tin
cans. He would soak off the labels of tin cans like he was too poor to buy paper
or stationery. So he would just use scraps of paper. Sometimes he would fish
paper out of the wastebasket in the post office and then write on the back of them.
How did magicians feel about so many classic principles being exposed to the general public?
MG: They didn't seem to mind (chuckle). I don't even know if they knew
about the book when it first came out. I got some complimentary letters from
some mathematicians and from magicians.
But you had permission from the magicians to include their work?
MG: Yeah. I had permission from them to include their work.
How did the book sell in the early days?
MG: Apparently it sold pretty well. Since I didn't have a royalty
contract, I didn't get a report on it. But it did lead to a friendship of
Haywood Cirker who was head of Dover and I later did quite a number of things
The height exceeds the circumference, right? No! Demonstrating a classic
illusion—the failure to appreciate of the value of π—with a scrap of paper
and a tall skinny glass.
1956 was also the year your first Scientific American column appeared.
Do you think that the book publication played a role in your ability to
convince Scientific American that you could do a monthly column?
MG: I don't think they knew about the book at all.
Dover didn't have the distribution that it has today?
MG: They did have a good distribution, but I don't think Scientific
American knew about the book. I don't recall.
Over the 25 years you wrote for Scientific American, you were the first
to break many mathematical stories, from hexaflexagons to Conway's Game of Life,
Penrose tilings and public key cryptography. Along the way you were also the
first to bring to the public's attention many notably mathematical card
principles, including Alex Elmsley's work on Faro shuffles, Norman Gilbreath's
riffle-shuffle discoveries and Martin Kruskal's last key card principle.
MG: Well I owe a big debt to the mathematicians that contributed the
material to the column. When I first started the column, I was not in touch
with any mathematicians, and then gradually mathematicians who were creative in
the field found out about the column and began corresponding with me. So my
most interesting columns were columns based on material that I got from them,
so I owe them a big debt of gratitude. Solomon Golomb was another mathematician
that contributed a lot of material to my column.
Would you typically meet these people or just correspond?
MG: Mainly corresponded with them. I didn't meet Golomb until many many
years later. I met Ron Rivest [of RSA Cryptography] who read my column
and sent me a letter and said that he would like to come and visit me and talk
about his system. He came out and explained it to me and that is how that column
started. When that column appeared, by the way, I mentioned in the column that
if you wanted wanted more details about this system they could write to Ron
Rivest and he would send a published article on the material. Well the government found out about
that and they clamped down and refused me permission to mail out anything from
Rivest and so it was several years before... I would get a flood of letters from
readers saying that they wrote to Rivest and never got a reply. It was because
the government refused to allow Rivest to send out anything. Later they relented
and allowed him mail out material. But for a while the government was very upset
about that that column because it was giving away some secrets in cryptography
that the enemy could use.
Did you get approached by somebody to tell you not to do...?
MG: Yes. I got calls from the government, and officials from the
government, telling me that I could not mail out anything by Rivest.
You stopped writing a regular Scientific American column in the early
1980s. What brought that about?
MG: Well, I stopped the column because I figured it was time for someone
younger to take it over and it was getting more and more of a burden on me to
write it and also I had all kinds of books that I wanted to write and I just
didn't have time to keep up the column and do the books. So I resigned from the
magazine and Doug Hofstadter took it over.
The fifteen collected Scientific American columns books are now available
from the MAA.
MG: That's right, they are. I was very happy that they did that, and
particularly pleased because they included on the CD a very complete index of
everything in the column and that was a big help to me. I am always getting
letters from readers who want to know where I discussed this and that problem
and it takes me maybe an hour or two to find out what book it is in. Now I
can check it on CD. Or people can check it on the CD themselves.
Never one to sit down on the job: Martin often likes to work standing.
Are there plans to reprint those books with new notes and updates?
MG: There are tentative plans to issue all the books in uniform binding,
and I'm hoping that the deal will go through by the end of the year and if it
does, I will go to work writing additional material for all the books.
It sounds like a big job.
MG: Yes. That is a big job.
So you'll take them one at a time?
MG: Yes. I have already started on the first book.
How long have you been a member of the MAA, a long time?
