Matematikkens historie

ChatGPT og de moderne AI-chatrobotter har allerede revolutioneret mange aspekter af vores hverdag. Men vi befinder os fortsat i den spæde begyndelse af AI-epoken.Vi står i disse tider over for verdenshistoriens største teknologiske revolution. AI – eller kunstig intelligens, som teknologien kendes på dansk – er en samfundsændrende teknologi, der vil transformere alle aspekter af vores liv over de kommende år. AI vil revolutionere vores hverdag, arbejdsplads, skolevæsen og meget mere.Anders Bæk er AI-ekspert og en af landets mest benyttede foredragsholdere, når det gælder kunstig intelligens. I denne bog tager han læseren på en rundvisning ind i fremtiden. Han fortæller gennem konkrete eksempler, hvordan vores fremtid vil blive forandret på både godt og ondt takket være denne science fiction-lignende teknologi.Det kan allerede afsløres nu, at det ikke er småting vores civilisation har i vente …Anders Bæk (f. 1992) er AI-ekspert og en af landets mest benyttede foredragsholdere til at fortælle om den store AI-revolution. Er uddannet civilingeniør i software- og forretningsudvikling, og har studeret AI’s udvikling siden 2015. Han er fast paneldeltager i landets største erhvervspodcast “Millionærklubben”, udtaler sig ofte til landets medier om AI- og tech-emner, og han udgiver en af landets mest lyttede podcasts om kunstig intelligens, ”AI Revolutionen”.

A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.¿A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

A compulsively readable look at the secret language of numbers- their role in nature, movies, science, and everything in between. What do Fight Club, wallpaper patterns, George Balanchine's Serenade, and Italian superstitions have in common? They're all included in the entry for the number 17 in this engaging book about numbers- detailing their unique properties, patterns, appeal, history, and lore. Author Derrick Niederman takes readers on a guided tour of the numbers 1 to 300-covering everything from basic mathematical principles to ancient unsolved theorems, from sublime theory to delightfully arcane trivia. Illustrated with diagrams, drawings, and photographs, plus 50 challenging mathematical brainteasers (with answers), this book will fascinate and engage readers of all levels of mathematical skill and knowledge. Includes such gems as: ? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials "H" and "A" are the eighth and first numbers in the alphabet respectively

This book is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background.

This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include:A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schemaA quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematiciansThe depiction and perception of Émilie Du Châtelet¿s scientific contributions as viewed through the frontispieces designed for books written by or connected to herA study of the Cambridge Women¿s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth centuryAn examination of the researchand writing process of mathematicians by looking at their drafts and other preparatory notesA global history of al-Khw¿r¿zm¿¿s Kit¿b al-jabr wa-l-muq¿bala as obtained by tracing its reception through numerous translations and commentariesWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

From the bestselling author of Quantum Computing for Everyone, a concise, accessible, and elegant approach to mathematics that not only illustrates concepts but also conveys the surprising nature of the digital information age.Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math, Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved. Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions.

The book offers an analysis of Joachim Jungius¿ Texturæ Contemplatio - a hitherto-unpublished manuscript written in German and Latin that deals with weaving, knitting and other textile practices, attempting to present as well various fabrics and textile techniques in a scientifical and even mathematical framework. The book aims to provide the epistemological, technical and historic framework for Jungius¿ manuscript, inspecting fabrics, weaving techniques as well as looms and other textile machines in Holy Roman Empire during the Early Modern Period. It also offers a unique investigation of the notion and metaphor of ¿texture¿ during this period, and explores, within the wider context of the ¿meeting¿ or ¿trading zones¿ thesis, the relations between artisans and natural philosophers during the 17th century. The book is of interest to historians of philosophy and mathematics, as well as historians of technology.

Dieses Standardwerk zu philosophischen Hintergründen des mathematischen Denkens und Sprechens, Lehrens und Lernens bietet einen umfangreichen Abriss zur Geschichte der Philosophie der Mathematik bis hin zu aktuellen Strömungen. Es diskutiert mathematische und philosophische Grundfragen der historischen wie der modernen Mathematik. Über Mengenlehre, Logik und Axiomatik führt es in mathematische Grundlagen ein, untersucht das Verhältnis von Wahrheit und Beweis und stellt fundamentale Ergebnisse, ungelöste und unlösbare Probleme vor.

The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic.The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics.The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

This volume presents the beautiful memoirs of Euler, Lagrange and Lambert on geography, translated into English and put into perspective through explanatory and historical essays as well as commentaries and mathematical notes. These works had a major impact on the development of the differential geometry of surfaces and they deserve to be studied, not only as historical documents, but most of all as a rich source of ideas.