Bečvář, J. Bečvářová, M. : Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 


J. Bečvář, M. Bečvářová: Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 

3 TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 3 Table of Contents . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bartel Leendert van der Waerden (1903–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vojtěch Jarník (1897–1970) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 57 Monographs and Textbooks in Algebra at the Turn of the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 61 Van der Waerden’s Allgemeine Idealtheorie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Mathematical and Historical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Van der Waerden’s Moderne Algebra . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 207 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .222 Index of Names . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245


3

PREFACE

This publication is devoted to unique archival materials – Jarník’s mathematical notebooks, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contain a record of the

lecture course he attended given by Bartel Leendert van der Waerden titled

Allgemeine Idealtheorie [General Theory of Ideals].

The book Jarník’s notes of the lecture course Punktmengen und reelle

Funktionen by P.S. Aleksandrov (G¨ottingen 1928 ) published in 20101 and the

interests of German and Russian mathematicians and historians of mathematics

were the great motivation and inspiration for continuation in our mathematical

and archival studies to write this second book.

The first chapter of the present text gives a short description of van der

Waerden’s life and scientific results in mathematics and history of mathematics

as well as pedagogical activities in Amsterdam, G¨ottingen, Leipzig and Zurich.

The second chapter briefly deals with the founding of the University in

G¨ottingen and the development of mathematical studies and research there.

The productive and inspiring atmosphere in the G¨ottingen mathematical center

in the 1920s and 1930s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The third chapter is devoted to Jarník’s life and work in Prague and mainly

to his studies at the University in G¨ottingen in the academic years 1923/1924,

1924/1925 and 1927/1928.2

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his sixth and seventh notebooks which contain van

der Waerden’s lectures titled Allgemeine Idealtheorie.

The fifth chapter analyses the most famous textbooks on algebra which were

written in German, French, English and Italian from the end of the 19th century

until the beginning of the 1930s, i. e. before the birth of van der Waerden’s

Modern Algebra. The contents, structure, authors of interpretations as well as

their influences on the development of algebra are recalled.

1 M. Bečvářová, I. Netuka: Jarník’s notes of the lecture course Punktmengen und

reelle Funktionen by P.S. Aleksandrov (G¨ottingen 1928), Edition History of Mathematics,

volume 43, Matfyzpress, Prague, 2010, 143 pages ([BeNe]).

2 The second and third chapters are modifications of the chapters in [BeNe] and they are

taken with the permission of the coauthor.

4

The heart of this publication is the sixth chapter and the seventh chapter.

Firstly, van der Waerden’s lectures are transcribed from Jarník’s manuscript

and then detailed mathematical, historical and bibliographic comments are

connected.

The final appendix summarizes the most important information about the

origins of van der Waerden’s textbook Moderne Algebra and the literature

recommended by the author to study. It shows how the content of van der

Waerden’s textbook has changed over nearly four decades. At the end of the

appendix, an overview of all editions of this textbook, available in European

and American libraries, is included, with links to reviews published in reference

and mathematical journals.

These three chapters allow the reader to compare the content, organization

and interpretation of algebra in van der Waerden’s lecture delivered in

1927/1928 with the content, organization and interpretation in the first edition

of his two-part textbook Moderne Algebra (1930/1931), respectively in the

second edition (1937/1940) to the seventh/fifth edition (1966/1967).

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

Our text is based on archival documents deposited in the following institutions: the Archive of the Academy of Sciences of the Czech Republic, the Archive

of Charles University in Prague, the Archive of the University in G¨ottingen.

We also used sources from the following libraries: the Library of the Faculty of

Mathematics and Physics of Charles University in Prague, the Library of the

Academy of Sciences of the Czech Republic, the Library of the Mathematical

Institut of the Academy of Sciences of the Czech Republic, the National Library

of the Czech Republic, the Library of the Institut f¨ur Geschichte der Naturwissenschaften, the Ludwig-Maxmilian Universit¨at in Munich. We are grateful to

the colleagues from these institutions for their support and assistance in providing archival materials and literature.

We wish to thank Michaela Chocholová for her advice concerning the

transcription of German words. We are also very indebted to Ivan Netuka

and Antonín Slavík for their help with English translation.

In preparation of the present book we have received valuable suggestions

from several colleagues and friends. In particular, we would like to extend our

thanks to Hana Kábová, Ivan Netuka, and Antonín Slavík.

