2010 Winner

## Patterns of Change, Linguistic Innovations in the Development of Classical Mathematics

by### Ladislav Kvasz

#### About the book

This book offers a reconstruction of linguistic innovations in the history of mathematics; innovations which changed the ways in which mathematics was done, understood and philosophically interpreted. It argues that there are at least three ways in which the language of mathematics has been changed throughout its history, thus determining the lines of development that mathematics has followed.

The book also offers tools of analysis by means of which scholars and students of the history and philosophy of mathematics can attain better understanding of the various changes, which the subject of their study underwent in the course of history. The book brings also important insights for mathematics education connecting growth of language with the development of mathematical thought.

Birkhäuser Basel

ISBN 978-3-7643-8839-3

261 pages · 261

#### About the author

Ladislav Kvasz graduated in 1986 in mathematics at the Comenius University in Bratislava. In 1995 he received a PhD in philosophy with the thesis Classification of Scientific Revolutions.

Since 1986 he has been employed at the Faculty of Mathematics and Physics of Comenius University. In 1993 he won the Herder Scholarship and spent one year at the University of Vienna studying the philosophy of Wittgenstein. In 1995 he won the Masaryk Scholarship of the University of London and spent one year at King’s College London working on the philosophy of Imre Lakatos. In 1997 he won the Fulbright Scholarship and spent one semester at the University of California at Berkeley, working on philosophy of geometry. In 2000 he won the Humboldt Scholarship and spent two years at the Technical University in Berlin working on the scientific revolution. In 2007 he moved to Prague, where he became in 2010 a professor of mathematics education.

He was the co-editor of Appraising Lakatos (Kluwer 2002) and author of Patterns of Change (Birkhauser 2008).

### The First Fernando Gil Prize for Philosophy of Science

The jury has decided to award the first Fernando Gil prize for philosophy of science to Ladislav Kvasz , who is professor at the Charles University in the Czech Republic for his book: Patterns of Change, Linguistic Innovations in the Development of Classical Mathematics, published in 2008.

Professor Kvasz graduated in 1986 in mathematics at the Comenius University In Bratislav, which was then part of the communist world. He first thought of following a career in applied mathematics, and went to Moscow where he worked on some complicated problems in astrophysics. However, after the fall of communism, his interest shifted to the philosophy of mathematics. From 1993 to 2002, he won a series of prestigious scholarships to pursue his research in this area in the main centres of the Western world: Vienna, London, Berkeley in Calfornia, and Berlin. During these years, he developed the ideas which appear in his book.

The main criteria which led the jury to decide in favour of Professor Kvasz’s book for the prize was the originality of his work and the scholarly way in which he supported his position. His book concerns the way in which mathematics develops, and it formulates three important patterns of change which are named: recoding, relativization, and reformulation. The first two of these are entirely novel, and show the great originality of Professor Kvasz’s work. However, Professor Kvasz is not content merely to state that these patterns occur. He demonstrates his thesis by numerous examples from the history of mathematics of which he has a profound and scholarly knowledge.

When new concepts are introduced into mathematics, this nearly always involves the introduction of a new symbolic language, and Professor Kvasz’s book discusses how these new languages are developed. When discussing his pattern of relativization, he makes use of some of the ideas of Wittgenstein, but gives these a dynamic development. Wittgenstein in his early thinking on language claimed that there is a form of the language which cannot be expressed in the language itself. Professor Kvasz’s idea is that one can, however, create a new language by adding the form of the old language to the language. He shows that it was in this way that major conceptual advances such as the introduction of non-Euclidean geometry took place. This dynamic and historical account of the way in which language develops gives Professor Kvasz’s work an interest which goes beyond mathematics into general questions of language and thought.

Altogether Professor Kvasz’s book is an exciting and stimulating one, which should help to make the Fernando Gil prize a significant factor in future developments of philosophy of science.