Editorial
Editorial
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 
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
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 
, 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. ![[]](editorial-endproof.png)
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 
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 
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.
