In this fascinating study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings. While previous architectural studies have searched for abstract 'universal rules' to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture. Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge. Highly illustrated with plans, diagrams and figures, this book is essential reading for all scholars of Ancient Egypt and the architecture of ancient cultures.

Dyma gyfrol sy’n croniclo bywyd a gwaith Griffith Davies (1788–1855), o’i blentyndod tlawd yn ardal chwareli Arfon i’w waith fel sefydlydd ysgolion mathemateg yn Llundain cyn gosod sylfaen i’r proffesiwn actiwari. Tri mis yn unig o addysg ffurfiol a dderbyniodd Davies, a dyna pryd y sylweddolwyd fod ganddo allu rhyfeddol mewn mathemateg. Mentrodd i Lundain, ac ar ôl blynyddoedd wedi ymroi i hunan ddysgu cyhoeddodd lyfrau mewn mathemateg, ac yn y pen draw fe’i penodwyd yn brif actiwari i gwmni yswiriant Guardian yn y ddinas. Wrth i’w yrfa ddatblygu, daeth yn Gymrawd o’r Gymdeithas Frenhinol a derbyniodd glod ac anrhydeddau am ei waith. Bu’n weithgar ym mywyd Cymraeg Llundain gan sefydlu cyfres o ddarlithoedd gwyddonol yn ei famiaith, ac ymgyrchodd yn llwyddiannus dros hawliau tyddynwyr bro ei febyd a thros addysg i’w gyd-wladwyr. Mae hanes bywyd Griffith Davies yn stori sy’n ysbrydoli.

This is a study and translation of the Zhou bi suan jing, a Chinese work on astronomy and mathematics which reached its final form around the first century AD. The author provides the first easily accessible introduction to the developing mathematical and observational practices of ancient Chinese astronomers and shows how the generation and validation of knowledge about the heavens in Han dynasty China related closely to developments in statecraft and politics. The book will be of equal interest to historians of science and those studying the history of Chinese culture.

The Soviet school, one of the glories of twentieth-century mathematics, faced a serious crisis in the summer of 1936. It was suffering from internal strains due to generational conflicts between the young talents and the old establishment. At the same time, Soviet leaders (including Stalin himself) were bent on ``Sovietizing'' all of science in the USSR by requiring scholars to publish their works in Russian in the Soviet Union, ending the nearly universal practice of publishing in the West. A campaign to ``Sovietize'' mathematics in the USSR was launched with an attack on Nikolai Nikolaevich Luzin, the leader of the Soviet school of mathematics, in Pravda. Luzin was fortunate in that only a few of the most ardent ideologues wanted to destroy him utterly. As a result, Luzin, though humiliated and frightened, was allowed to make a statement of public repentance and then let off with a relatively mild reprimand. A major factor in his narrow escape was the very abstractness of his research area (descriptive set theory), which was difficult to incorporate into a propaganda campaign aimed at the broader public. The present book contains the transcripts of five meetings of the Academy of Sciences commission charged with investigating the accusations against Luzin, meetings held in July of 1936. Ancillary material from the Soviet press of the time is included to place these meetings in context.

What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area?

By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot.

Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, "When Least Is Best" is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

Volume 2.3, containing the Greek translations of books II-IV, completes the edition of the Conica of Apollonius of Perga. It is arranged according to the same principle as the previous volume on book I: the critical edition of the Greek text is accompanied by numerous notes and a lexicon of all mathematical terms. An introduction and a French translation provide further insights into the text. The edition of the Greek books of the Conica will be thematically complemented by volume 3 of the SGA series, containing the critical edition of Eutocius of Ascalon's commentary on the Conica and its French translation.

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009.

Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.

As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.

This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine.

The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging."

This work documents the history of techniques that statisticians have used to manipulate economic, meteorological, biological and physical data taken from observations recorded over time. The manipulation tools include per cent change, index numbers, moving averages and 'first differences', i.e., subtracting one observation from the previous value. Professor Klein argues that nineteenth-century business journals, such as The Economist, were as important to the development of time series analysis as Latin treatises on probability theory. While examining the roots of mathematical statistics in commercial practice, she traces changes in analytical forms from table to graph to equation. Klein cautions that we risk measurement without history in unduly mechanistic blending of stationary probability theory with the practical dynamics of commercial traders. This history is accessible to students with a basic knowledge of statistics as well as financial analysts, statisticians and historians of economic thought and science.

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. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last--this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.

When John Napier published his invention of logarithms in 1614 he was announcing one of the greatest advances in the history of mathematics, and log tables were used universally until the mid 1970s. With his Rabdologia, an ingenious calculating tool composed of numbered rods which came to be known as 'Napier's Bones', he enabled people in the marketplace to do multiplication sums without knowing any multiplication tables. Perhaps the most extraordinary thing about this most extrordinary man was that his great inventions were made without the stimulus of talking to other mathematicians in mainstream Europe. Working away in comparative isolation in a tower house in Scotland, Napier produced methods of calculation that literally changed lives all over the world. He is the father of the slide-rule and the grandfather of today's calculators. Despite his achievements, he remains curiously uncelebrated, and this absorbing story of his life aims to give John Napier his true status. This new edition has been redesigned in a new format and has a new cover.

Charles Babbage (1791–1871) is today remembered mainly for his attempt to complete his difference and analytical engines, the principles of which anticipate the major ideas of the modern digital computer. This book describes the evolution of Babbage’s work on the design and implementation of the engines by means of a detailed study of his early mathematical investigations. Babbage is an almost legendary figure of the Victorian era, yet relatively little is known about him and no authoritative account of his life and work has appeared. He was primarily a mathematician and his early working life was devoted mainly to the study of pure mathematics. While containing much biographical information, this book concentrates on this crucial aspect of Babbage’s work.

This book provides a way to understand a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests on a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.

How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? Experience shows that disentangling scientific knowledge from opinion is harder than one might expect. Full of illuminating examples and quotations, and with a scope ranging from psychology and evolution to quantum theory and mathematics, this book brings alive issues at the heart of all science.

An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. It was also the era of new math. Introduced to US schools in the late 1950s and 1960s, the new math was a curricular answer to Cold War fears of American intellectual inadequacy. In the age of Sputnik and increasingly sophisticated technological systems and machines, math class came to be viewed as a crucial component of the education of intelligent, virtuous citizens who would be able to compete on a global scale. In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period's political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students' calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American by the numbers.

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic's background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.