``It's so easy to become obsolete.'' Prof. James Ezeilo, pausing over a plate of pasta in the dining room of the International Center for Theoretical Physics, speaks with a broad smile. Here, at least, the British-trained mathematician from the University of Nigeria can fight off obsolescence by rubbing shoulders with other researchers visiting this center from around the world and, as he says, recharging his batteries. But his words go to the pith of a problem facing the world's developing nations. It is not exactly ``brain drain'' - although the permanent movement of bright, Western-trained thinkers from south to north remains a serious cause for alarm. It is, instead, a problem for those who don't choose to leave home: How can they keep abreast of the latest developments so they can be productive researchers and stimulating teachers? Professor Ezeilo knows that problem first-hand. A while ago, he says, he arrived in Europe with ``something I thought I'd proved'' - only to find he had duplicated work that had just appeared in a journal his university couldn't afford to order.

But isn't this a rather esoteric problem? After all, what's the relevance of a new insight into differential equations to nations facing malnutrition and poverty on a daily basis? At the very least, some say, the immediate requirement is not for calculus but for cookstoves - and for what is now fashionably called ``technology transfer.''

The developing nations, to be sure, can benefit greatly from new technology. But Ezeilo, like so many of his developing-world colleagues sitting around the table here, sees something even more important: a need not only for a transfer of technology but of science. Technology, after all, also becomes obsolete. The long-term need is for an understanding of the sciences out of which new technologies, especially those adapted to the problems of the developing world, can grow.

``A lot of our countries are in shambles,'' explains Prof. L.K. Shayo, a mathematician from the University of Dar es Salaam. ``Why is that? It may be that the training has not gone far enough.''

What's to be done? Professor Shayo has a plan that, it seems, deserves more than a little consideration. He and an African colleague, Prof. L.Eells, are proposing a ``Project for Mathematics in Africa'' to set up ``focal points'' or ``centers of excellence'' at eight universities in eight African nations. Their purpose: to bring together a few postgraduate students from all across the continent for up to two years of further work in mathematics. Their long-term goals: to help popularize the study of mathematics throughout Africa; to encourage talented young students to develop their mathematical skills; to help train the next generation of African teachers of mathematics; and ultimately to help combat what they describe as the ``physical and mental migration'' of mathematicians out of Africa.

But why, of all possible subjects, should Africa focus on mathematics? Professors Eells and Shayo, in a paper now circulating among a number of African mathematicians, point to three reasons: mathematics is the basis of the physical sciences; it often requires nothing more expensive than paper and blackboards for teaching and research; and ``the state of mathematics in Africa is desperately low at all levels of education.''

On this last point, Eells and Shayo cite evidence of recent steep declines in the quality and numbers of mathematics staff and students across 148 university-level departments of mathematics in 51 African countries.

Among the world's pressing problems, the need for mathematical ``centers of excellence'' in Africa may appear to rank low - until you reflect that these nations comprise some 380 million people who, having won political independence in this century, must win economic, educational, technological, and scientific independence in the next. How can they do so unless they adapt Western technology to address their own unique problems? And how will that happen without the growth of an indigenous capacity for scientific research out of which the technologies can grow?

In the world's range of expensive solutions to long-term problems, in fact, this one may be among the more elegant - and the least costly. Eells and Shayo recommend an annual budget of about $2 million.

At that price, one can hope that their proposal will attract the attention of a few thoughtful foundations. At that level of funding, however, these centers obviously won't train great numbers of students. But numbers won't be the measure of success. The success will arise from the inestimable difference such ``battery-charging'' centers can make in the lives of men like Ezeilo - and in the lives of the students who benefit from his teaching and example.

``If we do things that inspire others to more noble objectives...'' Ezeilo says, his voice trailing off. ``Mind you, we might be dreamers,'' he adds. ``But every country needs its dreamers.''

A Monday column