Felix Klein : visions for mathematics, applications, and education / Renate Tobies ; revised by the author and translated by Valentine A. Pakis.

Format:

Book

Author/Creator:

Tobies, Renate, author.

Contributor:

Pakis, Valentine A., translator.

Series:

Vita mathematica ; Volume 20.

Vita Mathematica ; Volume 20

Language:

English

Subjects (All):

Klein, Felix, 1849-1925.

Klein, Felix.

Mathematicians--Germany--Biography.

Mathematicians.

Reformers--Germany--Biography.

Reformers.

Physical Description:

1 online resource (697 pages)

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

About Felix Klein, the famous Greek mathematician Constantin Carathéodory once said: "It is only by illuminating him from all angles that one can come to understand his significance." The author of this biography has done just this. A detailed study of original sources has made it possible to uncover new connections; to create a more precise representation of this important mathematician, scientific organizer, and educational reformer; and to identify misconceptions. Because of his edition of Julius Plücker's work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23. By exchanging ideas with his most important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen Program. Various other visionary programs followed, in which Klein involved mathematicians from Germany and abroad. Klein was the most active promoter of Riemann's geometric-physical approach to function theory, but he also integrated the analytical approaches of the Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has often been claimed, it must be emphasized that Klein expressly opposed national chauvinism. He promoted mathematically gifted individuals regardless of their nationality, religion, or gender. Many of his works have been translated into English, French, Italian, Russian, and other languages; more than 300 supporters from around the world made it possible for his portrait to be painted by the prominent impressionist Max Liebermann. Inspired by international developments, Klein paved the way for women to work in the field of mathematics. He was instrumental in reforming mathematical education, and he endorsed an understanding of mathematics that affirmed its cultural importance as well as itsfundamental significance to scientific and technological progress.

Contents:

