- “A Contribution to the Mathematical Theory of Big Game Hunting”, Pétard 1938
- “A New Method of Catching a Lion”, Good 1965
- “On a Theorem of H. Pétard”, Roselius 1967
- “Some Modern Mathematical Methods in the Theory of Lion Hunting”, Morphy 1968
- “Further Techniques in the Theory of Big Game Hunting”, Dudley et al 1968
- “15 New Ways To Catch A Lion”, Barrington 19761
- “Lion-Hunting with Logic”, Euler 1985
- “Hogyan fogjunk oroszlánt? [How to catch a lion?]” (HU), Géza 19992
- “Big Game Hunting for Graduate Students in Mathematics”, Athreya & Khare 2009
- “COM3200: Programming Language Semantics: Chapter 5. Induction Techniques. 5.5. Backward Induction and Pétard’s BGH Theorem”, Birtwistle 2009
Catching Lions With Mathematics
In Princeton I usually had dinner with a group of (mostly) mathematicians. One of the things we talked about was mathematical methods for catching lions. There were many jokes in this vein circulating at Princeton at that time. Below are a few examples:
- The method of inversive geometry. We place a spherical cage in the desert, enter it, and lock it. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside.
- The Peano method. Construct by standard methods a continuous curve passing through every point of the desert. It has been remarked [by Hilbert] that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion can move his own length.
- A topological method. We observe that a lion has the connectivity of the torus. We transport the desert into 4-space. It is then possible to carry out such a deformation that the lion can be returned to 3-space in a knotted condition. He is then helpless.
Frank Smithies (who was visiting from Cambridge, England) and I undertook to write an article about this interesting field, inventing a few extra methods as we went along. We picked Pondicherry (one of the French enclaves in India) as a pseudonym, spelling it Pondiczery to make it look Slavic; we thought of Pondiczery as being Poldavian like Bourbaki3. We submitted our article to the American Mathematical Monthly with a cover letter saying that the author, afraid of repercussions, wanted to use the pen name H. Pétard. In an endeavor to establish a reputation for Pondiczery, we imitated Bourbaki by publishing short notes under his name. Later, when I was teaching at the Pre-Flight School during World War II and wasn’t supposed to publish anything, Pondiczery wrote a substantial number of reviews for Mathematical Reviews.
At Smithies’s suggestion I spent the second year of my fellowship in Cambridge, England, to which he was returning. The fellowship was not supposed to allow foreign travel, but I persuaded the authorities to let me go if I paid my own way, which I could do because I had saved enough from my $15,189$16001948 stipend. In Cambridge I learned quite a lot about England and quite a lot of mathematics. I attended lectures by Hardy, Littlewood, and Besicovitch and also Hardy and Littlewood’s conversation class (American: seminar), which met in Littlewood’s rooms but always without Littlewood.
…Reminiscences of Ralph Boas, Frank Smithies:
At some time that winter we were told about the mathematical methods for lion-hunting that had been devised in Göttingen, and several of us came up with new ones; who invented which method is now lost to memory. Ralph and I decided to write up all the methods known to us, with a view to publication, conforming as Closely as we could to the usual style of a mathematical paper. We chose H. Pétard as a pseudonym (“the engineer, hoist with his own petard”; Hamlet, Act III, Scene IV), and sent the paper to the American Mathematical Monthly, over the signature of E. S. Pondiczery (we liked the name, and confused matters by spelling it as if it were Polish), who explained that he would prefer to publish the paper pseudonymously. Pondiczery’s existence was established by the publication of a short note in the May 1938 number of the Monthly, and his name has since appeared in various periodicals; the most recent occurrence that I know of was in the Mathematical Intelligencer, 4, p. 2 (1982). The lion-hunting paper was duly accepted for publication, with one editorial alteration: our footnote to a footnote was ruthlessly removed.4 The paper succeeded beyond our wildest dreams; we gathered afterwards, for instance, that Steinhaus read a translation of it to the mathematical seminar in Lwów: and it has been reprinted in other places.
…Ralph’s family (his parents and his sister Marie, later Marie Boas Hall and well known as a historian of science) spent some time in London in the spring of 1939, and we all met there on several occasions. In the Easter vacation Ralph visited my native city of Edinburgh for a few days, and I was able to show him some of the local sights.
The climax of that academic year, as far as we were concerned, came in the Easter term. André Weil, Claude Chabauty, and Louis Bouckaert (from Louvain) were all in Cambridge, and the proposal was mooted that a marriage should be arranged between Bourbaki’s daughter Betti and Hector Pétard; the marriage announcement was duly printed in the canonical French style—on it Pétard was described as the ward of Ersatz Stanislas Pondiczery—and it was circulated to the friends of both parties. A couple of weeks later the Weils, Louis Bouckaert, Max Krook (a South African astrophysicist), Ralph, and myself made a river excursion to Grantchester by punt and canoe to have tea at the Red Lion; there is a photograph (of which I still have a copy) of Ralph and myself, with our triumphantly captured lion between us, and André Weil looking benevolently on: from the same occasion derives a picture of Weil looking coyly over the top of some of the first proof-sheets of Bourbaki.
…Section 1: Lion Hunting
As explained in the reminiscence of Frank Smithies earlier and in the autobiographical essay by Boas himself, the collection of methods for catching a lion that they published under the pseudonym, H. Pétard, appeared in the American Mathematical Monthly in 1938. As is evident from the other articles in this section, the idea prompted a good many others to add to this literature. We include those articles of which we are aware—we make no claim that this is a complete compendium of contributions to this area of mathematics.
