Julia Robinson continued from page 78 ready printed so he offered to withdraw his much more understandable paper and I told him to. It is a decision I have always regretted. Now I think the problem of learning what is known is much more critical than turning out results whose only virtue is that they are 'new'." She had known that the problem was nearly hopeless: " is right about getting a job. However it is crazy because good expository writing is more n e e d e d t h a n further research at the present time. Once you have tenure you can do what you want and at worst not get advanced as fast. I don't see any way to beat the system. The schools that don't demand research have heavy teaching loads which are not compatible with writing." But now, with the presidency and the fellowship, she had the position, leisure, and money to promote good mathematical exposition, logic, and mathematics. Unfortunately, her health failed and a lot of her energy was devoted to battling the disease. In May of 1985, she received one last h o n o u r w h e n she was elected to membership in the American Academy of Arts and Sciences. Julia Robinson requested that those wishing to make

a gift in her memory contribute to the Alfred Tarski Fund, which is administered by the U.C. Berkeley Mathematics Department. Less affluent friends ought to consider writing survey papers.

Julia R o b i n s o n ' s m o s t i m p o r t a n t papers 1. Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98-114. 2. Existential definability in arithmetic, Trans. AMS 72 (1952), 437-449. 3. (with Martin Davis and Hilary Putnam) The decision problem for exponential diophantine equations, Ann. of Math. (2) 74 (1961), 425-436. 4. Diophantine decision problems, in: W. J. LeVeque, ed., Studies in Number Theory, MAA, 1969. 5. (with Jurii Matijasevi~) Reduction of an arbitrary diophantine equation to one in 13 unknowns, Acta Arithmetica 17 (1975), 521-553. 6. (with Martin Davis and Jurii Matijasevi~) Hilbert's tenth problem. Diophantine equations: positive aspects of a negative solution, in: F. E. Browder, ed., Mathematical Developments Arising From Hilbert' s Problems, AMS, Providence, 1976. Department of Mathematics & Computer Science San Jose University San Jose, California 95192

The Lost Folios of Wunschtraum's Lost N o t e b o o k by Nelson Riddle As an avid antipodean subscriber to the Intelligencer I read with astonishment Prof. Van Dongen's amazing discovery of the Lost Notebook of Georg Hindenburg Wunschtraum. It is an unusual name, and it happens to be that of my maternal grandfather, Wilhelm Wolfgang Wunschtraum, who emigrated from Bavaria to New Zealand in 1895. Recalling that my mother had kept a box of her father's papers, I rescued them from their resting place in a cow-byre, and examined them on the offchance that they might shed some light on the matter. Most of the documents were uninteresting; mainly old bills, programmes from the Wellington Operatic Society (of which m y grandfather was a f o u n d e r member), and pedigree certificates for his sheep. However, inside a tattered leather binder, I found a sheaf of papers, obviously mathematical in content, and some photographs. On the back of one photograph was the message " W i t h fondest memories, Georg". Moreover the mathematical writings alluded more than once to " m y solution of the Waring conjecture". The pages are numbered in a Germanic hand: they start at 236 and end at 311, exactly the numbers of the missing folios of the Notebook! To my disappointment, on further examination, I found that several

A page from the notebook. Continued on page 80

THEMATHEMATICALINTELLIGENCERVOL.8. NO.2, 1986 79

Wunschtraum's Notebook continued from page 79 pages had been eaten by mice; but nonetheless a considerable amount of material remains. I have forwarded copies of the documents to Prof. Van Dongen, but I can here reveal that Wunschtraum, not content with solving the Waring conjecture, had made penetrating investigations into two of the most notorious open questions in mathematics. As we all know, the notion of a manifold goes back to Riemann's Habilitationsvortrag of 1854. That of a vector field w a s k n o w n to S o p h u s Lie in 1876. Wunschtraum developed these ideas in a series of investigations between May 1887 and July 1893. (I assume that for some reason he sent them to my grandfather, though w h y he should tear them out remains a mystery, especially since Wilhelm Wolfgang was an ignoramus at mathematics.) His terminology and notation is somewhat unorthodox. In particular he refers to a vector field as a Kesselsteinansetzung, or "furring". In this imagery he was no doubt anticipating the Hairy Ball Theorem, and indeed he states (and proves!) something called the Pelzballsatz ("Fur-ball Theorem"), that the surface of a sphere cannot be nonsingularly

furred. The proof is ingenious. The sphere is realized as the Riemann sphere C* = C U {~}, and tiled by the image under stereographic projection of the integer lattice in C. Generalizing the work of Legendre on elliptic integrals of the first and second kind, Wunschtraum defines integrals of the furred kind (or fibre-preserving transfurmations). These appear to be related to the Haar (Hairy) Integral. From any nonsingular furring of the sphere, he constructs an integral of the furred kind, taking values + 1 at 0, ~ respectively, and having no poles. This contradicts Liouville's Theorem. W u n s c h t r a u m d e v e l o p s t w o further geometric ideas. The first he calls a Fussdecke ("mat") and is essentially the modern notion of a covering space. The second, Kragen ("collar") is exactly the modern notion of a collar on a manifold with boundary. Wunschtraum proves two theorems. The first is that the connected components of the fibres of a mat can be given a 0-dimensional furring. The second is that any collar has a nonsingular furring (flow along the fibres (0,1) x m of (0,1) x 3M). Thus by 1893, Wunschtraum was in possession of solutions to both the Fur Mat Conjecture and the Fur Collar Theorem.

The Stamp Corner Designed by Robin Wilson*

Sir William Rowan Hamilton (1805-1865) was a child prodigy who had mastered several languages, modern, classical and oriental, by the age of 14. While still a teenager he discovered an error in Laplace's Trait~ de M~canique C~leste, and was appointed Astronomer Royal of Ireland while an u n d e r g r a d u a t e at Trinity College, Dublin. He did important theoretical work in dynamics and geometrical optics, and revolutionized algebra by his investigations into non-commutative systems. This stamp w a s issued by Eire in 1983 to commemorate Hamilton's discovery of quaternions in 1843.

*Faculty of Mathematics, The Open University, Milton Keynes MK 7 6AA, England. 80

THE MATHEMATICAL INTELL1GENCER VOL. 8, NO. 2, 1986

Jean LeRond d'Alembert (1717-1783) was a French mathematician, philosopher and scientist who was a leading figure of the French Enlightenment. His Traitd de Dynamique was published in 1743, in which he presented the so-called 'd'Alembert principle'. During the next few years he applied this principle to fluid dynamics and the vibration of strings, and he carried out pioneering work in the study of partial differential equations; he also used the principle to solve the problem of the precession of the equinoxes. He was a strong proponent of a sound foundation for analysis, and he introduced the ratio test for the convergence of series. In later years he worked on the Encyclopddie with Denis Diderot, and wrote most of the mathematical articles in it.

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