La collana Matematica e cultura, attraverso un cammino iniziato dodici anni fa, in modo sempre nuovo, sorprendente e affascinante prova a descrivere influenze e legami esistenti tra il mondo della matematica e quello del cinema, della musica, dell'economia, ma anche dell arte, del teatro, della letteratura o della storia"

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for "n" > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the mathematics and physics of today with the mathematics and physics of the Greeks, which, however renowned, was not yet capable of this abstractness. Originally published in 1966. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Archimedes Palimpsest is the name given to a Byzantine prayer book that was written over a number of earlier manuscripts, including one that contained two unique works by Archimedes, unquestionably the greatest mathematician of antiquity. Sold at auction in 1998, it has since been the subject of a privately funded project to conserve, image, and transcribe its texts. Images and transcriptions of three of these manuscripts are provided here. The first contains seven treatises by Archimedes, including two unique texts, Method and Stomachion, as well as the only extant Greek version of Floating Bodies. Previously unknown speeches by Hyperides and a second- or third-century commentary on Aristotle's Categories follow. The product of ten years of conservation, imaging, and scholarship, this book will be of interest to manuscript scholars, classicists, and historians of science.

Matematica e cultura, binomio sorprendente? Potrebbe sembrare ma da qualche anno si sono aperti dei grandi ponti tra le "due culture." A Venezia, citta' di ponti e di culture, si parla da oramai dieci anni di cultura e di matematica, si parla di arte, architettura, cinema, letteratura, ambiente, filosofia, di bolle di sapone, di Corto Maltese ed Hugo Pratt, delle investigazioni criminali. In questo nuovo libro, il decimo della serie iniziata a Venezia con gli incontri "Matematica e cultura" che tanti hanno cercato di imitare, si parla di tutto questo e tra gli altri ne scrivono Simon Singh (autore del best seller "L'ultimo teorema di Fermat"), alla sua terza presenza a Venezia, e Siobhan Roberts (autrice di "Il re dello spazio infinito. Storia dell'uomo che salvo la geometria"). Venezia ponte tra la matematica e la cultura.

A New York Times Book Review Editor's Choice: A vivid account of the generations-long dispute over Bayes' rule, one of the greatest breakthroughs in the history of applied mathematics and statistics "An intellectual romp touching on, among other topics, military ingenuity, the origins of modern epidemiology, and the theological foundation of modern mathematics."-Michael Washburn, Boston Globe "To have crafted a page-turner out of the history of statistics is an impressive feat. If only lectures at university had been this racy."-David Robson, New Scientist Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years-at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

Lo scibile matematico si espande a un ritmo vertiginoso. Nel corso degli ultimi cinquant'anni sono stati dimostrati piu teoremi che nei precedenti millenni della storia umana. Per illustrare la ricchezza della matematica del Novecento, il presente volume porta sulla ribalta alcuni dei protagonisti di questa straordinaria impresa intellettuale, che ha messo a nostra disposizione nuovi e potenti strumenti per indagare la realta che ci circonda.

Presentando matematici famosi accanto ad altri meno noti al grande pubblico - da Hilbert a Godel, da Turing a Nash, da De Giorgi a Wiles - i ritratti raccolti in questo volume ci presentano personaggi dal forte carisma personale, dai vasti interessi culturali, appassionati nel difendere l'importanza delle proprie ricerche, sensibili alla bellezza, attenti ai problemi sociali e politici del loro tempo.

Ne risulta un affresco che documenta la centralita della matematica nella cultura, non solo scientifica ma anche filosofica, artistica e letteraria, del nostro tempo, in un continuo gioco di scambi e di rimandi, di corrispondenze e di suggestioni.

Imagine a giant snowflake in 196,884 dimensions... This is the story of a mathematical quest that began two hundred years ago in revolutionary France, led to the biggest collaboration ever between mathematicians across the world, and revealed the 'Monster' - not monstrous at all, but a structure of exquisite beauty and complexity. Told here for the first time in accessible prose, it is a story that involves brilliant yet tragic characters, curious number 'coincidences' that led to breakthroughs in the mathematics of symmetry, and strange crystals that reach into many dimensions. And it is a story that is not yet over, for we have yet to understand the deep significance of the Monster - and its tantalizing hints of connections with the physical structure of spacetime. Once we understand the full nature of the Monster, we may well have revealed a whole new and deeper understanding of the nature of our Universe.