MG: For a good many years. Actually they made me an honorary member. I get their periodicals free. I am very pleased with that.
If you had continued writing columns for Scientific American for another 25 years, what mathematical development would you have like to have written about?
Oh gosh, I don't know. There's so much been happening in mathematics that I
could write about. It is just hard to pick a topic.
As you heard about things, there must have been a time when you said, "I wish I
could have written about that"?
Yeah. That is true. I don't think any particular topic comes to mind but there
are surely lots of them.
What mathematical magic development has got your attention in the last few decades?
Well, there has been a big explosion of interest in mathematical card tricks, as
you surely know, and also a lot of other tricks coming on the market that are
based on mathematical principles. I can certainly do a sequel to my old
Mathematics, Magic and Mystery, but I will probably never get around to
An ace trick of his own devising.
Well maybe you should (chuckle).
You published your first magic trick 75 years ago.
Oh yeah. How did you find that out? (chuckle)
What is your secret to such a long and successful writing career?
Oh gosh, I don't know. I have always followed Bertrand Russell, somewhere it
says that someone asked him about the secret of his writing style. He said that
whenever he thought of a simpler word to substitute for a more complicated word
he would use the simpler word. That's a piece of advice that I've tried to
follow. Russell's style is something I very much admire by the way, another one
of my heroes.
Looking back on your own education and how you got into journalism, obviously
with the Scientific American career you became very well known. If you
could do it all over again, would you do anything differently?
I don't think so. Starting the column with Scientific American was really
the great break in my literary career. I was not really earning much of a living
until I started that column. I was paid well for the column and then I was paid
again for the books. So I really owe the publisher Gerry Piel a great debt of
gratitude because he was the one that saw the great possibility of the column
and I jumped at the chance. It was a time when the public I think was hungry for
popular writings about mathematics. One of the reasons I think that Gerry Piel
suggested the column was because their book review editor whose name was James
Newman had done a four volume book on mathematics [The World of Mathematics].
That book was a runaway best seller with Simon and Schuster. He was at that
time the book review editor for Scientific American and I think was a
great success of that book that convinced Gerry Piel that there was a huge
market out there for popular writing about mathematics. Now I miss doing that
Colm, that was a great great time. I met a lot of good mathematicians (chuckle).
You have written over 70 books. What are you planning to write next?
Well I am working on two book projects right at the moment. One is a collection
of essays about the fiction of Gilbert (G.K.) Chesterton who is one of my heroes.
The other is a collection of linguistics play, and word play, that would be based
on half on columns I written about word play and half on new material that I will
be putting in the book and I am also working on that periodically. When I
finish the Chesterton book I will turn to the word play book.
And if the Scientific American revision books...
Oh that will take up all my time if that deal goes through. I will have to stop
working on everything but that.
(Interview conducted March 2006, in Norman, Oklahoma. October 2006 update:
Both the Chesterton and word play books have been completed; the latter will be
put out by Sterling Press. In addition, the MAA and Cambridge University Press
will jointly publish the fifteen revised Scientific American column books,
which Martin is already busy updating.)
A Pyramid Scheme That Works
Wouldn't it be nice to have the thirteen cards of your favourite suit arranged
in a packet, face down, in such an order that when you spelled out their names,
starting with the Ace, moving a card from top to bottom for each letter, the last
card so moved each time—which is then set aside—turns out to be the
card whose name was just spelled? It's not too hard to reverse engineer this,
figure out the desired order of the cards at the outset, and then assemble the
packet by brute force so as to be able to pull this off.
Even nicer would be a "natural" way to get the packet in the required order,
which could be done under your audience's nose without arousing suspicion. We
present such a method here, recently sent by Martin Gardner, using just ten
cards: Ace, 2, ..., 8, 9 and King, with the last listed representing Zero.
Monarchists should feel free to use a Joker instead of the King.
(Readers are invited to email
solutions using the usual thirteen cards and values.)
First, the punchline: the cards need to be in the order 7, 4, 8, King, 6,
3, Ace, 9, 5, 2 from the top.
Assume for now that this is the case, all cards being
face-down. Explain that you are going to count from zero to nine, and that the
King is zero.
