Böcker i Sources and Studies in the History of Mathematics and Physical Sciences-serien

Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old.The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''

Goedel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers.

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. the third deals with the status of mathematical objects and the problem of mathematical generality;

This volume aims to make Stephen of Pisa and Antioch's work on the celestial sciences accessible to a wider readership, providing not just the text but a translation and introduction as well. It is split into two parts: the first provides an extensive introduction to Stephen and his work, while the second features the edition and translation.

The science of magic squares witnessed an important development in the Islamic world during the Middle Ages, with a great variety of construction methods being created and ameliorated.

It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh-which together constitute the third unpublished part of their History of Hindu Mathematics-that were revised and updated by Prof.

This book on focuses on the work of Ferdinand Frobenius in linear algebra, its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. Also covers the Berlin school of mathematics and the guiding force of Weierstrass.

This volume contains the texts and translations of two Arabic treatises on magic squares, which are undoubtedly the most important testimonies on the early history of that science.

Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today.

This book provides the first critical edition of Ibn al-Haytham's On the Shape of the Eclipse with English translation and commentary, which records the first scientific analysis of the camera obscura.

The book will be of particular interest to scholars engaged in the study of Islamic theoretical astronomy, but is accessible to a general readership interested in learning what constituted an introduction to Ptolemaic astronomy in Islamic lands.

This book details the history of complex function theory. It examines the rise of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables.

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich.

This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. Coverage extends to the historical development of analytical probability theory and its tools.

"The Almagest", by the Greek astronomer and mathematician Ptolemy, is the most important surviving treatise on early mathematical astronomy, offering historians valuable insight into the astronomy and mathematics of the ancient world. This title provides students of the history of astronomy with a self-contained introduction to the "Almagest".

The discovery of a gradual acceleration in the moon's mean motion by Edmond Halley in the last decade of the seventeenth century led to a revival of interest in reports of astronomical observations from antiquity.

This is the second and final volume of Dutch physicist Hendrik Antoon Lorentz's scientific correspondence with Dutch colleagues, including Pieter Zeeman and Paul Ehrenfest.

This book provides a critical edition, translation, and study of the version of Euclid's treatise made by Thabit ibn Qurra, which is the earliest Arabic version that we have in its entirety.

This book covers the works of Bhaskara, in particular, his monumental treatise on astronomy, the Siddhantasiromani, his astronomical handbook, the Karanakutuhala, and his two mathematical treatises, the Lilavati and the Bijaganita, on arithmetic and algebra, respectively.

This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry;

This book provides a critical edition, translation, and study of the version of Euclid's treatise made by Thabit ibn Qurra, which is the earliest Arabic version that we have in its entirety.

This is the second and final volume of Dutch physicist Hendrik Antoon Lorentz's scientific correspondence with Dutch colleagues, including Pieter Zeeman and Paul Ehrenfest.

Here is a selection of more than 400 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz, covering the period from 1883 until just before his death. The letters have been selected primarily according to scientific interest.

First published in 1202, Fibonacci's Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.