This classic study by the eminent Dutch historian of science E. J. Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the text, and then undertakes a comprehensive examination of all the extant writings.

Originally published in 1987.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy student and teacher sewn softcover edition in one volume, with minimal notes and a new index/glossary.

E' opinione diffusa che sia la filosofia che la matematica non abbiano una immediata utilitA pratica. La (TM)una servirebbe solo a rispondere alle grandi questioni etiche, religiose ed esistenziali; la (TM)altra a risolvere problemi scientifici e tecnologici circoscritti.

In questo libro si mostra invece che molti metodi di risoluzione dei problemi delle organizzazioni (aziendali e non) si fondano su premesse attinte, anche inconsapevolmente proprio dalla filosofia, dalla matematica, ma anche da nuclei di pensiero sistemico ben visibili in filosofi ante litteram. Gli esempi sono numerosissimi e attraversano la (TM)intera storia della cultura umana. Si pensi ad esempio alle Proporzioni di Talete, alla Distanza di Pitagora, alla Maieutica di Socrate alla Logica di Aristotele, al Rasoio di Occam, alle Tavole e agli Idola di Bacone, alle ProbabilitA di Pascal, ai discorsi sul Metodo di Cartesio, ai Grafi di Eulero, ai Giudizi di Kant, alla teoria degli Errori di Gauss, ai Sistemi di Bertalanffy, al Problem solving di Popper, al concetto di Modello di Von Neumann, alla Programmazione lineare di Dantzig, alla RazionalitA limitata di Simon, ecc.

Questa rapida mappatura della genealogia filosofica e matematica dei metodi di risoluzione dei problemi organizzativi mostra la centralitA della visione sistemica e del lavoro di gruppo ribaditi dalla (TM)autore, anche con alcune esemplificazioni, nella conclusione del volume.

Rivolto a tutti coloro che lavorano nelle organizzazioni (manager e professional) e agli studenti che si preparano ad accedervi, il libro si offre come un mezzo per conoscere le radici culturali delle idee, dei metodi e degli strumenti di problem solving e per meglioqualificarne gli usi e le applicazioni nei diversi contesti operativi.

Durante la II guerra mondiale hanno avuto luogo numerosi risultati di rilievo nel campo della crittografia militare. Uno dei meno conosciuti e quello usato dal servizio di intelligence svedese, nei confronti del codice tedesco per le comunicazioni strategiche con i comandi dei paesi occupati nel nord Europa, le cui linee passavano per la Svezia. In tal modo, durante la fase piu critica della guerra la direzione politica e militare svedese era in grado di seguire i piani e le disposizioni dei Tedeschi, venendo a conoscenza dei piu arditi progetti per modificare la propria politica, tenendo la Svezia fuori dalla guerra.

La violazione del codice tedesco e narrata in dettaglio, per la prima volta, con elementi che gli permettono di essere un ottima introduzione al campo della crittografia, oltre che un ritratto vitale e umano della societa del tempo: una disperata condizione bellica, l'intrigo politico e spionistico, il genio del matematico Arne Beurling, le difficolta e i trucchi del mestiere, e il lavoro sistematico e oscuro di una folla di decrittatori.

The Association for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM covers a span from AWM's beginnings through the following fifty years. The volume celebrates AWM and its successes but does not shy away from its challenges. The book is designed for a general audience. It provides interesting and informative reading for people interested in mathematics, gender equity, or organizational structures; teachers of mathematics; students at the high school, college, and graduate levels; and members of more recently established organizations for women in mathematics and related fields or prospective founders of such organizations.

