Edmund Landau

“It is one thing to reflect, as Bieberbach did, for instance on the relative pedagogical merit of different ways to introduce π in a calculus class: geometrically via the circle, or in Landau's way via the zeroes of the cosine, with this function being defined by the power series. And it is quite a different matter to use such reflections as a basis for the forced removal of a distinguished colleague from teaching. Bieberbach's behaviour came all the more as a shock as nothing in his previous biography seemed to prepare one for it...”

“The present work is inspired by Edmund Landau's famous book, Handbuch der Lehre von der Verteilung der Primzahlen, where he posed two extremal questions on cosine polynomials and deduced various estimates on the distribution of primes using known estimates of the extremal quantities. Although since then better theoretical results are available for the error term of the prime number formula, Landau's method is still the best in finding explicit bounds. In particular, Rosser and Schonfeld used the method in their work "Approximate formulas for some functions of prime numbers".”

“The thorough analysis of even simple problems in arithmetic may require the application of advanced mathematics. A striking example is that of the distribution of prime numbers. The solution of this problem lies in finding a general formula which tells us the number of primes that lie in any given numerical interval. ...Edmond Landau ...wrote two large volumes analyzing this problem without solving it, using the most advanced mathematics known at the time. Even in the elementary aspects of mathematics we are thus dealing with complex topics which make great demands on our mathematical skills.”

“Not only the physical but also the intellectual landscape of German-language mathematics in the early 1930s would be impossible to imagine without German-Jewish mathematicians. Indeed, some fields of mathematics were completely transformed by their contributions. Number theory was transformed by Hermann Minkowski and Edmund Landau, algebra by Ernst Steinitz and Emmy Noether, set theory and general topology by Felix Hausdorff, Abraham Fraenkel and several others—to mention but a few examples.”

“My book is written, as befits such easy material, in merciless telegram style ("Axiom," "Definition," "Theorem," "Proof," occasionally "Preliminary Remark")... I hope I have written this book in such a way that a normal student can read it in two days. And then (since he already knows the formal rules from school) he may forget its contents.”

“The multiplication table will not occur in this book, not even the theorem,{{center/s}}2 \cdot 2 = 4,{{center/e}}but I would recommend, as an exercise, that you define{{center/s}}2 = 1 + 1,4 = (((1 + 1) + 1) + 1){{center/e}}and then prove the theorem.”

“I will ask of you only the ability to read English and to think logically—no high school mathematics, and certainly no higher mathematics.”

“Please don't read the preface for the teacher.”

“Bitte vergiß alles was Du auf der Schule gelernt hast; denn Du hast es nicht gelernt.”

“Wir Mathematiker sind alle ein bißchen meschugge.”

“Die Zahlentheorie ist nützlich, weil man mit ihr promovieren kann.”