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The Science of Conjecture
Author: James Franklin
Publisher: JHU Press
ISBN: 1421418800
Pages: 520
Year: 2015-05-11
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How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk. "A remarkable book. Mr. Franklin writes clearly and exhibits a wry wit. But he also ranges knowledgeably across many disciplines and over many centuries."— Wall Street Journal " The Science of Conjecture opens an old chest of human attempts to draw order from havoc and wipes clean the rust from some cast-off classical tools that can now be reused to help build a framework for the unpredictable future."— Science "Franklin's style is clear and fluent, with an occasional sly Gibbonian aside to make the reader chuckle."— New Criterion James Franklin is a professor in the School of Mathematics and Statistics at the University of New South Wales.
The Science of Conjecture
Author: James Franklin
Publisher: JHU Press
ISBN: 1421418819
Pages: 520
Year: 2015-07-09
View: 485
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How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk. -- Giora Hon
The Science of Conjecture
Author: James Franklin
Publisher: Taylor & Francis
ISBN: 0801871093
Pages: 497
Year: 2002
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"A magisterial acount of matters as diverse as the Talmud, Justinian's Digest, torture, witch hunts, Tudor treason trials, ancient and medieval astronomy and physics, humanist historiography, scholastic philosophy, speculations in public debt, and 17th century mathematics." -- International Journal of Evidence and Proof
Conjectures and Refutations
Author: Karl Popper
Publisher: Routledge
ISBN: 1135971374
Pages: 608
Year: 2014-05-01
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Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.
The Art of Conjecture
Author: Bertrand de Jouvenel
Publisher: Routledge
ISBN: 1351305662
Pages: 325
Year: 2017-09-29
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Commissions of experts regularly meet to reply to questions such as: What will be the population of the country, or even of our planet, in ten, fifteen or twenty-five years? In what proportion will production have increased, what modifications will its composition and utilizations have undergone? The attraction of efforts to forecast the future continues. That is a fact. How does it proceed? That is a problem, one on which de Jouvenel focuses on in this book. The Art of Conjecture clearly explains what the "study of the future" can mean. De Jouvenel emphasizes the logical and political problems of forecasting and discusses methods in economics, sociology, and political science by which the future can be studied. More importantly, he discusses the fallacies to which the "study of the future" is peculiarly likely to give rise. The author argues that it is natural and necessary for the population to have visions of the future. Without this, he states, we would only be able to set one opinion of the future against another. If the origins and meanings of these predictions remained obscure, only the event could decide among the opinions. If any man can be said to have created the serious "study of the future" in our time, it is Bertrand de Jouvenel. Futuribles, a periodical he created, continues to represent a major turning point in contemporary social science. Jouvenel aimed to show how "the art of conjecture" could inform prudential judgment and allow citizens and statesmen to detect troubles before they arise.
Darwin's Conjecture
Author: Geoffrey M. Hodgson, Thorbjørn Knudsen
Publisher: University of Chicago Press
ISBN: 0226346900
Pages: 290
Year: 2010-12-01
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Of paramount importance to the natural sciences, the principles of Darwinism, which involve variation, inheritance, and selection, are increasingly of interest to social scientists as well. But no one has provided a truly rigorous account of how the principles apply to the evolution of human society—until now. In Darwin’s Conjecture, Geoffrey Hodgson and Thorbjørn Knudsen reveal how the British naturalist’s core concepts apply to a wide range of phenomena, including business practices, legal systems, technology, and even science itself. They also critique some prominent objections to applying Darwin to social science, arguing that ultimately Darwinism functions as a general theoretical framework for stimulating further inquiry. Social scientists who adopt a Darwinian approach, they contend, can then use it to frame and help develop new explanatory theories and predictive models. This truly pathbreaking workat long last makes the powerful conceptual tools of Darwin available to the social sciences and will be welcomed by scholars and students from a range of disciplines.
Uncle Petros and Goldbach's Conjecture
Author: Apostolos Doxiadis
Publisher: Faber & Faber
ISBN: 057129569X
Pages: 224
Year: 2012-11-15
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Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.
The Poincare Conjecture
Author: Donal O'Shea
Publisher: Bloomsbury Publishing USA
ISBN: 0802718949
Pages: 304
Year: 2009-05-26
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Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.
The Art of Causal Conjecture
Author: Glenn Shafer
Publisher: MIT Press
ISBN: 026219368X
Pages: 511
Year: 1996
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In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy.The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes and high levels of precision in the measurement of their effects. The practical sciences--medicine, business, engineering, and artificial intelligence--must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both of these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making in the practical sciences.Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government, and science. The Art of Causal Conjecture shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated, and confronted by statistical evidence.
The Smith Conjecture
Publisher: Academic Press
ISBN: 0080874312
Pages: 240
Year: 1984-05-01
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The Smith Conjecture
Conjecture and Proof
Author: Miklós Laczkovich
Publisher: Cambridge University Press
ISBN: 0883857227
Pages: 118
Year: 2001-01-01
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How to prove interesting and deep mathematical results from first principles, with exercises.
Markov's Theorem and 100 Years of the Uniqueness Conjecture
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3319008889
Pages: 257
Year: 2013-07-18
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This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Mathematical Reasoning
Author: Raymond Nickerson
Publisher: Taylor & Francis
ISBN: 1136945393
Pages: 595
Year: 2011-06-23
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The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores a vast range of psychological questions related to mathematical cognition, and provides fascinating insights for researchers and students of cognition and instructors of mathematics.
Etale Cohomology and the Weil Conjecture
Author: Eberhard Freitag, Reinhardt Kiehl
Publisher: Springer Science & Business Media
ISBN: 3662025418
Pages: 320
Year: 2013-03-14
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Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to publish the book in English. We had the good fortune that Professor W. Waterhouse and his wife Betty agreed to translate our manuscript. We want to thank them very warmly for their willing involvement in such a tedious task. We are very grateful to the staff of Springer-Verlag for their careful work.
The Local Langlands Conjecture for GL(2)
Author: Colin J. Bushnell, Guy Henniart
Publisher: Springer Science & Business Media
ISBN: 354031511X
Pages: 340
Year: 2006-08-29
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The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

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