This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.

This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine. This work is addressed to all those who have an interest in Mathematics.

This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture.

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This volume in the series “Imagine Math” casts light on what is new and interesting in the relationships between mathematics, imagination and culture. The book opens by examining the connections between modern and contemporary art and mathematics, including Linda D. Henderson’s contribution. Several further papers are devoted to mathematical models and their influence on modern and contemporary art, including the work of Henry Moore and Hiroshi Sugimoto. Among the many other interesting contributions are an homage to Benoît Mandelbrot with reference to the exhibition held in New York in 2013 and the thoughts of Jean-Pierre Bourguignon on the art and math exhibition at the Fondation Cartier in Paris. An interesting part is dedicated to the connections between math, computer science and theatre with the papers by C. Bardainne and A. Mondot. The topics are treated in a way that is rigorous but captivating, detailed but very evocative. This is an all-embracing look at the world of mathematics and culture.

"A work of major importance for the interpretation of Descartes's development and for the understanding of the function of the imagination in Descartes's early works. Descartes's Imagination will be a must in Descartes and imagination studies. It is long overdue."--Eva T. H. Brann, author of The World of Imagination: Sum and Substance "A significant contribution to our understanding of the development of Descartes's philosophy."--William R. Shea, author of The Magic of Numbers and Motion: The Scientific Career of Rene Descartes