Jindřich Bečvář and Martina Bečvářová










J. Bečvář, M. Bečvářová: Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 

3 TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 3 Table of Contents . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bartel Leendert van der Waerden (1903–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vojtěch Jarník (1897–1970) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 57 Monographs and Textbooks in Algebra at the Turn of the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 61 Van der Waerden’s Allgemeine Idealtheorie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Mathematical and Historical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Van der Waerden’s Moderne Algebra . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 207 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .222 Index of Names . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245


3

PREFACE

This publication is devoted to unique archival materials – Jarník’s mathematical notebooks, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contain a record of the

lecture course he attended given by Bartel Leendert van der Waerden titled

Allgemeine Idealtheorie [General Theory of Ideals].

The book Jarník’s notes of the lecture course Punktmengen und reelle

Funktionen by P.S. Aleksandrov (G¨ottingen 1928 ) published in 20101 and the

interests of German and Russian mathematicians and historians of mathematics

were the great motivation and inspiration for continuation in our mathematical

and archival studies to write this second book.

The first chapter of the present text gives a short description of van der

Waerden’s life and scientific results in mathematics and history of mathematics

as well as pedagogical activities in Amsterdam, G¨ottingen, Leipzig and Zurich.

The second chapter briefly deals with the founding of the University in

G¨ottingen and the development of mathematical studies and research there.

The productive and inspiring atmosphere in the G¨ottingen mathematical center

in the 1920s and 1930s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The third chapter is devoted to Jarník’s life and work in Prague and mainly

to his studies at the University in G¨ottingen in the academic years 1923/1924,

1924/1925 and 1927/1928.2

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his sixth and seventh notebooks which contain van

der Waerden’s lectures titled Allgemeine Idealtheorie.

The fifth chapter analyses the most famous textbooks on algebra which were

written in German, French, English and Italian from the end of the 19th century

until the beginning of the 1930s, i. e. before the birth of van der Waerden’s

Modern Algebra. The contents, structure, authors of interpretations as well as

their influences on the development of algebra are recalled.

1 M. Bečvářová, I. Netuka: Jarník’s notes of the lecture course Punktmengen und

reelle Funktionen by P.S. Aleksandrov (G¨ottingen 1928), Edition History of Mathematics,

volume 43, Matfyzpress, Prague, 2010, 143 pages ([BeNe]).

2 The second and third chapters are modifications of the chapters in [BeNe] and they are

taken with the permission of the coauthor.

4

The heart of this publication is the sixth chapter and the seventh chapter.

Firstly, van der Waerden’s lectures are transcribed from Jarník’s manuscript

and then detailed mathematical, historical and bibliographic comments are

connected.

The final appendix summarizes the most important information about the

origins of van der Waerden’s textbook Moderne Algebra and the literature

recommended by the author to study. It shows how the content of van der

Waerden’s textbook has changed over nearly four decades. At the end of the

appendix, an overview of all editions of this textbook, available in European

and American libraries, is included, with links to reviews published in reference

and mathematical journals.

These three chapters allow the reader to compare the content, organization

and interpretation of algebra in van der Waerden’s lecture delivered in

1927/1928 with the content, organization and interpretation in the first edition

of his two-part textbook Moderne Algebra (1930/1931), respectively in the

second edition (1937/1940) to the seventh/fifth edition (1966/1967).

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

Our text is based on archival documents deposited in the following institutions: the Archive of the Academy of Sciences of the Czech Republic, the Archive

of Charles University in Prague, the Archive of the University in G¨ottingen.

We also used sources from the following libraries: the Library of the Faculty of

Mathematics and Physics of Charles University in Prague, the Library of the

Academy of Sciences of the Czech Republic, the Library of the Mathematical

Institut of the Academy of Sciences of the Czech Republic, the National Library

of the Czech Republic, the Library of the Institut f¨ur Geschichte der Naturwissenschaften, the Ludwig-Maxmilian Universit¨at in Munich. We are grateful to

the colleagues from these institutions for their support and assistance in providing archival materials and literature.

We wish to thank Michaela Chocholová for her advice concerning the

transcription of German words. We are also very indebted to Ivan Netuka

and Antonín Slavík for their help with English translation.

