Uber Schaaren von quadratischen und bilinearen Formen + Uber die congruenten Transformationen der bilinearen Formen

1874. Kronecker, Leopold (1823-91). (1) Uber Schaaren von quadratischen und bilinearen Formen. Offprint from Monatsbericht der K. Akad. Wissensch. Berlin (Jan.-Mar. 1874). 55, [1]pp. (2) Uber die congruenten Transformationen der bilinearen Formen. Offprint from ibid. (April 1874). 53, [1]pp. Together 2 offprints, 8vo. 226 x 137 mm. Original tan printed wrappers, a little dust-soiled. Light toning, but very good. First Separate Editions. Kronecker was part of a formidable group of Berlin mathematicians whose members also included Kummer, Borchardt and Weierstrass.

"Kronecker's greatest mathematical achievements lie in his efforts to unify arithmetic, algebra, and analysis, and most particularly in his work on elliptical functions. His boundary formulas are particularly noteworthy in this regard, since they laid bare the deepest relationships between arithmetic and elliptical functions and provided the basis for Erich Hecke's later analytic-arithmetical investigations. Kronecker also introduced a number of formal refinements in algebra and in the theory of numbers, and many new theorems and concepts" (DSB).

Kronecker was the first of the intuitionists, a school of mathematicians that opposed the theory of irrational numbers, continuous functions and transcendental numbers. Kronecker's mathematical philosophy is best expressed in his famous quotation: "God made the integers; all else is the work of Man." Kline, Mathematical Thought, p. 1197.

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