Autor:

S. Domoradzki:

cena je předběžná

2011, 331 pages,

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Contents

Introduction ............................................................................................................... 7

The culture of mathematics .................................................................................................... 7

Brief history of Galicia in the period of autonomy ................................................................ 11

Chapter I

Gymnasia ......................................................................................................................... 17

1.1. Introduction ..................................................................................................................... 17

1.2. Gymnasia in the memories of Hugo Steinhaus and Franciszek Leja .............................. 17

1.3. Programs of teaching ...................................................................................................... 22

1.3.1. Teaching programs of mathematics in classical gymnasium ................................ 24

1.3.2. Teaching programs of mathematics in gymnasium of real type ........................... 33

1.3.3. Business School .................................................................................................... 43

1.4. Some statistics on gymnasium ........................................................................................ 45

1.5. Teachers of mathematics in c.k.* Gymnasium named after of Francis Joseph in Lvov . 48

1.6. Preparation of teachers of mathematics .......................................................................... 50

1.7. Scientific Publications of mathematics teachers ............................................................. 53

Chapter II

Universi ty ....................................................................................................................... 80

2.1. Mathematics at the University ........................................................................................ 80

2.2. Mathematical lectures in the years 1880–1920 ............................................................... 83

2.3. Mathematical studies of Franciszek Leja ........................................................................ 93

2.4. Mathematical studies of Stanisław Ruziewicz ................................................................ 105

2.5. Professors and readers of mathematics ........................................................................... 110

2.6. Activities for environment .............................................................................................. 151

2.7. Some statistics ................................................................................................................. 155

Chapter III

Polytechnic School in Lvov ............................................................................... 164

3.1. Introduction ..................................................................................................................... 164

3.2. The role of mathematics in polytechnic education ......................................................... 172

3.2.1. Mathematical subjects ........................................................................................... 174

3.2.2. Content of lectures ................................................................................................ 179

3.3. Professors and readers of mathematics ........................................................................... 191

Chapter IV

Societies, conventions, publications .......................................................... 204

4.1. Introduction ..................................................................................................................... 204

4.2. Lvov scientific societies and their transformations after 1918 ....................................... 204

4.3. Other Lvov Societies ....................................................................................................... 208

4.4. Conventions of Polish Naturalists and Physicians .......................................................... 212

4.5. Mathematical Society in Lvov ........................................................................................ 219

* Cesarsko-Królewski [i.e. Imperial-Royal].

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4.6. Periodicals ....................................................................................................................... 225

4.7. Gymnasium textbooks..................................................................................................... 231

Chapter V

Specia l cas es ................................................................................................................ 236

5.1. Introduction ..................................................................................................................... 236

5.2. Puzyna’s work Teorya funkcyj analitycznych [Theory of Analytic Functions]; an attempt

of discusssion .................................................................................................................. 236

5.3. Mathematical articles, which appeared in Kosmos, the magazine of the (Polish)

Copernicus Society of Naturalists ................................................................................... 257

5.4. Sessions of the Mathematical Society in Lvov................................................................ 260

5.5. A forgotten mathematician Lucjan Böttcher (1872–1937) ............................................ 265

App endi ces ...................................................................................................................... 280

A1 Requirements for entrance gymnasium examination ....................................................... 280

A2 Examples of tasks from maturity examination ................................................................ 280

A3 List of publications on teaching of mathematics in Muzeum .......................................... 291

A4 Composition of the Philosophical Faculty of the c. k. Emperor Francis I University in

Lvov based on the Composition of professorial staff (1881/1882 and 1905/1906) ...... 297

A5 Mathematics at the General Department of the Mining Faculty at the c. k. Polytechnic

School ............................................................................................................................. 305

A6 Map of Galicia and Lodomeria ........................................................................................ 309

A7 Map of Galicia and Bukovina .......................................................................................... 310

A8 Map of the parliamentary electoral constituencies in 1900 ............................................. 311

A9 The list of professors of mathematics at the University of Lvov in the period of

autonomy........................................................................................................................ 312

Index of si gnificant names ................................................................................. 313

Bi bliograp hy ................................................................................................................ 320

One looks for things from the past

that are still interesting today.1

W przeszłości szuka się tego,

co interesuje człowieka dziś.

