When Sir Cyril Burt died in 1971, he was widely recognized as Britain's most eminent educational psychologist whose studies of gifted and delinquent children, contributions to the development of factor analysis, and research on the inheritance of intelligence brought widespread acclaim. Within five years of his death, however, he was publicly denounced as a fraud who had fabricated data to conclude that intelligence is genetically determined. Examiners of the published data found serious inconsistencies that raised questions about their authenticity; the case has divided the scientific community ever since. Were the charges justified, or was he a victim of critics fearful of validating such a politically unacceptable scientific theory? This is an up-to-date and unbiased analysis of one of the most notorious scandals in science, now more timely and widely discussed than ever with the publication of The Bell Curve, the best-selling polemic that raises arguments comparable to Burt's. The distinguished contributors examine the controversial areas of Burt's work and argue that his defenders have sometimes, but by no means always, been correct, and that his critics have often jumped to hasty conclusions. In their haste, however, these critics have missed crucial evidence that is not easily reconciled with Burt's total innocence, leaving the perception that both cases are seriously flawed. An introductory chapter lays the background to the case, followed by an examination of Burt's work that relates to the controversy. The book concludes with a chapter on Burt's character, other cases of apparent scientific fraud, and the impact of Burt's alleged fabrications. These findings have profound implications not only for the study of psychology, but for the wider issues relating to integrity in scientific research, and the impact of intelligence testing on social policy.

Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.

Ancient Greek Philosophy routinely relied upon concepts of number to explain the tangible order of the universe. Plotinus' contribution to this tradition, however, has been often omitted, if not ignored. The main reason for this, at first glance, is the Plotinus does not treat the subject of number in the Enneads as pervasively as the Neopythagoreans or even his own successors Lamblichus, Syrianus, and Proclus. Nevertheless, a close examination of the Enneads reveals that Plotinus systematically discusses number in relation to each of his underlying principles of existence--the One, Intellect, and Soul. Plotinus on Number offers the first comprehensive analysis of Plotinus' concept of number, beginning with its origins in Plato and the Neopythagoreans and ending with its influence on Porphyry's arrangement of the Enneads. It's main argument is that Plotinus adapts Plato's and the Neopythagoreans' cosmology to place number in the foundation of the intelligible realm and in the construction of the universe. Through Plotinus' defense of Plato's Ideal Numbers from Aristotle's criticism, Svetla Slaveva-Griffin reveals the founder of Neoplatonism as the first post-Platonic philosopher who purposefully and systematically develops what we may call a theory of number, distinguishing between number in the intelligible realm and number in the quantitative, mathematical realm. Finally, the book draws attention to Plotinus' concept as a necesscary and fundamental linke between Platonic and late Neoplatonic schools of philosophy.

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practice it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.
The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. This Handbook will be a vital reference for graduates and researchers in mathematics, historians of science, and general historians.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

In Between Tradition and Innovation, Ad Meskens traces the profound influence of a group of Flemish Jesuits on the course of mathematics in the seventeenth century. Using manuscript evidence, this book argues that one of the Flemish mathematics school's professors, Gregorio a San Vicente (1584-1667), had developed a logically sound integration method more than a decade before the Italian mathematician Bonaventura Cavalieri. Although San Vincente's superiors refused to grant him permission to publish his results, his methods went on to influence numerous other mathematicians through his students, many of whom became famous mathematicians in their own right. By carefully tracing their careers and outlining their biographies, Meskens convincingly shows that they made a number of ground-breaking contributions to fields ranging from mathematics and mechanics to optics and architecture.

This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics.   Some of the topics explored include Arabic editions of Euclid’s Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual tradition Portuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica  A Cambridge correspondence course in arithmetic for women in England in the late nineteenth century The mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet  The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literature The use of Latin squares for agricultural crop experiments at the Rothamsted Experimental Station The many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960s The volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

This book studies the Dutch mathematician Simon Stevin (1548-1620) as a new type of 'man of knowledge'. Traditionally, Stevin is best known for his contributions to the 'Archimedean turn'. This innovative volume moves beyond this conventional image by bringing many other aspects of his work into view, by analysing the connections between the multiple strands of his thinking and by situating him in a broader European context. Like other multi-talents ('polymaths') in his time (several of whom are discussed in this volume), Stevin made an important contribution to the transformation of the ideal of knowledge in early modern Europe. This book thus provides new insights into the phenomenon of 'polymaths' in general and in the case of Stevin in particular.

A fascinating look into how the transformative joys of mathematical experience are available to everyone, not just specialists

Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from René Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have “no special talent,” they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination.

David Bessis guides us on an illuminating path toward deeper mathematical comprehension, reconnecting us with the mental plasticity we experienced as children. With simple, concrete examples, Bessis shows how mathematical comprehension is integral to the great learning milestones of life, such as learning to see, to speak, to walk, and to eat with a spoon.

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives. Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies.