Mathematics, mathematical physics and developing countries M. Guenin, Geneva It is not self-evident that mathema people abroad for too long con We make the asumption that it is tics and perhaps, even more, mathe siderably reduces the danger of the easier to attract somebody of high matical physics can be useful to the brain drain. What developing countries level as the first in a given domain, establishment and growth of scientific need most and fast, is a very large if you have already got very good communities in developing countries. number of very competent primary and people in neighbouring fields. This Not everyone will agree that they do secondary school teachers, techni assumption is not necessarily always have a role to play and though many cians and engineers on the spot. So true but should apply in a majority of of the ideas presented here have been many can only be educated in the cases. discussed with friends, they are essen country itself, if there exists there a tially the author’s own views based on valid scientific community. It is an What is Mathematical Physics what is recognized to be a quite sub elementary point but one which must So far, nothing of what we have said jective analysis. be repeated again and again, that the value of the teaching, crucially de seems to imply that mathematical phy sics can be of any use in resolving Need for a Scientific Community pends upon the value of the teacher. the problems posed, and for most physicists, mathematical physics is A strong scientific community exists Establishing a Scientific Community in all the developed countries and just one of many marginal fields of there is no doubt that it has con The question of how to establish physics. That is a fair point of view tributed greatly to the general welfare and maintain a strong scientific com if the parameter used in the assess of such countries. It is generally munity is of course very complex. We ment is the number of people involved accepted that it could also signifi shall simplify it by concentrating on and also if only a restrictive definition cantly help less favoured countries three factors which we think are de is employed. In the broadest sense, and in two ways. First, by providing cisive in making a scientist want to mathematical physics is that part of skills, knowledge and experience come and stay at a given place. These theoretical physics which is not purely where they are needed and second, factors we describe by the catchwords phenomenological, together with the by allowing the formation and training Finances, Geography, Science, Under part of mathematics which is devoted of the younger generation directly in finances, we group the elements that to the study of the abstract structures the countries where they will have to go to make up the standard of living of physics. It does not comprise com work. which can be offered to the scientist. putational physics. Even if such an The first point is clear as soon as It is an aspect that cannot be cha embracing definition is not considered it is appreciated that the most im racterized by a universal figure, be acceptable, the marginality of mathe portant factor in the brain drain away cause cost of living, fringe benefits, matical physics appears completely from the developing countries, is that etc. vary considerably from place to different from that of other domains, their scientists and doctors, trained at place. Under geography we bring to because every problem of physics high cost in industrialized countries, gether all the factors connected with embodies an aspect which fits into find themselves completely isolated the actual location of the place in the framework of mathematical phy when they return home. Recognition question, such as educational facilities sics. In a sense, mathematical physics of this fact was incidentally a prime for the children, the cultural life, cli would be better called fundamental motivation for the creation of the Inter mate, recreation possibilities, histor physics, if only every branch of phy national Centre for Theoretical Phy ical or artistic surrounding, facilities sics were not, in fact, fundamental. So sics in Trieste, whose purpose is to for communications etc. Finally under we shall keep the nomenclature ma enable physicists from developing science, we have all the factors which thematical physics for lack of a better countries, periodically to spend a few influence scientific life : number and one. months re-establishing contact with level of colleagues and the colla the main stream of research. boration that is to be found, technical Mathematical Physics The second point is even more facilities and equipment, the teaching in Teaching Programmes obvious. Teaching and training young load and so on. It has not infrequently been said that people is cheaper and can be more Even a superficial observation of the one should teach people mainly specifically aimed if it is done in the evolution of the existing research and things which lie outside what they are developing countries themselves. As teaching centres, shows that in order going to do, because what they will for the cost, it is clear that even if one to achieve a reasonably rapid and need for their job they will have to has to offer a very attractive salary stable development, it is desirable that learn anyway, whereas once studies to a teacher to have him come to the all three factors should be positive. are terminated (with very few ex country, it is still much cheaper than Even if only two are adequately ceptions), they are not going to sending the students abroad, at least covered, something can still be acquire much knowledge outside their so long as the teacher does not need achieved ; but if there is only one specialized field. To some this may equipment. Moreover, a large fraction good point, it had better be the sound a little like a joke, but if not of the salary of the teacher will be science. In any case, the science side pushed to its extreme it contains in spent where he lives, which is more is usually the only one which can be our opinion a certain amount of truth. favourable to the balance of payments modified by scientists, so it seems That is why personally I have always than sending students away. At the pertinent to ask where to start, espe insisted on teaching future experimen same time, not sending the younger cially if the means are not unlimited. talists and phenomenologists a sub-
