Fifty Years of Eureka

In January 1939, the first editors of Eureka, F. J. Collinson (Newnham), E. P. Hicks (St. John’s) and A. Jackson (Emmanuel), set out in the first editorial the reasons for its existence. Quoting from the then President, they said:

“... The chief thing is to make it interesting to every Cambridge mathematician, to help build up the corporate interest in the subject... to link together students, researchers and dons, other English and foreign universities. We must aim to stimulate informed discussion, especially as to Cambridge questions...”

They continue: “We realise how inadequately this first issue fulfils these high ideals.” In fact, this is modesty on their part; they had received encouragement from the University of Chicago and the University of Wisconsin, for example, and their first issue is extremely thought-provoking. There are articles on mathematics as practised in other universities and countries, an article celebrating the 150th anniversary of the publication of Lagrange’s Méchanique Analytique, a classic recreational article on Mathematics and Chess (beginning “Chess is a game in which 25 particles move in a finite space. In this respect it resembles the Universe, in which we are told there are 136 . 2^{256} particles”), a history of the Mathematical Association, commentary on the beginnings of student representation in the running of the Faculty, and many other worthy items.

Looking through the very early Eurekas, one is struck by the fact that at once the times in which they lived were so different, and that the people making up the Society were so similar. In the war-time Eurekas, although little explicit reference is made, one finds (in issue 7) a Heffer’s advertisement offering catalogues “as often as the paper control regulations allow”; it is recorded (in issue 3) that Maths teachers evacuated to teach evacuees were made members of the Society; collections were made for medical aid to the Soviet Union; and so on. There is debate as to whether Part IB students should be called up immediately, or be allowed to finish their degrees first. On a lighter note, the age of Eureka can be judged from such things as discussion of whether Noel Coward is considered “too lowbrow” by Cambridge mathematicians, and a book review (in issue 1) of E. T. Bell’s classic Men of Mathematics.

In 1949, D. J. Wheeler (now Prof. D. J. Wheeler!) describes an amazing machine called EDSAC, being built by Dr. M. V. Wilkes (now Prof. M. V. Wilkes!) in which numbers are “stored in the form of supersonic bursts of waves travelling in mercury contained in a tube”. This machine seems to have captured the interest of the Society, and much is written about its earlier years: although the modern reader may not think much of its abilities, he would do well to read J. C. P. Miller’s report in 1951 (issue 14) that the record for the largest known prime (previously 2127 - 1, found by Lucas seventy-five years before) had been broken, using EDSAC to reduce the time needed for a Fermat test to base 2 to only a few minutes and had found

P = 5,210,644,015,679,228,794,060,694,325,390,955,853,335,898,483,908,056,458,352,183,851,018,372,555,735,221.

On the other hand, the recreational content of Eureka has changed hardly at all, and the regular content of surreptitious or merely ludicrous content has always been with us. There are far too many gems in Eureka to report them all, but reference must be made to the classic article in issue 2 by P. M. Grundy on “Mathematics and Games”, which seems to be the first indication that the game Nim contains the theory of all such games. Other recreations have included finding which real numbers could be closely approximated using normal mathematical symbols but only four 4’s (J. H. Conway and M. J. T. Guy, in issue 25, following up a puzzle in issue 13: it is rather hard to explicitly do for interesting reals such as Euler’s constant \gamma, for example) and analyses of the Boat Race (issue 46), First Division football results (issue 33), collecting every different free gift from packets of breakfast cereal in a promotion (issue 36), and maximizing Tripos performance (issue 34). More recently, investigations appear of the possible proportions of pairs of elements of finite groups which commute (issue 43), and of the justly celebrated Audioactive Chemistry (issue 46).

Many people who have now become famous mathematicians of the past wrote for Eureka: G. H. Hardy, P. Hall, P. A. M. Dirac, W. Hodge and M. Cartwright to name but a few. The list of mathematicians in the Faculty here and elsewhere who wrote for or were connected with Eureka is longer yet: a startling proportion of the present lecturers and Professors here may be found in the pages of suitably early issues. In view of the difficulty in recruiting Business Managers for Eureka, I am tempted to observe that the present Head of D.A.M.T.P. is Professor H. K. Moffatt, and that one H. K. Moffatt was Business Manager in 1957...

There have been many humorous items in Eureka, but my favourite must be the classic article in Eureka 16 on “A Contribution to the Mathematical Theory of Big Game Hunting” by H. Pétard, which also (more famously) appeared in the American Mathematical Monthly. This classic monograph in the field draws results from such sources as the Trivial Club of St. John’s College (now euphemistically known as the Adams’ Society, some might think), to the problem of catching the lion, felis leo in the desert. Many methods are given, including:

The Peano Method    Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked 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. []

The Schrödinger Method    At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.[]

A Topological Method    We observe that the lion has at least the connectivity of a torus. We transport the desert into four-space. It is then possible to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.[]

Eureka has featured satires and parodies of just about everything, from the Ring cycle (issue 30) to two different mathematical versions of 1066 and All That (issues 12 and 21). For many years it was customary to write poetry rather than prose, and a sample of the results may be found elsewhere in this issue. Another diverting item (in issue 39) is a collection of photographs of some of the lecturers of the time. Many of those depicted are still at Cambridge, and some have even changed their hair-styles. I particularly recommend the photograph of Dr. Körner.

I have been asked to reprint the details of the Archimedeans’ tie, which was adopted in 1950 (as reported in issue 13): “the design consists of Archimedean spirals with \epsilon\upsilon\rho\eta\kappa\alpha between them”.

Since 1942, Eureka has almost always featured a Society column, in which our activities are recorded. This has ranged from thanking the speakers (who have included such worthies as Sir Arthur Eddington and Dr. F. Hoyle, along with just about everyone else who has been a mathematician here in the last fifty years) to veiled remarks about members falling in the Cam on the annual Punt Trip (which seems to have its origins in the antiquity of the Society). The most unlikely I can find reference to is the Telepathy Evening, reported in issue 13, at which the Archimedeans present were revealed to be (slightly) significantly worse at guessing Zener card designs than a random strategy. Reading through the Society columns, one observes a certain periodicity in their contents, but it is nevertheless amusing to note, for example, that Chris Zeeman threw the Archimedeans’ Christmas Party in 1947, exactly forty years before the committee I was on did.

Similarly, the Problems Drive problems have been published almost every year since 1949, with the custom of this year’s winners setting next year’s problems apparently having survived since then. In addition, Eureka has always contained short problems along with the larger items; this issue is no exception. These range from such as: “Show that there exist intelligible sentences containing (14 . 3^n - 3) successive had’s, where n is any non-negative integer” (issue 18), to alphametics such as EUREKA + EUREKA + AN = ANSWER, contributed by Dr. Partington (in issue 38). Crosswords and crossnumbers have been particularly fruitful. Quite apart from an analysis of “crosswordiness” (issue 5), crosswords of almost every kind have appeared: with letters, with numbers, three-dimensional, hexagonal and even in Roman numerals (“Crux Verborum”, in issue 12). The Eureka crossword makes a hopefully welcome return in this issue.

In conclusion, I can only say that I hope the first editors would approve of the course Eureka has taken through the years. May it continue for many more.

Reproduced from Eureka 49 pages 2-4.
HTML conversion Copyright © 2004 The Archimedeans.

Additional notes to the online version

Erratum: the analysis of the Boat Race was in issue 43, not issue 46.

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