A lively activity: To do mathematics

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

A chapter in The Beauty of Doing Mathematics, 1985, pp 29-69 from Springer

Abstract: Summary Interest in solving equations in integers or rational numbers dates back from antiquity. I tried to show some fundamental problems which are still unsolved. Euclid and Diophantus already solved the equation a2 + b2 = c2, and gave a formula for all the solutions. The next hardest equation like y2 = x3 + ax + b has given rise to very great problems which have been at the center of mathematics since the 19th century. No one knows how to give an effective method for finding all solutions. I described some of the structures which the solutions have, and the context in which one would like to find such a method.

Keywords: High School Student; Rational Number; Rational Point; Integral Point; Elliptic Curf (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1102-0_2

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DOI: 10.1007/978-1-4612-1102-0_2

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