A little bucket, one-third full, is 8 inches deep, and its upper and lower diameters are 7 inches and 6 inches, respectively. How large is the frog which, jumping into the bucket, causes the water to rise 3 inches? Word problems not unlike this example are a staple on math tests and of abiding interest to students, teachers, and professional mathematicians alike. Frank Swetz, a highly regarded mathematics educator, gathers hundreds of these problems in this fun and fascinating introduction to mathematics from around the world.

"Mathematical Expeditions" is a collection of over 500 culturally and historically diverse mathematical problems carefully chosen to enrich mathematics teaching from middle school through the college level. What better way to teach students the multicultural aspects of math than by assigning them problems first composed on clay tablets by Babylonian scribes, included in the Rhind papyrus, or Vedic problems scratched on tree bark? From Egypt to Greece to China to India, Swetz's problems--both practical and abstract--span centuries and cultures.

Swetz has organized the problems by culture and historical period, showing, through the various constructs and contexts of the problems, the history and development of mathematics throughout the world. Along the way, he tells us what various cultures knew about math and how they came to learn it, providing instructors with a wonderful way to incorporate multicultural mathematics into the middle school, high school, and college classroom.

In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard's mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors--William Fogg Osgood and Maxime Bocher--undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators--students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.

Questo numero delle Note, curato da Lorenzo Magnani e da Riccardo Dossena, e dedicato alla ripresentazione del programma di Erlangen, nella classica traduzione italiana di Gino Fano, arricchita da un'introduzione di Jean Dieudonne e da un saggio di Francois Russo. Quest'ultimo contributo in particolare presenta la genesi del programma, a partire dai primi decenni dell' Ottocento, concentrando la propria attenzione sulla costituzione - con Poncelet - della Geometria proiettiva in forma di dottrina e sulla scoperta delle Geometrie non euclidee. Fu questa una vera e propria "avventura" internazionale, cui parteciparono matematici tedeschi (Klein, Staudt, Grassmann, Helmholtz, Riemann), russi (Lobacevskiy), ungheresi (Bolyai), inglesi (Cayley), francesi (Poncelet, Chasles), italiani (Beltrami).

How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? Experience shows that disentangling scientific knowledge from opinion is harder than one might expect. Full of illuminating examples and quotations, and with a scope ranging from psychology and evolution to quantum theory and mathematics, this book brings alive issues at the heart of all science.

Thomas Hankins and Robert Silverman investigate an array of instruments from the seventeenth through the nineteenth century that seem at first to be marginal to science--magnetic clocks that were said to operate by the movements of sunflower seeds, magic lanterns, ocular harpsichords (machines that played different colored lights in harmonious mixtures), Aeolian harps (a form of wind chime), and other instruments of "natural magic" designed to produce wondrous effects. By looking at these and the first recording instruments, the stereoscope, and speaking machines, the authors show that "scientific instruments" first made their appearance as devices used to evoke wonder in the beholder, as in works of magic and the theater. The authors also demonstrate that these instruments, even though they were often "tricks," were seen by their inventors as more than trickery. In the view of Athanasius Kircher, for instance, the sunflower clock was not merely a hoax, but an effort to demonstrate, however fraudulently, his truly held belief that the ability of a flower to follow the sun was due to the same cosmic magnetic influence as that which moved the planets and caused the rotation of the earth. The marvels revealed in this work raise and answer questions about the connections between natural science and natural magic, the meaning of demonstration, the role of language and the senses in science, and the connections among art, music, literature, and natural science. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Like it or not, maths is a part of everyday life. Whether we learned only basic arithmetic, or went on to study calculus and beyond, we need it, and use it, constantly. But only very rarely were we taught its back story. From the theories of Pythagoras (did you know he ran a secret brotherhood that studied maths, music and gymnastics?) to Ada Lovelace (one of the few notable pre-twentieth-century female mathematicians who is considered to be the first ever computer programmer), From 0 to Infinity shows how the major discoveries and developments fundamentally changed the way we see the world. Do you want to learn about why the Ancient Greeks knew so much maths? Or why there was so little maths studied in the Dark Ages? Read this fascinating book to uncover the surprising stories behind maths.

