Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical PracticeStanford University Press, 2002 - 293 pagina's This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the sixteenth century. Leading mathematicians like Hariot, Stevin, Galileo, and Cavalieri began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. As enterprising explorers in search of treasures of knowledge, these mathematicians described themselves as sailing the treacherous seas of mathematics, facing shipwreck on the shoals of paradox, and seeking shelter and refuge on the shores of geometrical demonstrations. Mathematics, formerly praised for its logic, clarity, and inescapable truths, was for them a hazardous voyage in inhospitable geometrical lands. Significantly, many of the same practitioners who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period--the infinitesimal methods. This was no coincidence: the heroic tales of exploration and discovery helped shape a new form of mathematical practice, complete with new questions, new acceptable answers, and new standards of evidence. It was this new vision of mathematics as a grand adventure that allowed for the development of the new techniques that led to the Newtonian calculus. In demonstrating this, the book moves from real voyages to imaginary ones, from the coasts of the Canadian Arctic to the tropical forests of Guyana, and from the inner structure of matter to the intricacies of the mathematical continuum. Throughout, a common rhetoric and imagery of exploration and discovery run like a thread through these diverse elements and bind them together. |
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Achilles America approach atoms B.L. Add Bacon Baffin Island Blundeville Bonaventura Cavalieri Briefe and True Briggs Briggs's British Library calculate Cavalieri Chapter claim coast Columbus composed crusade discussion Dorado early modern Elizabethan English equiangular spiral Evangelista Torricelli expedition exploration and discovery Frobisher Frobisher's Galileo gold Guyana Hakluyt hidden secrets Ibid imagery infinite number Infinitis interior islands John John Dee John Wallis Kepler Keymis knowledge labyrinth latitude lines London mathe mathematical practitioners mathematicians matical medium Mercator Mercator projection Meta Incognita method of exhaustion method of indivisibles narrative of exploration Northwest Passage obstacles optical Oughtred Oxford paradox Petworth House Philosophy problem radius vectors Raleigh refraction rhetoric of exploration rhumb Richard Hakluyt riches rivers Science secrets of nature standard narrative Stevin strait structure tale of exploration Thomas Hariot tion Torricelli traditional treatise triangles True Report truth University Press Virginia voyages Wallis William Oughtred