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Constantin Carathéodory - Mathematics and Politics in Turbulent Times is the biography of a mathematician, born in Berlin in 1873, who became famous during his life time, but has hitherto been ignored by historians for half a century since his death in 1950, in Munich. In a thought-provoking approach, Maria Georgiadou devotes to Constantin Carathéodory all the attention such a personality deserves. With breathtaking detail and the appropriate scrutiny she elucidates his oeuvre, life and turbulent political and historical surroundings. A descendant of the the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a life of effort to mathematics and education. He studied and embarked on an international academic career, haunted by wars, catastrophes and personal tragedies. Over the last years of his life, he stayed in Munich despite World War II, an ambiguous decision upon which the author sheds unprecedented light. Carathéodory's most significant mathematical contributions were to the calculus of variations, the theory of point set measure and the theory of functions of a real variable, pde's, also to complex function theory. The interdisciplinary nature of the text allows easy access for both scholars and readers with a general interest in mathematics, politics and history. The thoroughness of the author’s research and evaluations is certain to leave everyone impressed and more knowledgeable. .

Carathéodory, Constantin --- Mathematicians --- Caratheodory, Constantin, --- Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematicians - Greece - Biography --- Caratheodory, Constantin, - 1873-1950

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Volume II focuses on notes for lectures on the foundations of the mathematical sciences held by Hilbert in the period 1894-1917. They document Hilbert's first engagement with 'impossibility' proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his work on geometry in the 1890s; his engagement with foundational problems raised by the work of Cantor and Dedekind; his early investigations into the relationship between arithmetic, set theory, and logic; his advocation of the use of the axiomatic method generally; his first engagement with the logical and semantical paradoxes; and, the first formal attempts to develop a logical calculus. The Volume also contains Hilbert's address from 1895 which formed the preliminary version of his famous "Zahlbericht" (1897).

Mathematics. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical. --- Mathématiques --- Logique symbolique et mathématique --- Knowledge, Theory of --- Physics --- Quantum theory --- Relativity (Physics) --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Epistemology --- Theory of knowledge --- Philosophy --- Psychology

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From the reviews of the first edition: "There are many books on the history of mathematics in which mathematics is subordinated to history. This is a book in which history is definitely subordinated to mathematics. It can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience...we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer) "The discussion is at a deep enough level that I suspect most trained mathematicians will find much that they do not know, as well as good intuitive explanations of familiar facts. The careful exposition, lightness of touch, and the absence of technicalities should make the book accessible to most senior undergraduates." (American Mathematical Monthly) "...The book is a treasure, which deserves wide adoption as a text and much consultation by historians and mathematicians alike." (Physis - Revista Internazionale di Storia della Scienza) "A beautiful little book, certain to be treasured by several generations of mathematics lovers, by students and teachers so enlightened as to think of mathematics not as a forest of technical details but as the beautiful coherent creation of a richly diverse population of extraordinary people...His writing is so luminous as to engage the interest of utter novices, yet so dense with particulars as to stimulate the imagination of professionals." (Book News, Inc.) This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises expalining how they relate to the preceding section, and how they foreshadow later topics. The index has been given added structure to make searching easier, the references have been redone, and hundreds of minor improvements have been made throughout the text.

51:93 --- 93 --- algebra --- complexe getallen --- functieleer --- getallenleer --- mechanica --- meetkunde --- oneindige reeksen --- rekenkunde --- topologie --- vergelijkingen --- wiskunde --- Mathematics --- 51 <09> --- 51 --- 51 Mathematics --- Math --- Science --- History --- Mathematics--Geschiedenis van .. --- History. --- Mathématiques --- Histoire --- Histoire. --- 51 Wiskunde. Mathematiek --- Wiskunde. Mathematiek --- Mathematics. --- Geometry. --- Number theory. --- Mathematical analysis. --- Analysis (Mathematics). --- History of Mathematical Sciences. --- Number Theory. --- Analysis. --- Annals --- Auxiliary sciences of history --- 517.1 Mathematical analysis --- Mathematical analysis --- Number study --- Numbers, Theory of --- Algebra --- Euclid's Elements --- Mathematics--Geschiedenis van . --- Mathematics--Geschiedenis van --- Mathematics - History --- Mathématiques