The history of cryptography is punctuated by the invention of clever systems to encipher messages and, sometime later, equally clever systems for cryptanalysing the enciphered messages to determine their meaning. Most enciphering schemes of any worth enjoy a relatively lengthy period of prominence before sufficiently determined cryptanalysts undermine their security by figuring out how to attack them. In response, cryptographers devise new and improved schemes and then the cycle repeats. Cryptographers have learned from history that it is dangerous to declare any enciphering scheme unbreakable; at best they are considered to be very secure. But there is one scheme, a scheme that has been around since 1917, that truly is unbreakable. It is the perfect cipher.

A great deal of attention has recently been given to the problem of revising both school and university syllabuses of pure mathematics. Though applied mathematics has not escaped attention, it has been discussed less intensively. It is therefore of interest that in his inaugural lecture, Professor Bonnor subjected the London University syllabuses in this subject to searching criticism on the ground that it gives a possibly unnecessarily thorough training in classical theoretical physics. He noted that, excepting Imperial College, most of the subject matter contained in the London B.Sc. Special Examination contains ideas which are eighty years old, or older.

Consider a thin thread (preferably nylon, which is strong, has low loss, and is resilient) attached to an electromagnetically-driven reed or tuning fork at one end, the other passing over a pulley, and tensioned by a weight W Suppose the free length of the thread is about 1 metre, and that the reed vibrates transversely to the thread. By adjusting W to get the correct tension, the first overtone of the thread may be obtained, there being a node at the middle. The frequency of the thread is the same as that of the reed. If the latter is rotated through 90° (the length of the thread baing unaltered), vibration occurs along the thread, thereby causing its tension to vary periodically The main frequency of tho thread is now half that of the reed, so a subharmonic of order two occurs, there being no node at the middle. This was demonstrated by F. Melde ninety years ago, using a tuning fork excited by a violin bow.

Note 74.11 from Nick Lord in the March 1990 Gazette looks at the fascinating Simpson's paradox starting from a complex number situation; and in the same issue John Haigh, reviewing Cox and Snell's Analysis of Binary Data, gives a (fictitious) example; but the fascination of the paradox stems from the real occurrences.

If from a point, regarded as a centre of inversion, a radius is drawn on which are two points at distances r1 and r2 from the centre, satisfying the condition r1r2=r2 = constant, the points defined by r1 and r2 are said to be inverses one of the other.

The cracking or tearing of thin sheets of material is of considerable interest in modern-day engineering. A recent investigation into the behaviour of concrete indicated that it would be of interest to consider a probabilistic model in which a crack is regarded as some form of non-self-intersecting random walk in the plane. This paper considers some simple models and in the Appendix are included some results on paper tearing.

We consider here the positive integers with respect to their unique decimal expansions, where each n ∈ ℕ is given by for some non-negative integer k and digit sequence αkαk-1 … α0. With slight abuse of notation, we also use n to denote αkαk-1 … α0. For such sequences of digits (as well as for the numbers represented by the corresponding expansions) we write x ⊲ y if x is a subsequence of y, which means that either x = y or x can be obtained from y by deleting some digits of y. For example, 514 ⊲ 352148. The main problem is as follows: Given a set S ⊂ ℕ, find the smallest possible set M ⊂ S such that for all s ∈ S there exists m ∈ M with m ⊲ s.