The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd updated and enlarged edition.

*(English)*Zbl 1331.01039
Cham: Birkhäuser/Springer (ISBN 978-3-319-22896-9/hbk; 978-3-319-22897-6/ebook). xviii, 322 p. (2015).

This is the second English edition of the famous “Ksiȩga Szkocka” – the first edition [Zbl 0485.01013] appeared in 1981 by Birkhäuser (one should mention here also two limited Los Alamos editions edited, and one produced, by Stanisław Ulam – they appeared in 1957 and 1977, resp.). Originally, the “Ksiȩga Szkocka” was a notebook (bought by Banach’s wife) used by mathematicians of the Lwów School of Mathematics for writing there problems meant to be solved. The notebook was named after the Scottish Café where Lvov mathematicians met and where the notebook was kept.

The book under review consists of four parts. Part I contains a collection of some of the talks given at the “Scottish Book Conference” held at North Texas State University in May 1979. One finds here lectures by Stanisław Ulam, Mark Kac, Antoni Zygmund, Paul Erdős and Andrzej Granas. Part II is devoted to problems from the “Ksiȩga Szkocka”. They are given with commentaries (some of them are new and have been added to the second edition). This part contains also a problem subject index and an index of the authors of the problems. Quite new in comparison with the first edition are Parts III and IV of the book under review. They are devoted to the Wrocław New Scottish Book – in fact the “Scottish Book” has been continued in Wrocław where many Lvov mathematicians moved after the Second World War. Part III contains an article “Lwów of the West” written by P. Biler, P. Krupski, G. Plebanek and W. A. Woyczyński – it is a brief history of the New Scottish Book. Part IV contains a selection of problems from this book augmented with information on their solutions. The book was active from 1946 through 1979 (seven problems were entered between 1979 and 1987 – it was a special time in the history of Poland, namely the time of the historical Solidarity movement and many Wrocław mathematicians were engaged in it). The book under review is interesting not only for historians of mathematics. It gives a vivid picture of the mathematical life in Lvov between the world wars and offers an opportunity to see the people and ideas of that time that had an enormous influence on the development of mathematics.

The book under review consists of four parts. Part I contains a collection of some of the talks given at the “Scottish Book Conference” held at North Texas State University in May 1979. One finds here lectures by Stanisław Ulam, Mark Kac, Antoni Zygmund, Paul Erdős and Andrzej Granas. Part II is devoted to problems from the “Ksiȩga Szkocka”. They are given with commentaries (some of them are new and have been added to the second edition). This part contains also a problem subject index and an index of the authors of the problems. Quite new in comparison with the first edition are Parts III and IV of the book under review. They are devoted to the Wrocław New Scottish Book – in fact the “Scottish Book” has been continued in Wrocław where many Lvov mathematicians moved after the Second World War. Part III contains an article “Lwów of the West” written by P. Biler, P. Krupski, G. Plebanek and W. A. Woyczyński – it is a brief history of the New Scottish Book. Part IV contains a selection of problems from this book augmented with information on their solutions. The book was active from 1946 through 1979 (seven problems were entered between 1979 and 1987 – it was a special time in the history of Poland, namely the time of the historical Solidarity movement and many Wrocław mathematicians were engaged in it). The book under review is interesting not only for historians of mathematics. It gives a vivid picture of the mathematical life in Lvov between the world wars and offers an opportunity to see the people and ideas of that time that had an enormous influence on the development of mathematics.

Reviewer: Roman Murawski (Poznań)