In preparation of the present book we have received valuable suggestions

from several colleagues and friends. In particular, we would like to extend our

thanks to Hana Kábová, Ivan Netuka, and Antonín Slavík.

Jindřich Bečvář and Martina Bečvářová










J. Bečvář, M. Bečvářová: Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 

3 TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 3 Table of Contents . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bartel Leendert van der Waerden (1903–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vojtěch Jarník (1897–1970) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 57 Monographs and Textbooks in Algebra at the Turn of the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 61 Van der Waerden’s Allgemeine Idealtheorie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Mathematical and Historical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Van der Waerden’s Moderne Algebra . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 207 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .222 Index of Names . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245


3

PREFACE

This publication is devoted to unique archival materials – Jarník’s mathematical notebooks, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contain a record of the

lecture course he attended given by Bartel Leendert van der Waerden titled

Allgemeine Idealtheorie [General Theory of Ideals].

The book Jarník’s notes of the lecture course Punktmengen und reelle

Funktionen by P.S. Aleksandrov (G¨ottingen 1928 ) published in 20101 and the

interests of German and Russian mathematicians and historians of mathematics

were the great motivation and inspiration for continuation in our mathematical

and archival studies to write this second book.

The first chapter of the present text gives a short description of van der

Waerden’s life and scientific results in mathematics and history of mathematics

as well as pedagogical activities in Amsterdam, G¨ottingen, Leipzig and Zurich.

The second chapter briefly deals with the founding of the University in

G¨ottingen and the development of mathematical studies and research there.

The productive and inspiring atmosphere in the G¨ottingen mathematical center

in the 1920s and 1930s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The third chapter is devoted to Jarník’s life and work in Prague and mainly

to his studies at the University in G¨ottingen in the academic years 1923/1924,

1924/1925 and 1927/1928.2

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his sixth and seventh notebooks which contain van

der Waerden’s lectures titled Allgemeine Idealtheorie.

The fifth chapter analyses the most famous textbooks on algebra which were

written in German, French, English and Italian from the end of the 19th century

until the beginning of the 1930s, i. e. before the birth of van der Waerden’s

Modern Algebra. The contents, structure, authors of interpretations as well as

their influences on the development of algebra are recalled.

1 M. Bečvářová, I. Netuka: Jarník’s notes of the lecture course Punktmengen und

reelle Funktionen by P.S. Aleksandrov (G¨ottingen 1928), Edition History of Mathematics,

volume 43, Matfyzpress, Prague, 2010, 143 pages ([BeNe]).

2 The second and third chapters are modifications of the chapters in [BeNe] and they are

taken with the permission of the coauthor.

4

The heart of this publication is the sixth chapter and the seventh chapter.

Firstly, van der Waerden’s lectures are transcribed from Jarník’s manuscript

and then detailed mathematical, historical and bibliographic comments are

connected.

The final appendix summarizes the most important information about the

origins of van der Waerden’s textbook Moderne Algebra and the literature

recommended by the author to study. It shows how the content of van der

Waerden’s textbook has changed over nearly four decades. At the end of the

appendix, an overview of all editions of this textbook, available in European

and American libraries, is included, with links to reviews published in reference

and mathematical journals.

These three chapters allow the reader to compare the content, organization

and interpretation of algebra in van der Waerden’s lecture delivered in

1927/1928 with the content, organization and interpretation in the first edition

of his two-part textbook Moderne Algebra (1930/1931), respectively in the

second edition (1937/1940) to the seventh/fifth edition (1966/1967).

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

Our text is based on archival documents deposited in the following institutions: the Archive of the Academy of Sciences of the Czech Republic, the Archive

of Charles University in Prague, the Archive of the University in G¨ottingen.

We also used sources from the following libraries: the Library of the Faculty of

Mathematics and Physics of Charles University in Prague, the Library of the

Academy of Sciences of the Czech Republic, the Library of the Mathematical

Institut of the Academy of Sciences of the Czech Republic, the National Library

of the Czech Republic, the Library of the Institut f¨ur Geschichte der Naturwissenschaften, the Ludwig-Maxmilian Universit¨at in Munich. We are grateful to

the colleagues from these institutions for their support and assistance in providing archival materials and literature.

We wish to thank Michaela Chocholová for her advice concerning the

transcription of German words. We are also very indebted to Ivan Netuka

and Antonín Slavík for their help with English translation.