Intro

PREFACE

CONTENTS

1 INTRODUCTION

1.1 THE STATE OF RESEARCH

1.2 GUIDING QUESTIONS

1.3 EDITORIAL REMARKS

Acknowledgements

2 FORMATIVE GROUPS

2.1 THE KLEIN-KAYSER FAMILY

2.1.1 A Royalist and Frugal Westphalian Upbringing

2.1.2 Talent in School and Wide Interests as Gifts from His Mother's Side

2.1.3 Felix Klein and His Siblings

2.2 SCHOOL YEARS IN DÜSSELDORF

2.2.1 Earning His Abitur from a Gymnasium at the Age of Sixteen

2.2.2 Examination Questions in Mathematics

2.2.3 Interests in Natural Science During His School Years

2.3 STUDIES AND DOCTORATE IN BONN

2.3.1 Coursework and Seminar Awards

2.3.2 Assistantship and a Reward for Winning a Physics Contest

2.3.3 Assisting Julius Plücker's Research in Geometry

2.3.4 Doctoral Procedure

2.4 JOINING ALFRED CLEBSCH'S THOUGHT COMMUNITY

2.4.1 The Clebsch School

2.4.2 The Journal Mathematische Annalen

2.4.3 Articles on Line Geometry, 1869

2.5 BROADENING HIS HORIZONS IN BERLIN

2.5.1 The Professors in Berlin and Felix Klein

2.5.2 Acquaintances from the Mathematical Union: Kiepert, Lie, Stolz

2.5.3 Cayley's Metric and Klein's Non-Euclidean Interpretation

2.6 IN PARIS WITH SOPHUS LIE

2.6.1 Felix Klein and French Mathematicians

2.6.2 Collaborative Work with Sophus Lie

2.6.2.1 Notes on W-Configurations

2.6.2.2 Principal Tangent Curves of the Kummer Surface

2.6.3 A Report on Mathematics in Paris

2.7 THE FRANCO-PRUSSIAN WAR AND KLEIN'S HABILITATION

2.7.1 Wartime Service as a Paramedic and Its Effects

2.7.2 Habilitation

2.8 TIME AS A PRIVATDOZENT IN GÖTTINGEN

2.8.1 Klein's Teaching Activity and Its Context

2.8.2 An Overview of Klein's Research Results as a Privatdozent

2.8.3 Discussion Groups

2.8.3.1 A Three-Man Club with Clebsch and Riecke.

2.8.3.2 The Mathematical and Natural-Scientific Student Union

2.8.3.3 A Scientific Circle: Eskimo

2.8.3.4 The "Social Activity" of Bringing Mathematicians Together

3 A PROFESSORSHIP AT THE UNIVERSITY OF ERLANGEN

3.1 RESEARCH TRENDS AND DOCTORAL STUDENTS

3.1.1 The Vision of the Erlangen Program

3.1.2 Klein's Students in Erlangen

3.1.3 New Research Trends

3.1.3.1 On a New Type of Riemann Surface

3.1.3.2 The Theory of Equations

3.2 INAUGURAL LECTURE: A PLAN FOR MATHEMATICAL EDUCATION

3.3 FIRST TRIP TO GREAT BRITAIN, 1873

3.4 TRIPS TO ITALY

3.5 DEVELOPING THE MATHEMATICAL INSTITUTION

3.6 FAMILY MATTERS

3.6.1 His Friends Marry and Klein Follows Suit

3.6.2 Klein's Father-in-Law, the Historian Karl Hegel

3.6.3 Anna Hegel, Felix Klein, and Their Family

4 A PROFESSORSHIP AT THE POLYTECHNIKUM IN MUNICH

4.1 A NEW INSTITUTE AND NEW TEACHING ACTIVITY

4.1.1 Creating a Mathematical Institute

4.1.2 Reorganizing the Curriculum

4.2 DEVELOPING HIS MATHEMATICAL INDIVIDUALITY

4.2.1 The Icosahedron Equation

4.2.2 Number Theory

4.2.3 Elliptic Modular Functions

4.2.4 Klein's Circle of Students in Munich

4.2.4.1 Phase I: 1875-1876

4.2.4.2 Phase II: 1876-1880

4.3 DISCUSSION GROUPS IN MUNICH

4.3.1 A Mathematical Discussion Group with Engineers and Natural Scientists

4.3.2 The Mathematical Student Union and the Mathematical Society

4.3.3 The Meeting of Natural Scientists in Munich, 1877

4.4 "READY AGAIN FOR A UNIVERSITY IN A SMALL CITY"

