Jens Høyrup - Böcker

In the 1920s it was recognized, largely as a result of work by Otto Neugebauer and his colleagues that Babylonian cuneiform texts included many mathematical texts. These were chiefly concerned with metrology and computation, but some also appeared to deal with algebra. But then, what could have been the reasons that induced the Babylonians to work on, for example, second-degree equations? In this new examination of the texts, Jens Hoyrup proposes a different interpretation, based on the fact that the tablets are almost entirely students' workbooks. The knowledge of mathematics expressed in these tablets is entirely "practical," for use in surveying, accounting, and building, rather than theoretical. Hoyrup argues that the notion of algebraic manipulation, like other parts of a theoretical mathematics is indeed a later invention. Craftsmen, he argues, prefer to know how to solve a problem, rather than why the answer will be true, and it is only the latter attitude that characterizes mathematics; the former is, perhaps, more akin to modern engineering. The book provides a detailed reading of many tablets and a careful examination of the context in which they were produced.

In this examination of the Babylonian cuneiform "algebra" texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens Høyrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice.

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice.

The abbacus was a thorough and complete system of arithmetical calculations, which saw its dawn in the Indian and Arabic tradition of the Middle Ages, but which was developed in its fully fledged aspects especially in Italy, between Genoa, Milan, Venice and the region of Umbria.

The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Viète's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps.

This book is the first of a three-volume set introducing the history of scientific thought (including social and human science). The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

This book is the first of a three-volume set introducing the history of scientific thought (including social and human science). The area covered in this volume is ancient Mesopotamia, classical Antiquity and the Islamic Middle Ages. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

This book is the second of a three-volume set introducing the history of scientific thought (including social and human science) and covers the Latin Middle Ages, the Renaissance period, and the 17th century.

This book is the second of a three-volume set introducing the history of scientific thought (including social and human science) and covers the Latin Middle Ages, the Renaissance period, and the 17th century. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

This book is the third of a three-volume set introducing the history of scientific thought (including social and human science). The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

This book is the third of a three-volume set introducing the history of scientific thought (including social and human science). The area covered in this volume is Western Europe during the 18th and 19th centuries. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

Volume I introduces the history of scientific thought (including social and human science). The area covered in this volume is ancient Mesopotamia, classical Antiquity and the Islamic Middle Ages. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts. Volume II introduces the history of scientific thought (including social and human science) and covers the Latin Middle Ages, the Renaissance period, and the 17th century. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts. Volume III introduces the history of scientific thought (including social and human science). The area covered in this volume is Western Europe during the 18th and 19th centuries. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

Mathematics has for centuries been stimulated, financed and credited by military purposes. Some mathematical thoughts and mathematical technology have also been vital in war. During World War II mathematical work by the Anti-Hitler coalition was part of an aspiration to serve humanity and not help destroy it. At present, it is not an easy task to view the bellicose potentials of mathematics in a proper perspective.The book presents historical evidence and recent changes in the interaction between mathematics and the military. It discusses the new mathematically enhanced development of military technology which seems to have changed the very character of modern warfare.

This book deals with one of the earliest surviving "abbacus" treatises, one that is by far more orderly than any of the extant predecessors and is also the first to contain a presentation of algebra. The book contains an edition and an English translation of a manuscript from c. 1450. In addition, it features an extensive discussion of the contents of the treatise and its location within early abbacus culture.