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How to cite abstract = ^n$, che si suppongono familiari al lettore. The result is possibly a "demanding" reading, not necessarily "recreational", but which, in our intentions, should reward the reader with a quite faithful image of these extraordinary intellectual achievements, individual and collective, composing one of the greatest and deepest pages of the history of mathematics. In the limits and possibilities of a review paper, we wanted to present in a mathematically satisfactory way at least some of the crucial notions and ideas, starting from the precise formulation of the conjecture, using only basic concepts of linear algebra, geometry and differential calculus in the Euclidean space ℝ n, that should be familiar to the reader. Our aim is to present, at least partially, the great twine of ideas, techniques and concepts developed around the Poincaré conjecture, from its formulation at the beginning of last century to its solution due to Grisha Perelman at the beginning of the new millennium, completing the program based on the Ricci flow of Riemannian metrics on a 3-manifold, outlined and developed by Richard Hamilton since the '80s. Comments are closed.La Congettura di Poincaré e il Flusso di Ricci We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished.
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We demonstrate that the use of these concepts has been problematic in several aspects. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition.
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This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century.
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