10 stantial amount of mathematics and the ninth symphony, or Hamlet but it obtained at a total cost of about abstract theoretical physics, and on is, in addition, the language of one million dollars and its yearly sending future theoreticians into the science. Mathematical physics on the running costs for acquisitions are laboratory. With the exception of those other hand cannot be taught at all of the order of magnitude of 50,000 who later will be doing research in levels. Only for future mathematicians dollars. Such a library can also be mathematical physics, for most, ma and physicists (whatever their future used with very little supplements thematics and abstract theoretical field of specialization might be), can for the whole field of physics. The physics is the baggage for life that it be allowed to become a dominant rest of the costs are only salaries they assembled by the time they got part of the curriculum. and building and maintenance of their diploma. This abstract formation simple office rooms. Big computers has the disadvantage that the people Mathematical Physics and Creation are not an absolute must, even if who received it are less immediately of Scientific Communities they sometimes can be useful. Apart efficient than those which will already from mathematics, one cannot have have practised a lot in their future We now come, to the reasons why any cheaper science. Finally, one has field of specialization, but it has at we believe that mathematical physics to realize that mathematical physics is least the tremendous advantage of can make a useful contribution to the a good departure point for further being much more time resistant. Ma creation and development of scientific developments. There is a continuous thematical theorems remain true even communities in less favoured regions passage from the most abstract ma after twenty years and someone of the world. There is, first, a question thematical consideration to very con who has got into the habit of discern of “market”. Mathematical physics is crete phenomenological study and ing the basic structures of existing not fashionable, and the number of also to definitely applied problems. An theories will have a much easier time people working in the field is small ; extension to neighbouring fields is recycling himself, because he will be a few hundreds only are really active therefore relatively easy to perform, able to extract the basic features of in the whole world. That means that especially if there are highly com the theories which are going to there is a great deal to be done and petent people who are continuing in emerge in his subsequent work. new-comers have a fair chance of the more abstract domains. If it is agreed that an abstract and reaching really international level. The mathematical formation becomes ob second point is that those who are Conclusions solete more slowly than other training, working very far from the main re the question may then be asked : why search centres, are not placed at any We believe that these arguments are not only pure mathematics ? This real disadvantage. All that they need sufficiently strong to make out the could be envisaged, but there is a big is a decent library and a good case that mathematical physics can difference between pure mathematics mail system. If furthermore they can be useful in the development of and mathematical physics, and that attend one conference or school in science, especially where it has not difference lies in Nature. The abstract the year, they will not feel discri yet established itself. It has never theories of physics are not allowed minated against in respect to others. theless to be stated that this is not an to be only pure constructions of the The situation is very different for attempt to position it at the top of mind, like mathematics. They ul phenomenologists. The field is very some scale of values. We do not think timately must represent a model of crowded, and you have no chance, if that mathematical physics is in any the world, or at least some classes you are not in direct touch with the way more important or more inte of phenomena which, up to a given big laboratories, of being aware of any resting than other ways of looking at approximation can be fitted to exper development before it actually appears physical problems. We only think that iment. Mathematics is, in any case, a in the literature. A third point is the it is a convenient place to make a must for every education. It belongs relative cheapness of the investments start ; but to stop there would, of to culture in exactly the same way as needed. A first class library can be course, be a pity.
Conference Report Pluridimensional Radiative Transfer
The solar atmosphere shows con diative transfer (PDRT) and the Application to Structures in Stellar vective and magnetic structure on committee preparing the establish Atmospheres”. The meeting, sponsor scales down to the observational re ment of the Solar Physics Section of ed by the EPS and supported by the solution (= 200 km). The radiative the Astronomy and Astrophysics Di Consiglio Nazionale della Recerche, transport in the small structures, can vision, supported a plan to bring was attended by 15 participants. not be adequately treated by means these people together in a workshop, The Workshop was arranged in of one dimensional radiative transfer i.e. an informal meeting of participants three stages : in mean models, describing the invited of rather restricted numbers 1. Each participant summarized the thermodynamic and magnetogasdy- upon application. PDRT problem which arose in his namic parameters as a function of one The Workshop was organized in the work by indicating the astrophysical spatial coordinate only. In recent Osservatorio Astronomico di Capodi- background, the physical and geo years, several astrophysicists in Eu monte in Naples, 14-16 September, metrical simplifications, the mathem rope have become engaged in pro under the tittle : “Pluridimensional atical methods, and results obtained blems involving pluridimensional ra Radiation Transfer — Theory and and/or problems encountered. These
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