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
Total Pages: 468
Release: 2006
Genre: Mathematics
ISBN: 9780801882357

"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
Total Pages: 206
Release: 2021-03-12
Genre: Philosophy
ISBN: 0813234166

“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.

Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture
Author: Apostolos Doxiadis
Publisher: Faber & Faber
Total Pages: 148
Release: 2012-11-15
Genre: Fiction
ISBN: 057129569X

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 Weil Conjectures

The Weil Conjectures
Author: Karen Olsson
Publisher: Macmillan + ORM
Total Pages: 167
Release: 2019-07-16
Genre: Biography & Autobiography
ISBN: 0374719632

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.

The Art of Conjecture

The Art of Conjecture
Author: Bertrand de Jouvenel
Publisher: Routledge
Total Pages: 265
Release: 2017-09-29
Genre: Philosophy
ISBN: 1351305662

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.

Character Theory and the McKay Conjecture

Character Theory and the McKay Conjecture
Author: Gabriel Navarro
Publisher: Cambridge University Press
Total Pages: 253
Release: 2018-04-26
Genre: Mathematics
ISBN: 1108428444

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
Total Pages: 125
Release: 2010-07-08
Genre: Mathematics
ISBN: 1848001851

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
Total Pages: 257
Release: 2012-10-19
Genre: Mathematics
ISBN: 3642306748

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.

The Science of Conjecture

The Science of Conjecture
Author: James Franklin
Publisher: JHU Press
Total Pages: 767
Release: 2015-08-01
Genre: Science
ISBN: 1421418819

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.