Let K be a field, K[X] = K[X1, . . . , Xn] the polynomial ring in n variables over K for some n ∈ N, and K(X) the field of fractions of K[X]. Assume that L is a subfield of K(X) containing K. Then, the Fourteenth Problem of Hilbert asks whether the Ksubalgebra L ∩K[X] of K[X] is finitely generated. Zariski [17] showed in 1954 that the answer to this problem is affirmative if the transcendence d...

SCHOOL HEALTH: A guide for Medical Officers of Schools. By the Medical Officers of Schools Association. Fourteenth Edition. (Pp. xii+ 141. 15s). London: J. & A. Churchill, 1969. THIS is the fourteenth edition of a handbook that first appeared in 1885 issued by the Medical Officers of Schools Association, because, to quote the preface to the first addition, ". . . claiming immediate attention wa...

The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’s 350-year-old conundrum. That same year, perhaps to console himself of Fermat’s demise, Ribenboim published a second book, this time on Catalan’s conjecture that there are no consecutive perfect pow...