5 A PROFESSORSHIP FOR GEOMETRY IN LEIPZIG

5.1 KLEIN'S START IN LEIPZIG AND HIS INAUGURAL ADDRESS

5.2 CREATING A NEW MATHEMATICAL INSTITUTION

5.3 TEACHING PROGRAM

5.3.1 Lectures: Organization, Reorientation, and Deviation from the Plan

5.3.2 The Mathematical Colloquium / Exercises / Seminar

5.4 THE KLEINIAN "FLOCK".

5.4.1 Post-Doctoral Mathematicians

5.4.2 Klein's Foreign Students in Leipzig

5.4.2.1 The First Frenchman and the First Briton

5.4.2.2 The First Americans

5.4.2.3 The Italians

5.4.2.4 Mathematicians from Switzerland and Austria-Hungary

5.4.2.5 Russian and Other Eastern European Contacts

5.5 FIELDS OF RESEARCH

5.5.1 Mathematical Physics / Physical Mathematics

5.5.1.1 Lamé's Function, Potential Theory, and Carl Neumann

5.5.1.2 On Riemann's Theory of Algebraic Functions and Their Integrals

5.5.2 Looking Toward Berlin

5.5.2.1 Gathering Sources

5.5.2.2 The Dirichlet Principle

5.5.2.3 Klein's Seminar on the Theory of Abelian Functions (1882)

5.5.2.4 Openness vs. Partiality

5.5.3 Looking Toward France

5.5.3.1 French Contributors to Mathematische Annalen

5.5.3.2 Klein's Correspondence with Poincaré

5.5.4 Three Fundamental Theorems

5.5.4.1 The Loop-Cut Theorem (Rückkehrschnitttheorem)

5.5.4.2 Theorem of the Limit-Circle (Grenzkreistheorem)

5.5.4.3 The (General) Fundamental Theorem

5.5.4.4 Remarks on the Proofs

5.5.5 The Polemic about and with Lazarus Fuchs

5.5.6 The Icosahedron Book

5.5.7 A Book on the Theory of Elliptic Modular Functions

5.5.7.1 Supplementing the Theory

5.5.7.2 Who Should Be the Editor? - Georg Pick

5.5.8 Hyperelliptic and Abelian Functions

5.6 FELIX KLEIN AND ALFRED ACKERMANN-TEUBNER

5.7 FELIX KLEIN IN LEIPZIG'S INTELLECTUAL COMMUNITIES

5.7.1 A Mathematicians' Circle

5.7.2 The Societas Jablonoviana

5.7.3 The Royal Saxon Society of Sciences in Leipzig

5.8 TURNING HIS BACK ON LEIPZIG

5.8.1 Weighing Offers from Oxford and Johns Hopkins

5.8.2 The Physicist Eduard Riecke Arranges Klein's Move to Göttingen

5.8.3 The Appointment of Sophus Lie as Klein's Successor - and the Reactions.

6 THE START OF KLEIN'S PROFESSORSHIP IN GÖTTINGEN, 1886-1892

6.1 FAMILY CONSIDERATIONS

6.2 DEALING WITH COLLEAGUES, TEACHING, AND CURRICULUM PLANNING

6.2.1 The Relationship Between Klein and Schwarz

6.2.2 The Göttingen Privatdozenten Hölder and Schoenflies

6.2.3 Klein's Teaching in Context

6.3 INDEPENDENT AND COLLABORATIVE RESEARCH

6.3.1 The Theory of Finite Groups of Linear Substitutions: The Theory of Solving Equations of Higher Degree

6.3.2 Hyperelliptic and Abelian Functions

6.3.3 The Theory of Elliptic Modular Functions (Monograph)

6.3.4 The Theory of Automorphic Functions (Monograph)

6.3.5 The Theory of Lamé Functions and Potential Theory

6.3.6 Refreshing His Work on Geometry

6.3.7 Visions: Internationality, Crystallography, Hilbert's Invariant Theory

6.3.7.1 An Eye on Developments Abroad

6.3.7.2 Arthur Schoenflies and Crystallography

6.3.7.3 Felix Klein and Hilbert's Invariant Theory

6.4 BRINGING PEOPLE AND INSTITUTIONS TOGETHER

6.4.1 The Professorium in Göttingen

6.4.2 A Proposal to Relocate the Technische Hochschule in Hanover to Göttingen

6.4.3 The Idea of Reorganizing the Göttingen Society of Sciences

6.4.4 Felix Klein and the Founding of the German Mathematical Society

6.5 THE PIVOTAL YEAR OF 1892

6.5.1 Refilling Vacant Professorships in Prussia

6.5.1.1 Berlin, Breslau, and Klein's System for Classifying Styles of Thought

6.5.1.2 Hiring a Successor for H.A. Schwarz in Göttingen

6.5.2 A Job Offer from the University of Munich and the Consequences

7 SETTING THE COURSE, 1892/93-1895

7.1 KLEIN'S ASSISTANTS AND HIS PRINCIPLES FOR CHOOSING THEM

7.2 THE GÖTTINGEN MATHEMATICAL SOCIETY

7.3 TURNING TO SECONDARY SCHOOL TEACHERS

7.4 A TRIP TO THE UNITED STATES

7.4.1 The World's Fair in Chicago and the Mathematical Congress.

7.4.2 Twelve Lectures by Klein: The Evanston Colloquium

7.4.3 Traveling from University to University

7.4.4 Repercussions

7.5 THE BEGINNINGS OF WOMEN STUDYING MATHEMATICS

7.6 ACTUARIAL MATHEMATICS AS A COURSE OF STUDY

7.7 CONTACTING ENGINEERS AND INDUSTRIALISTS

7.8 THE ENCYKLOPÄDIE PROJECT

7.9 KLEIN SUCCEEDS IN HIRING DAVID HILBERT

8 THE FRUITS OF KLEIN'S EFFORTS, 1895-1913

8.1 A CENTER FOR MATHEMATICS, NATURAL SCIENCES, AND TECHNOLOGY

8.1.1 The Göttingen Association

8.1.2 Applied Mathematics in the New Examination Regulations and the Consequences

8.1.3 Aeronautical Research

8.2 MAINTAINING HIS SCIENTIFIC REPUTATION

8.2.1 Automorphic Functions (Monograph)

8.2.2 Geometric Number Theory

8.2.3 A Monograph on the Theory of the Spinning Top

8.2.4 Inspiring Ideas in the Fields of Mathematical Physics and Technology

8.2.4.1 Hydrodynamics / Hydraulics

8.2.4.2 Statics

8.2.4.3 The Theory of Friction

8.2.4.4 The Special Theory of Relativity

8.3 PROGRAM: THE HISTORY, PHILOSOPHY, PSYCHOLOGY, ANDINSTRUCTION OF MATHEMATICS

8.3.1 The History of Mathematics

8.3.2 Philosophical Aspects

8.3.3 Psychological-Epistemological Classifications

8.3.4 The "Kleinian" Educational Reform

8.3.4.1 Suggestions for Reform

8.3.4.2 A Polemic about the Teaching of Analysis at the University

8.4 INTERNATIONAL SCIENTIFIC COOPERATION

8.5 EARLY RETIREMENT AND HONORS

8.5.1 Recovering and Working in the Hahnenklee Sanatorium

8.5.2 Max Liebermann's Portrait of Felix Klein

8.5.3 The Successors to Klein's Professorship

9 THE FIRST WORLD WAR AND THE POSTWAR PERIOD

9.1 POLITICAL ACTIVITY DURING THE FIRST WORLD WAR

9.1.1 The Vows of Allegiance of German Professors to Militarism

9.1.2 A Plea for Studying Abroad.

9.2 HISTORY OF MATHEMATICS, THE "CRY FOR HELP OF MODERNPHYSICS," AND EDITION PROJECTS.

Notes:

Description based on print version record.

ISBN:

3-030-75785-4

OCLC:

1260346952