Société de Calcul Mathématique, SA 

We introduce the new book by Bernard Beauzamy:
Archimedes' Modern Works
A book you will be proud to show to your friends ! 

ISBN : 9782952145879, ISSN : 17671175. Size 15,3 x 24 cm. Hardcover, 220 pages.
This book is devoted to Archimedes' modern works: direct consequences of his ideas, leading to progresses in presently unexplored, or poorly explored, domains of science.
This, at first sight, may look quite strange, because Archimedes died more than 2 200 years ago, and most people think that everything he did, no matter how clever he was, has been long ago incorporated by modern science, and that he belongs to the past. Certainly, he is considered as one of the greatest geniuses of all times, but people think that his heritage must be simply of historical value.
But this is not true at all, as this book clearly demonstrates. Two main ideas, namely the "Archimedes Maps" and "the Method", lead to completely new approaches of present problems, with far more powerful tools than the ones which were produced otherwise.
The present book is organized as follows:
We start with a quick and simple historical presentation, just in order to remind the reader about Archimedes' times. This book is not intended to address any preoccupation about history of mathematics. In the First Part, we present Archimedes Maps, and their applications to modern problems, such as monitoring, surveillance, resource allocation, and many others, with concrete examples to present concerns.
Archimedes' approaches provide interesting and relevant research subjects, the kind of research subject which will be appreciated by all Governments and funded by all Agencies. It relates deep old mathematics to new socially important preoccupations. The most hostile project director, hearing such topics, will fall onto his knees, start crying, and draw his checkbook.
The impatient reader, who wants to return to his modern computations, will ask: "Is that all?". Of course, a vast majority of scientists would be more than happy to see that their work is still useful 2 200 years after their death, and that it is used for socially important questions, carries unsolved problems and generates new research topics. A vast majority of scientists But remember that here we deal with one of the greatest geniuses of all times. So it is not all, you have seen nothing yet. The benediction of the Governments and of the Agencies is not enough; Satan is in charge and Archimedes drives the show.
A second line of thought, developed in the second part of the present book, deals with the "weighing methods". The idea is to compare an unknown information to an artificially produced one (thus well known). Archimedes himself considered the "Method" as his masterpiece, and asked that the result (a sphere and a cylinder) should be engraved on his tomb. The Method was lost for more than 2 000 years, and, strangely enough, the mathematical contents were not rediscovered by anyone else during that time. This is strange indeed, because all classical concepts in mathematics, such as equations, polynomials, differential or integral calculus, were discovered independently many times, by many people, at many places. The Method is certainly not a classical concept; it does not fit with anything we know. It was discovered only once, and then lost.
The Method is a special case of general Greek Comparison Methods. But it is very special. Nobody knows how such an idea came to his mind, because there are no other examples. But the Method, as we see, is extremely powerful, and brings direct solutions to modern problems, such as electricity production. We present it in modern terms (which has never been done before) and investigate its modern applications to probabilities, systems of polynomial equations, optics, non destructive testing, and so on.
Then we give, for the reader's convenience, the few texts which present Archimedes life (mostly about the siege of Syracuse, 212 BC, when he died), and some comments about his abilities, compared to the abilities of modern mathematicians.
About the author : Bernard Beauzamy is a French mathematician, born 1949. He has been University Professor, 19791995. He established SCM SA in 1995, a company which does mathematical models. He has been chairman and CEO of this company since then. Among his previous books, "Introduction to Banach Spaces and their Geometry" and "Introduction to Operator Theory and Invariant Subspaces" have become classics.
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