Diophant Und Diophantische Gleichungen
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Die Wissenschaft arbeitet kumulativ. In der Mathematik und in den Naturwissenschaften gibt es keine unvollendeten Sympho- nien. �ber Jahrhunderte hinweg k�nnen thematische Problem- kreise ihre Dynamik behalten; im historischen R�ckblick erschei- nen dann lange, zusammenh�ngende Problemketten von einer faszinierenden Kontinuit�t des menschlichen Denkens. Es ist die Befriedigung grundlegender materieller und geistiger Bed�rfnisse der Menschheit, die dem weitgespannten Bogen zwischen Ver- gangenheit und Gegenwart Stabilit�t verleiht. Zugleich und andererseits liegt hierin der Umstand begr�ndet, da wissenschaftliche Fragestellungen der Vergangenheit in die Gegenwart und Zukunft hineinwirken k�nnen. Gerade die f�hren- den 'Wissenschaftler waren sich der Fruchtbarkeit historischen Selbstverst�ndnisses f�r ihre eigenen Forschungen bewu t. Die Abhandlungen von LAGRANGE zum Beispiel geh�ren zu den Kost- barkeiten auch der mathematik-historischen Literatur. Und wie w�ren die Leistungen von EULER und GAUSS, von EINSTEIN und v. LAUE m�glich gewesen ohne die von ihnen selbst vorgenommene Einordnung in eine wissenschaftliche Tradition? Auch die durch- greifenden Revolutionen in der 'Vissenschaft bedeuten nichts an- deres als die dialektische �berwindung eines zuvor best�tigten wissenschaftlichen Tatbestandes. In diesem Sinne stellt die hier dargestellte Geschichte der Dio- phantischen Analysis geradezu einen klassischen Fall aktueller Geschichte der Mathematik dar. Der historische Bogen spannt sich �ber mehr als 17 Jahrhunderte, vom Ausgang der Antike bis zum Beginn des 20. Jahrhunderts, ohne da eine k�nstliche Reaktivierung der Leistungen von DIOPHANT notwendig geworden w�re. 1* 4 Geleitwort Die Autorin des vorgelegten B�chleins ist eine erfahreneund er- folgreiche Historikerin der Mathematik. Frau Prof. Dr. I. G.
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