Questo volume raccoglie lo scambio epistolare tra Cantor e Dedekind, finora edito parte in tedesco e parte in francese. Sara la prima edizione italiana completa di questo fondamentale carteggio, in cui si vedono nascere la nozione di cardinale e ordinale transfiniti, in cui si dimostra la non numerabilita dell'insieme dei numeri reali R e si leggono i primi tentativi e le correzioni alla costruzione di una biiezione tra R e R2, e le discussioni fra Cantor e Dedekind sull'invarianza della nozione di dimensione. "Pochi scritti matematici possono competere - scrive Pietro Nastasi nell'Introduzione - con questa corrispondenza nell'evidenziare il complesso intreccio psicologico che presiede all'invenzione matematica. E nessun lavoro storiografico potrebbe far emergere, meglio di queste lettere, la differenza fra le due personalita implicate: focosa e fantasiosa quella di Cantor, pacata e critica quella del piu anziano amico".

This enthralling biography tells the complete story of one of Tudor England's most enigmatic figures. A Welshman born in Tenby, south Wales, c.1512, Robert Recorde was educated at both Oxford and Cambridge. This book, a detailed biography of this Tudor scholar, reviews the many facets of his astonishingly wide-ranging career and ultimately tragic life. It presents a richly detailed and fully rounded picture of Recorde the man, the university academic and theologian, the physician, the mathematician and astronomer, the antiquarian, and the writer of hugely successful textbooks. Crown appointments brought Recorde into conflict with the scheming Earl of Pembroke, and eventually set him at odds with Queen Mary I. As an intellectual out of his depth in political intrigue, beset by religious turmoil, Recorde eventually succumbed to the dangers that closed inexorably around him.

Presenter l'analyse de base en suivant grosso modo l'ordre suivant laquelle elle a ete decouverte, voici le fil conducteur de cet ouvrage. Complete par un grand nombre de dessins, d'exemples et de contre-exemples, cet ouvrage est redige avec un veritable souci de pedagogie. Il est truffe de remarques historiques et de commentaires explicitant la motivation profonde des developpements exposes.

The triple deck structure shows how a perturbation to the thin layer of a fluid immediately adjacent (boundary layer) to an obstacle such as an aeroplane wing develops as an interaction between the pressure and a displacement of the boundary layer. The theory was a major advance in fluid mechanics at the end of the twentieth century. This book provides a graduate level description of some history of boundary layer flow and the application of the triple deck in fluid mechanics.

Mark Peterson makes an extraordinary claim in this fascinating book focused around the life and thought of Galileo: it was the mathematics of Renaissance arts, not Renaissance sciences, that became modern science. "Galileo's Muse" argues that painters, poets, musicians, and architects brought about a scientific revolution that eluded the philosopher-scientists of the day, steeped as they were in a medieval cosmos and its underlying philosophy.

According to Peterson, the recovery of classical science owes much to the Renaissance artists who first turned to Greek sources for inspiration and instruction. Chapters devoted to their insights into mathematics, ranging from perspective in painting to tuning in music, are interspersed with chapters about Galileo's own life and work. Himself an artist turned scientist and an avid student of Hellenistic culture, Galileo pulled together the many threads of his artistic and classical education in designing unprecedented experiments to unlock the secrets of nature.

In the last chapter, Peterson draws our attention to the "Oratio de Mathematicae laudibus "of 1627, delivered by one of Galileo's students. This document, Peterson argues, was penned in part by Galileo himself, as an expression of his understanding of the universality of mathematics in art and nature. It is "entirely Galilean in so many details that even if it is derivative, it must represent his thought," Peterson writes. An intellectual adventure, "Galileo s Muse" offers surprising ideas that will capture the imagination of anyone scientist, mathematician, history buff, lover of literature, or artist who cares about the humanistic roots of modern science.

Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem. The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level course. To quickly get to the main points of the proof of the theorem, several topics that aid in the understanding of the proof are included in the appendices. These topics serve the purpose of providing familiarity with a large variety of tools used in the proof and adds to the flexibility of reading them independently.