Number Theory pp 159-308 | Cite as


  • André Weil
Part of the Modern Birkhäuser Classics book series (MBC)


Until the latter part of the seventeenth century, mathematics had sometimes bestowed high reputation upon its adepts but had seldom provided them with the means to social advancement and honorable employment. VIÈTE had made his living as a lawyer, FERMAT as a magistrate; even in Fermat’s days, endowed chairs for mathematics were few and far between. In Italy, the University of Bologna (“lo studio di Bologna”, as it was commonly called), famous throughout Europe, had indeed counted Scipione del FERRO among its professors in the early sixteenth century; but CARDANO had been active as a physician; BOMBELLI was an engineer, and so was Simon STEVIN in the Netherlands. NAPIER, the inventor of logarithms, was a Scottish laird, living in his castle of Merchiston after coming back from the travels of his early youth. Neighboring disciplines did not fare better. COPERNICUS was an ecclesiastical dignitary. Kepler’s teacher MAESTLIN had been a professor in Tübingen, but KEPLER plied his trade as an astrologer and maker of horoscopes. GALILEO’s genius, coupled with his domineering personality, earned him, first a professorship in Padova, then an enviable position as a protégé of the Grand-Duke of Tuscany, which saved him from the worst consequences of his disastrous conflict with the Church of Rome; his pupil TORRICELLI succeeded him as “philosopher and mathematician” to the Grand-Duke, while CAVALIERI combined the Bologna chair with the priorate of the Gesuati convent in the same city.


Number Theory Prime Divisor Diophantine Equation Elliptic Integral Quadratic Residue 


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© Springer Science+Business Media New York 2001

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  • André Weil

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