In preparation of the present book we have received valuable suggestions

from several colleagues and friends. In particular, we would like to extend our

thanks to Hana Kábová, Ivan Netuka, and Antonín Slavík.

Jindřich Bečvář and Martina Bečvářová










J. Bečvář, M. Bečvářová: Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 

3 TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 3 Table of Contents . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bartel Leendert van der Waerden (1903–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vojtěch Jarník (1897–1970) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 57 Monographs and Textbooks in Algebra at the Turn of the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 61 Van der Waerden’s Allgemeine Idealtheorie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Mathematical and Historical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Van der Waerden’s Moderne Algebra . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 207 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .222 Index of Names . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245


3

PREFACE

This publication is devoted to unique archival materials – Jarník’s mathematical notebooks, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contain a record of the

lecture course he attended given by Bartel Leendert van der Waerden titled

Allgemeine Idealtheorie [General Theory of Ideals].

The book Jarník’s notes of the lecture course Punktmengen und reelle

Funktionen by P.S. Aleksandrov (G¨ottingen 1928 ) published in 20101 and the

interests of German and Russian mathematicians and historians of mathematics

were the great motivation and inspiration for continuation in our mathematical

and archival studies to write this second book.

The first chapter of the present text gives a short description of van der

Waerden’s life and scientific results in mathematics and history of mathematics

as well as pedagogical activities in Amsterdam, G¨ottingen, Leipzig and Zurich.

The second chapter briefly deals with the founding of the University in

G¨ottingen and the development of mathematical studies and research there.

The productive and inspiring atmosphere in the G¨ottingen mathematical center

in the 1920s and 1930s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The third chapter is devoted to Jarník’s life and work in Prague and mainly

to his studies at the University in G¨ottingen in the academic years 1923/1924,

1924/1925 and 1927/1928.2

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his sixth and seventh notebooks which contain van

der Waerden’s lectures titled Allgemeine Idealtheorie.

The fifth chapter analyses the most famous textbooks on algebra which were

written in German, French, English and Italian from the end of the 19th century

until the beginning of the 1930s, i. e. before the birth of van der Waerden’s

Modern Algebra. The contents, structure, authors of interpretations as well as

their influences on the development of algebra are recalled.

1 M. Bečvářová, I. Netuka: Jarník’s notes of the lecture course Punktmengen und

reelle Funktionen by P.S. Aleksandrov (G¨ottingen 1928), Edition History of Mathematics,

volume 43, Matfyzpress, Prague, 2010, 143 pages ([BeNe]).

2 The second and third chapters are modifications of the chapters in [BeNe] and they are

taken with the permission of the coauthor.

4

The heart of this publication is the sixth chapter and the seventh chapter.

Firstly, van der Waerden’s lectures are transcribed from Jarník’s manuscript

and then detailed mathematical, historical and bibliographic comments are

connected.

The final appendix summarizes the most important information about the

origins of van der Waerden’s textbook Moderne Algebra and the literature

recommended by the author to study. It shows how the content of van der

Waerden’s textbook has changed over nearly four decades. At the end of the

appendix, an overview of all editions of this textbook, available in European

and American libraries, is included, with links to reviews published in reference

and mathematical journals.

These three chapters allow the reader to compare the content, organization

and interpretation of algebra in van der Waerden’s lecture delivered in

1927/1928 with the content, organization and interpretation in the first edition

of his two-part textbook Moderne Algebra (1930/1931), respectively in the

second edition (1937/1940) to the seventh/fifth edition (1966/1967).

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

Our text is based on archival documents deposited in the following institutions: the Archive of the Academy of Sciences of the Czech Republic, the Archive

of Charles University in Prague, the Archive of the University in G¨ottingen.

We also used sources from the following libraries: the Library of the Faculty of

Mathematics and Physics of Charles University in Prague, the Library of the

Academy of Sciences of the Czech Republic, the Library of the Mathematical

Institut of the Academy of Sciences of the Czech Republic, the National Library

of the Czech Republic, the Library of the Institut f¨ur Geschichte der Naturwissenschaften, the Ludwig-Maxmilian Universit¨at in Munich. We are grateful to

the colleagues from these institutions for their support and assistance in providing archival materials and literature.

We wish to thank Michaela Chocholová for her advice concerning the

transcription of German words. We are also very indebted to Ivan Netuka

and Antonín Slavík for their help with English translation.