Wer sich mit einer Wissenschaft bekannt machen will,

darf nicht nur nach den reifen Früchten greifen,

er muss sich darum bekümmern wie

und wo sie gewachsen sind.2

Kto chce zgłębiać jakąś wiedzę,

ten winien nie tylko zbierać dojrzałe owoce,

ale też zwracać uwagę na to jak

i gdzie one rosły.

Introduction

The culture of mathematics

Mathematics is now present everywhere. Hundreds of thousands of people

do it professionally today. Mathematical methods are used in many fields of

modern science, in natural science, engineering, economics, political science,

sociology, literary studies, management, linguistics and others. Mathematicians,

as A.L. Hammond3 noticed, stay away from public view, they are busy people.

It was not always so. There were cultures without mathematics, for example,

Roman or Indian, in which mathematics was only a part of the religious sphere.

In ancient Egypt mathematics was a part of the occult. In ancient Greece it was

a part of philosophy, in the Middle Ages it was preserved within the walls of

the monasteries, serving mainly to set the dates of movable feasts. Unlike, for

example, in China where the math was on the edge of the culture, in classical

Greece, strongly influenced by the Pythagoreans, it has grown to the status of

a tool to explore the world.

1 H. Samsonowicz, Przestrzeń historii [The space of history], Matematyka Społeczeństwo

Nauczanie 30–I(2003), pp. 4–8 .

2 Johann Christian Poggendorff (1796–1877).

3 A.L. Hammond, Matematyka – nasza niedostrzegalna kultura [Mathematics – our invisible

coulture], in: Matematyka współczesna. Dwanaście esejów [Mathematics today. Twelve informal

essays], L.A. Steen (ed.), WN–T, Warszawa, 1983, pp. 26–48.

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Its rank has increased enormously since the days of Galileo, Kepler and

Newton, as it became a key tool for exploring the world. People look at the

world mathematically and in some ways it has been a subject of mathematics.

But the mathematics was not just a tool; its creation by mathematicians had an

autonomous character, satisfying their own goals and ambitions.

Since the seventeenth century mathematics was developed as a science with

a very high degree of abstraction, one of the features of which is the distance

between the discoveries and applications. For example, Boolean functions in

the nineteenth century could be regarded as a kind of curiosity, and in the

twentieth century they became necessary in computer programming; or Riemann

geometry, which also turned out to be essential in the theory of relativity. Such

examples can be found in the history of mathematics in great numbers.

Developing science, including mathematics, requires adequate social base.

The aim of the book is to present formation of such a background in the years

1870–1920 in the area of impact of the Lvov University. We will try to present

the activity, in particular, of Lvov mathematicians and their great commitment,

and to demonstrate the importance of their work to raise the culture

of mathematics in Poland in the second half of XIX and early XX century.

After 1920, in Lvov there was one of the major schools of mathematics in

the world – the Lvov School of Mathematics, the ground for which has been

prepared during the preceding fifty years. In this book, the Lvov School of

Mathematics will not be discussed (see Duda, 2007).

Mathematical culture at an elementary level means appreciation for mathematics

as a certain intellectual activity, in particular, mastering of certain

techniques of calculation, understanding the idea of leading, having a clear

definition of terms and even the perception of the beauty of mathematics.

In its social dimension, the mathematical culture of society consists of

mathematical culture of individuals. Its expression is widespread in using

intellectual techniques such as abstraction, pattern recognition and formation,

generalizing, comparing, noticing analogies, sorting, classifying, defining,

arguing, making algorithms, or optimizing.

For M. Kordos4, the mathematical culture consists of skills allowing one to

see in a problem under consideration non-existing mathematical objects, which

however, amazingly efficiently, lead to solving this problem.

As R. Duda5 notices: Mathematics is an element of culture, and therefore when

looking for its sources it seems reasonable to begin from the history of the culture

where it is possible to try to uncover original sources of mathematical thinking.6

4 M. Kordos, Zobaczyć to czego nie widać, czyli kultura matematyczna w praktyce [To

see the unseen, or mathematical culture in practice], Publising House Aksjomat, Toruń, 2009.

5 Kultura matematyczna a kultura matematyków [Mathematical coulture and the culture of

mathematicians], Matematyka Społeczeństwo Nauczanie 21(VII 1998), pp. 27–31.

6 R. Duda, Co każdy o matematyce wiedzieć powinien [What everynody should know about

mathematics], Matematyka Społeczeństwo Nauczanie 31(VII 2003), pp. 2–7.