“John W. Tukey: His Life and Professional Contributions”, Brillinger 2002:
One graduate school entertainment was a collection of mathematical methods for catching lions! L. Spitzer [Dreams, Stars, and Electrons: Selected Writings of Lyman Spitzer, Jr, 1997] writes:
In 1935–1936, when I was a first-year graduate student at St John’s College, Cambridge, the light banter among us included how to catch a lion in the desert; we delighted in devising ingenious methods, preferably based on more recondite scientific laws or theorems. As I remember, some of the mathematics and physics faculty joined this challenging sport, using the most up-to-date principles.
During my 2 graduate-student years at Princeton, 1936–1938, this question of how we might capture our lion continued to intrigue us. Among those who joined the fun were mathematicians Ralph Boas and Frank Smithies, both in mathematics, and John Tukey in statistics. If I recall correctly, it was John Tukey, with active expertise in many of the physical sciences, who pushed for a publishable paper, presenting a few of the more interesting techniques that we had encountered or concocted for this problem. There was some discussion among us—who should be listed as authors of this spoof, and which of us would actually submit the paper for publication?
In the end, the article was sent off to the American Mathematical Monthly, together with a letter signed by one E. S. Pondicherry (of the Royal Institute of Poldavia), the name proposed by John as a cover for our group. This letter explained the author’s desire to publish his pioneering but possibly controversial work under a pen name, and proposed H. Pétard as a suitable pseudonym. I suppose it is seldom that a nonexistent individual has published in a serious professional journal under a pen name, especially one so appropriate for the subject.
It is a great pleasure for me to see this path-breaking paper reprinted here. As to recent progress in this field, I have no information, though some advances have surely been made over the years!
The material was written up by R. P. Boas and F. Smithies [Smithies 2002, personal communication] and appearedin [Pétard 1938]. Part of JWT’s assistance was in keeping the nonexistence of the nominal author, H. Pétard and of Pondiczery quiet when the Monthly enquired about the paper’s author. The full identification of Pondiczery was Ersatz Stanislas Pondiczery at the Royal Institute of Poldavia. The hope was that someday a document could be signed ESP RIP [Aspray & Tucker 1985].
John Tukey: The first year I was here I was soon drafted into what was known as “Fuhrocracy”.
William Aspray: Fuhrocracy?
Tukey: Yes. This was a group of people who sat at the near end of the first table on the right as you went into the dining hall in the graduate college. Lyman Spitzer, who is retired as chairman of the astronomy and astrophysics department here, was the Fuhrer. He sat at the head of the table. The rest of the group was probably 3⁄4 mathematicians and 1⁄4 physicists with a single Romance linguist, who was granted the authority to put people in Klein bottles (which have only one side). Frank Smithies, who was a functional analyst from Cambridge and here post Ph.D., and Ralph Boas, who was a slightly more conventional analyst and here as a National Research Fellow, and I tended to hang out together more than with the others. So while I never had much personal contact with Bochner, I heard lots about him from Ralph. His view was that if you came in and told Bochner about something new, there were two possible answers. Either such a thing “is impossible” or it “is trivial”.
…Albert Tucker: Was it that group that used the pseudonym “Pondiczery”?
Tukey: Yes, but with a somewhat broader reference.
Aspray: For what purpose?
Tukey: Well, the hope was that at some point Ersatz Stanislaus Pondiczery at the Royal Institute of Poldavia was going to be able to sign something ESP RIP. Then there’s the wedding invitation done by the Bourbakis. It was for the marriage of Betty Bourbaki and Pondiczery. It was a formal wedding invitation with a long Latin sentence, most of which was mathematical jokes, three quarters of which you could probably decipher. Pondiczery even wrote a paper under a pseudonym, namely “The Mathematical Theory of Big Game Hunting” by H. Pétard, which appeared in the Monthly. There were also a few other papers by Pondiczery.
Tucker: [Elton James] Moulton, the editor of the Monthly at that time, wrote to me saying that he had this paper and the envelope was postmarked Princeton and he assumed that it was done by some people in math at Princeton. He said he would very much like to publish the paper, but there was a firm policy against publishing anything anonymous. He asked if I, or somebody else that he knew and could depend on, would tell him that the authorship would be revealed if for any reason it became legally necessary. I did not know precisely who they were, but I knew that John [Tukey] was one of them. He seemed to be in the thick of such things. John agreed that I could accept Moulton’s terms. I sent a letter with this assurance to Moulton and he went ahead and published it. Which I thought was very flexible on …
Tukey: Somebody with a high principle. Pondiczery’s official residence was in Ong’s Hat, New Jersey5, which is a wide place in the road going southeast from Pemberton, but it does appear on some road maps. There is a gas station that has a sign out about Ong’s Hat.
Aspray: But no sign for Pondiczery?
Tukey: No sign for Pondiczery. Spelled c-z-e-r-y, by the way. Not like the area of India, Pondicherry, which is spelled c-h. Anyway, this was a good group, and it enjoyed its existence. I learned a lot from dinner table conversations.
Citation: Kós Géza 1999-02, Középiskolai Matematikai és Fizikai Lapok v49 #2 p. 76–86↩︎