Landau, Edmund

(b. Berlin, Germany, 14 February 1877; d. Berlin, 19 February 1938)

mathematics.

Landau was the sone of the gynecologist Leopold Landau and the former Johanna Jacoby. He attended the “Französische Gymnasium” in Berlin and then studied mathematics, primary also in Berlin. He worked mostly with George Frobenius and received his doctorate in 1899. Two years later he obtained the venia legendi, entitling him to lecture. He taught at the University of Berlin until 1909 and then became full professor at the University of Göttingen, succeeding Hermann Minkowski. David Hilbert nd Felix Klein were his colleagues. Landau was active Göttingen, until forced to stop etching by the National Socialist regime. After his returen to Berlin he lectured only outside of Germany, for example, in Cambridge in 1935 and in Brussels in 1937, shortly before his sudden death.

Landau was a member of several German academies, of the academies of St. Petersburg (now Leningrad) adn Rome, and an honorary member of the London Mathematical Society. In 1905 he married Marianne Ehrlich, daughter of Paul Ehrlich; they had two daughters adn one son.

Landua’s principal field of endeavor was analytic number theory and, inparticular, the distribution of prime numbers. In 1796 Gauss had conjectured the prime number theorem: If π(x) designates teh number of prime numbers below x, then π(x) is asymptotically equal to x/log x, i.e., as x→∞, the quotient of π(x) adn x/log x approaches 1. This theorem ws demonstrated in 1896 by Hadamard and de la Vallée-Poussin, working independently of each other. In 1903 Landau presented a new, fundamentally simpler proof, which, moreover, allowed the prime number theorem and a refinement made by de la Vallée-Poussin to be applied to the distribution of ideal primes in algebraic number fields. In his two volume Handbuch der Lehre von der Verteilung der Primazahlen (1909), Landau gave the first systematic presentation of analytic number theory. For decades it was indispensable in research and teaching and remains an important historical document. His three-volume Vorlesungen über Zahlentheorie (1927) provided an extremely comprehensive presentation of the various branches of number theory from its elements to the contemporary state of research.

Besides two further books on number theory, Landau was author of Darstellung und Begründung einiger neuerer Ergebnisse der Frunktionentheorie, which contains a collection of interesting and elegant theorems of the theory of analytic functions of a single variable. Landau himself discovered some of the theorems adn demonstrated others in a new and simpler fashion. In Grundlagen der Analysis he established arithmetic with whole, rational, irrational, and complex numbers, starting from Peano’s axioms for natural numbers. Also improtant is Einführung in die Differentialrechnung und Integralrechnung.

Written with the greatest care, Landau’s books are characterized b;y; argumentation which is complete, and as simple as possible. The necessary prerequisite knowledge is provided, and the reader is led securely, step by step, to the goal. The idea of the proof and teh general relationship are, to be sure, not always clearly apparent, especially in his later works, which are written in an extremely terse manner—the so-called Landau style. Through his books and his more than 250 papers Landau exercised a great influence on the whole developmet of number theory in is time. He was an enthusiastic teacher and sought contact with fellow scientists. Harald Bohr and G. H. Hardy were often his guests in Göttingen.

BIBLIOGRAPHY

I. Original Works. Landau was the author more than 250 papers published in various journals. His books are Handbuch der Lehre von der verteilung der Primzahlen 2 vols. (Leipzig-Berlin, 1909); Darstellung und Begrüundung einiger neuerer Ergebnisse der Funktionentheorie (Berlin, 1916; 2nd ed., 1929); Einführung in die elementare und analytische Theorie der algebraischen Zahlen und Ideale, (Leipzig-Berlin, 918; 2nd ed., 1927); Vorlesungen über Zahlentheorie, 3 vols. (Leipzig, 1927); Grundlagen der Analysis (Leipzig, 1930); Einführung in die Differential-rechnung und Integralrechnung (Groningen, 1934); über eilnige Forstchritte der additiven Zahlentheorie (Cambridge, 1937).

II. Secondary Literature. A biography with portrait is in Reichshandbuch der deutschen Gesellschaft, II (Berlin, 1931), 1060; sec also the obituaries in Nachrichten vonder Gesellschaft der Wissenschaftern zu Göttingen for 1937–1938, 10; by J. H. Hardy and Heilbronn in Journal of the London Mathematical Society, 13 (1938), 302–310; and by Konrad Knopp in Jahresberichte der Deutschen Mthematiker-vereinigung, 54 (1951), 55–62.

Bruno Schoeneberg