The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis
The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis

Author: Jacob Bernoulli

Publisher: JHU Press

Published: 2006

Total Pages: 468

ISBN-13: 9780801882357

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"Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability becomes manifest he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers."

The Art of Conjecture
The Art of Conjecture

Author: Clyde Lee Miller

Publisher: CUA Press

Published: 2021-03-12

Total Pages: 206

ISBN-13: 0813234166

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“Learned ignorance,” the recognition that God is beyond us and our knowing capacities is the theological concept for which Nicholas of Cusa is most famous. Despite God’s apparent absence Nicholas offers original ways to think about God that would unite his presence with his absence. He called these proposals “conjectures” (coniecturae). Conjecture and conjecturing are central to the methodology of Nicholas’s philosophical theology and to his thinking about human knowledge. By using concrete examples from the everyday life of his times as symbolic imagery Nicholas makes what we say about God imaginatively available and theoretically plausible. He called such conjectural symbols “aenigmata” (= “symbolic or ‘enigmatic’ conjectures”) because they partially clarify and likewise point to an exact truth that is beyond us. Novel and imaginative, Nicholas’s conjectural examples break with the traditional medieval Aristotelian examples and provide further evidence of his role as a figure bridging medieval and Renaissance thought. Following his earlier book, Reading Cusanus (The Catholic University of America Press, 2003), Clyde Lee Miller here examines and comments on the meaning of “conjecture” in Nicholas of Cusa. The Art of Conjecture: Nicholas of Cusa on Knowledge explores what Nicholas meant by conjecture and its import as demonstrated in his treatises and sermons. Beginning with Nicholas’ On Conjectures, Miller analyzes a series of conjectural symbols and proposals across Nicholas’s less frequently discussed texts and recently published sermons. This early Renaissance thinker offers an original and ground-breaking way of framing speculation in philosophical theology and more generally in philosophy itself.

The Art of Causal Conjecture
The Art of Causal Conjecture

Author: Glenn Shafer

Publisher: MIT Press

Published: 1996

Total Pages: 554

ISBN-13: 9780262193689

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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.

Uncle Petros and Goldbach's Conjecture
Uncle Petros and Goldbach's Conjecture

Author: Apostolos Doxiadis

Publisher: Faber & Faber

Published: 2012-11-15

Total Pages: 148

ISBN-13: 057129569X

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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 Art of Conjecture
The Art of Conjecture

Author: Bertrand de Jouvenel

Publisher: Routledge

Published: 2017-09-29

Total Pages: 325

ISBN-13: 1351305670

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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.

The Weil Conjectures
The Weil Conjectures

Author: Karen Olsson

Publisher: Macmillan + ORM

Published: 2019-07-16

Total Pages: 167

ISBN-13: 0374719632

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A New York Times Editors' Pick and Paris Review Staff Pick "A wonderful book." --Patti Smith "I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge." --Parul Sehgal, The New York Times An eloquent blend of memoir and biography exploring the Weil siblings, math, and creative inspiration Karen Olsson’s stirring and unusual third book, The Weil Conjectures, tells the story of the brilliant Weil siblings—Simone, a philosopher, mystic, and social activist, and André, an influential mathematician—while also recalling the years Olsson spent studying math. As she delves into the lives of these two singular French thinkers, she grapples with their intellectual obsessions and rekindles one of her own. For Olsson, as a math major in college and a writer now, it’s the odd detours that lead to discovery, to moments of insight. Thus The Weil Conjectures—an elegant blend of biography and memoir and a meditation on the creative life. Personal, revealing, and approachable, The Weil Conjectures eloquently explores math as it relates to intellectual history, and shows how sometimes the most inexplicable pursuits turn out to be the most rewarding.

Character Theory and the McKay Conjecture
Character Theory and the McKay Conjecture

Author: Gabriel Navarro

Publisher: Cambridge University Press

Published: 2018-04-26

Total Pages: 253

ISBN-13: 1108428444

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Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

Catalan's Conjecture
Catalan's Conjecture

Author: René Schoof

Publisher: Springer Science & Business Media

Published: 2010-07-08

Total Pages: 125

ISBN-13: 1848001851

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Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.

Rational Points and Arithmetic of Fundamental Groups
Rational Points and Arithmetic of Fundamental Groups

Author: Jakob Stix

Publisher: Springer

Published: 2012-10-19

Total Pages: 257

ISBN-13: 3642306748

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The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.