I happily write this foreword to Nimi Wariboko's book, Ethics and Society in Nigeria. Like the theology and ethics characteristic of Paul Tillich, the scholarship of Wariboko epitomizes correlational mastery. For Tillich, theology is hermeneutical— namely, interpreting the “situation” calling forth the voice of theology in every period. The “situation,” says Tillich, “cannot be neglected in theology without dangerous consequences. Only a courageous participation in the ‘situation,’ that is, in all the various cultural forms which express modern man's interpretation of his existence,” can overcome the present reluctance of most theology to reach the freedom implied in genuine theological analysis. Tillich further insists, “The ‘situation’ to which theology must respond is the totality of man's creative self-interpretation in a special period.” The “situation,” Tillich says, “refers to the scientific and artistic, the economic, political and ethical forms in which they express their interpretation of existence.” Tillich imprints on these passages a great sense of urgency and necessity in the theological work of interpreting the “situation” of our times. Thus, while there is always a need for historical research on any context, contextual analysis is but one pole of theological interpretation. The imperatives of theological interpretation, the urgency and necessity, are demanded by the “situation” begging for salvation.
In this book and in more than seventeen others, Wariboko responds to the sense of urgency and necessity. He dialectically critiques theological languages, vocabularies, images, and practices in response to the ways that the worlds of business, economics, finance, markets, and social and political global centers stake claim to the lives of people and nations. Wariboko synthesizes complex relations between faith, social systems, and centers of power. He engages and critiques globalizing economic and political power operating in the reaches of world financial organizations and multinational corporations, and contributing to governmental corruption and excesses that give legitimacy to their global holdings.
In this book, Wariboko turns his dialectical perspective on the geopolitics of contemporary Nigeria, whose people stand in urgent need of wholeness. He also looks to Nigeria's traditional African religious heritage as a powerful spiritual, social, political, and ethical source of transcendence from sociopolitical forces at work in Nigeria's debilitating statecraft, domination, corruption, and necropolitics.
For over one hundred years, the Mathematical Association of America has been publishing high-quality articles on the history of mathematics, some written by distinguished historians and mathematicians such as J. L. Coolidge, B. L. van der Waerden, Hermann Weyl and G. H. Hardy. Many well-known historians of the present day also contribute to the MAA's journals, such as Ivor Grattan-Guinness, Judith Grabiner, Israel Kleiner and Karen Parshall.
Some years ago, we decided that it would be useful to reprint a selection of these papers and to set them in the context of modern historical research, so that current mathematicians can continue to enjoy them and so that newer articles can be easily compared with older ones. The result was our MAA volume Sherlock Holmes in Babylon, which took the story from earliest times up to the time of Euler in the eighteenth century. The current volume is a sequel to our earlier one, and continues with topics from the nineteenth and twentieth centuries. We hope that you will enjoy this second collection.
A careful reading of some of the older papers shows that althoughmodern research has introduced some new information or has fostered some new interpretations, in large measure they are neither dated or obsolete. Nevertheless, we have sometimes decided to include two or more papers on a single topic, written years apart, to show the progress in the history of mathematics.
We wish to thank Don Albers, Director of Publications at the MAA, and Gerald Alexanderson, former chair of the publications committee of the MAA, for their support for the history of mathematics at the MAA in general, and for this project in particular.
In chapter 10 of his A History of Algebra , B. L. van der Waerden repeats much of what he wrote about Hamilton's discovery of quaternions. Interestingly, there he mentions Caspar Wessel as one of the originators of the geometric interpretation of complex numbers, while in the current article he ignores Wessel. But he also goes on to discuss Cayley's own use of quaternions to describe rotations in three-space, meanwhile pointing out the earlier results of Rodrigues. In addition, he deals with some applications of quaternions to the question of representing integers as sums of four squares. He concludes by discussing Hermann Hankel's 1867 book that presents many of Grassmann's results, but in a form that was easier to understand.
Simon Altmann writes in his article that we know “next to nothing” about Olinde Rodrigues, but in the next fifteen years he remedied this situation, publishing the results in his recent biography, Mathematics and Social Utopias in France: Olinde Rodrigues and His Times . Similarly, Karen Parshall went on to do further research on the life and work of Sylvester. Her results appear in her edition of Sylvester's letters  as well as in her magnificent biography of the English mathematician .
Israel Kleiner has expanded his paper on group theory and some of his other work on the history of algebra into a new book, A History of Abstract Algebra . Leo Corry's Modern Algebra and the Rise of Mathematical Structures  is another recent work that concentrates specifically on the development of abstraction in the nineteenth and twentieth centuries, but claims that true abstraction did not come into being until the work of Emmy Noether in the 1920s.
One of the most important aspects of geometry in the nineteenth century was the development of non-Euclidean geometry, and this chapter begins with two brief studies of aspects of its development. In the first, George Bruce Halsted reviews volume VII of Gauss's Werke and concludes from a study of many of Gauss's letters first published in that volume that Gauss's ideas on the subject had no influence on the independent discoveries of János Bolyai and Nikolai Lobachevsky, or on the earlier publication by Ferdinand Karl Schweikart (1780–1859). In the second article, Florence P. Lewis gives us a whirlwind tour through the history of the parallel postulate, from Proclus to Bolyai and Lobachevsky. She then proposes how this history, and its effect in how mathematicians understood the nature of a postulate, could affect the teaching of geometry in schools. In particular, she emphasizes that one reason for the study of geometry is its role in “training the mind.”
Another major aspect of nineteenth-century geometry was the development of projective geometry. That development began in the seventeenth-century work of Girard Desargues and Blaise Pascal, but, as Julian Lowell Coolidge notes, it then “dragged along” for about a century. In his article, Coolidge takes up the story in the nineteenth century, summarizing the work of such mathematicians as Jean-Victor Poncelet, Michal Chasles, Jacob Steiner, and Johann Karl Christian von Staudt. But then Coolidge remarks that by the end of the nineteenth century, the field of synthetic projective geometry was “pretty much worked out.”
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