Spell out "Zero" and move three cards one by one from top to bottom for the
first three letters. The next card on the top, corresponding to the letter "O",
is the King. Turn it over for all to see as you say "0" and set it aside. Now
spell out "Ace" and move two cards one by one from top to bottom for the first
two letters. The next card on the top, corresponding to the letter "E", is the
Ace. Turn it over for all to see as you say "E" and set on top of the face-up
King. Continuing, you can spell "Two, "Three" and so on, down to "Eight", with
the desired card always turning up as its spelling is completed. When you have
just one card left, waive it around comically three times to simulate movement
from top to bottom of the now depleted packet, as you spell out "N, I, N," and
then triumphantly turn it over, saying, "And E makes Nine. Zero to Nine, in
order. The basis of the decimal system as we know it. Actually, it's much
easier to do in binary! Thank you!"
We now move on to methods for getting cards in the correct order.
To start with, arrange the Ace, 2, ..., 8, 9 and King in a pyramid as follows,
leaving lots of space between the cards to facilitate sliding during the pickup.
To get the cards in order 7, 4, 8, King, 6, 3, Ace, 9, 5, 2, Martin Gardner
suggests picking up the cards along the "backslash" diagonals, from upper left
to lower right, and carefully assembling into a single packet. The sneaky part
is how the diagonals are slid together.
Here's one way to do it:
Pick up the 7 with the right hand and place it face-up in the left hand.
Use the right hand to slide the 4 under the 8, putting this pair on top
of the 7 in the left hand.
Use the right hand to slide the 2 over the 5 and slide those two
cards over the 9. Retain this packet in the right hand.
Drop the 2, 5, 9 packet on top of the Ace, and slide these over the 3, 6
and King in turn, to form a seven-card packet in the right hand.
Drop those seven cards as a unit on top of the three in the left hand.
Turn the fully assembled ten-card packet over.
Pick up the 7 and drop it on top of the 4, then pick up both cards and
drop them on top of the 8.
Pick up those three cards and drop on top of the 2, then drop that pile on
top of the 5, then drop that pile of top of the 9.
Pick up that six-card packet and use it to gather up the last diagonal,
as above, starting by dropping it on the Ace, then on the 3, 6, and finally
on the King.
Pick up up the resulting face up ten-card packet, and run off the top
three cards into the other hand casually, thereby reversing their order.
Drop the rest on top, and turn the packet face down.
Yet another possibility is to do this in reverse by picking up the four diagonals
in question in the other order, starting with the longest one and working back to the
lonesome 7, this time collecting the cards from lower right to upper left each
time. The result is the face-up packet King, 6, 3, Ace, 9, 5, 2, 8, 4, 7. Now
run off seven cards from the face, reversing their order, and tuck the remaining
three cards behind those. Finally, turn the packet over.
Once the cards are in the order 7, 4, 8, King, 6, 3, Ace, 9, 5, 2, however you
achieve this, you can then muddy the waters with various false shuffles, e.g.,
try the "quad run" false shuffle implicit in the first
Card Colm (see
Colm's Cards for details).
This allows you to try out some patter along the lines of "From order, we get
chaos," as you shuffle with no apparent purpose, followed a little later by,
"Now let's see if we can get back to order," as you start to spell.
This charming curiosity is the basis of an effect called "The Pyramid Spell"
which Martin published in an arcane publication put out in 1995 by Jeff Busby
(Arcane, No. 14). Its ingenious construction is guaranteed to cast a
real magical spell over the audience.
The original spelling principle can be found in Chapter 13 of Mathematical
Carnival (Alfred A. Knopf, 1975), which is on the
Scientific American books CD-ROM.
There, Martin records that it was Mrs. Myron Milbouer, of Wilmington, Delaware,
who noted the connection between the sequence 7, 4, 8, 0, 6, 3, 1, 9, 5, 2,
and the number pyramid shown above in card form.
How convenient it would be if there were an easy way to remember that sequence.
Ordered card mnemonic/device for a wonderful spell (an).
Since 1988, Colm Mulcahy
has been in the department of mathematics at Spelman College, where a recent
project of his was the creation and launching of the new
BIO SIGMAA webpage. He
can't help wondering if Martin Gardner's ninety second birthday was the
shortest one he's had for a decade. For more on mathematical card tricks,