Reactionary Mathematics
Reactionary Mathematics

Author: Massimo Mazzotti

Publisher: University of Chicago Press

Published: 2023-05-12

Total Pages: 350

ISBN-13: 0226826732

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A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena. The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the “very modern mathematics” of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics. For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world—in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti’s penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.

The Discrete Mathematical Charms of Paul Erdos
The Discrete Mathematical Charms of Paul Erdos

Author: Vašek Chvátal

Publisher: Cambridge University Press

Published: 2021-08-26

Total Pages: 270

ISBN-13: 1108934919

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Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

The Moscow Pythagoreans
The Moscow Pythagoreans

Author: Ilona Svetlikova

Publisher: Springer

Published: 2013-07-05

Total Pages: 290

ISBN-13: 1137338288

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In Russia at the turn of the twentieth century, mysticism, anti-Semitism, and mathematical theory fused into a distinctive intellectual movement. Through analyses of such seemingly disparate subjects as Moscow mathematical circles and the 1913 novel Petersburg, this book illuminates a forgotten aspect of Russian cultural and intellectual history.

Dynamics, Geometry, Number Theory
Dynamics, Geometry, Number Theory

Author: David Fisher

Publisher: University of Chicago Press

Published: 2022-02-07

Total Pages: 573

ISBN-13: 022680402X

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"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--

The DIM Hypothesis
The DIM Hypothesis

Author: Leonard Peikoff

Publisher: Penguin

Published: 2013-12-03

Total Pages: 402

ISBN-13: 0451466640

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With his groundbreaking and controversial DIM hypothesis, Dr. Leonard Peikoff casts a penetrating new light on the process of human thought, and thereby on Western culture and history. In this far-reaching study, Peikoff identifies the three methods people use to integrate concrete data into a whole, as when connecting diverse experiments by a scientific theory, or separate laws into a Constitution, or single events into a story. The first method, in which data is integrated through rational means, he calls Integration. The second, which employs non-rational means, he calls Misintegration. The third is Disintegration—which is nihilism, the desire to tear things apart. In The DIM Hypothesis Peikoff demonstrates the power of these three methods in shaping the West, by using the categories to examine the culturally representative fields of literature, physics, education, and politics. His analysis illustrates how the historical trends in each field have been dominated by one of these three categories, not only today but during the whole progression of Western culture from its beginning in Ancient Greece. Extrapolating from the historical pattern he identifies, Peikoff concludes by explaining why the lights of the West are going out—and predicts the most likely future for the United States.

The Broken Dice, and Other Mathematical Tales of Chance
The Broken Dice, and Other Mathematical Tales of Chance

Author: Ivar Ekeland

Publisher: University of Chicago Press

Published: 1996-06-15

Total Pages: 194

ISBN-13: 9780226199924

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Contemplating the randomness of nature, Ekeland extends his consideration of the catastrophe theory of the universe begun in Mathematics and the Unexpected, drawing upon rich literary sources and current topics in math and physics such as chaos theory, information theory, and particle physics. Line drawings.

Groups of Circle Diffeomorphisms
Groups of Circle Diffeomorphisms

Author: Andrés Navas

Publisher: University of Chicago Press

Published: 2011-06-30

Total Pages: 310

ISBN-13: 0226569519

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In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.

Lectures on Buildings
Lectures on Buildings

Author: Mark Ronan

Publisher: University of Chicago Press

Published: 2009-10-15

Total Pages: 244

ISBN-13: 0226724999

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In mathematics, “buildings” are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas. Almost twenty years after its original publication, Mark Ronan’s Lectures on Buildings remains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field. Lectures on Buildings will find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups. “Ronan’s account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings.”—Bulletin of the London Mathematical Society