In preparation of the present book we have received valuable suggestions

from several colleagues and friends. In particular, we would like to extend our

thanks to Hana Kábová, Ivan Netuka, and Antonín Slavík.

Jindřich Bečvář and Martina Bečvářová










J. Bečvář, M. Bečvářová: Jarník’s Notes of the Lecture Course Allgemeine Idealtheorie by B. L. van der Waerden (Göttinten 1927/1928), 

3 TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 3 Table of Contents . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bartel Leendert van der Waerden (1903–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Mathematics in G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Vojtěch Jarník (1897–1970) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Jarník’s Notebooks from G¨ottingen . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 57 Monographs and Textbooks in Algebra at the Turn of the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 61 Van der Waerden’s Allgemeine Idealtheorie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Mathematical and Historical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Van der Waerden’s Moderne Algebra . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 207 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Table of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .222 Index of Names . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245


3

PREFACE

This publication is devoted to unique archival materials – Jarník’s mathematical notebooks, which he wrote during his studies at the University in

G¨ottingen in the academic year 1927/1928 and which contain a record of the

lecture course he attended given by Bartel Leendert van der Waerden titled

Allgemeine Idealtheorie [General Theory of Ideals].

The book Jarník’s notes of the lecture course Punktmengen und reelle

Funktionen by P.S. Aleksandrov (G¨ottingen 1928 ) published in 20101 and the

interests of German and Russian mathematicians and historians of mathematics

were the great motivation and inspiration for continuation in our mathematical

and archival studies to write this second book.

The first chapter of the present text gives a short description of van der

Waerden’s life and scientific results in mathematics and history of mathematics

as well as pedagogical activities in Amsterdam, G¨ottingen, Leipzig and Zurich.

The second chapter briefly deals with the founding of the University in

G¨ottingen and the development of mathematical studies and research there.

The productive and inspiring atmosphere in the G¨ottingen mathematical center

in the 1920s and 1930s is brought to life with the help of long passages chosen

from the recollections of some outstanding mathematicians who lectured or

studied there.

The third chapter is devoted to Jarník’s life and work in Prague and mainly

to his studies at the University in G¨ottingen in the academic years 1923/1924,

1924/1925 and 1927/1928.2

The fourth chapter provides a general account of Jarník’s fourteen notebooks

and a short description of his sixth and seventh notebooks which contain van

der Waerden’s lectures titled Allgemeine Idealtheorie.

The fifth chapter analyses the most famous textbooks on algebra which were

written in German, French, English and Italian from the end of the 19th century

until the beginning of the 1930s, i. e. before the birth of van der Waerden’s

Modern Algebra. The contents, structure, authors of interpretations as well as

their influences on the development of algebra are recalled.

1 M. Bečvářová, I. Netuka: Jarník’s notes of the lecture course Punktmengen und

reelle Funktionen by P.S. Aleksandrov (G¨ottingen 1928), Edition History of Mathematics,

volume 43, Matfyzpress, Prague, 2010, 143 pages ([BeNe]).

2 The second and third chapters are modifications of the chapters in [BeNe] and they are

taken with the permission of the coauthor.

4

The heart of this publication is the sixth chapter and the seventh chapter.

Firstly, van der Waerden’s lectures are transcribed from Jarník’s manuscript

and then detailed mathematical, historical and bibliographic comments are

connected.

The final appendix summarizes the most important information about the

origins of van der Waerden’s textbook Moderne Algebra and the literature

recommended by the author to study. It shows how the content of van der

Waerden’s textbook has changed over nearly four decades. At the end of the

appendix, an overview of all editions of this textbook, available in European

and American libraries, is included, with links to reviews published in reference

and mathematical journals.

These three chapters allow the reader to compare the content, organization

and interpretation of algebra in van der Waerden’s lecture delivered in

1927/1928 with the content, organization and interpretation in the first edition

of his two-part textbook Moderne Algebra (1930/1931), respectively in the

second edition (1937/1940) to the seventh/fifth edition (1966/1967).

Illustrations and copies from Jarník’s notebook and some archival materials

and documents can be found at the end of the book, followed by an index of

names.

Our text is based on archival documents deposited in the following institutions: the Archive of the Academy of Sciences of the Czech Republic, the Archive

of Charles University in Prague, the Archive of the University in G¨ottingen.

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