The Scottish Café () was a café in Lwów,

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...

(now Lviv,

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

and

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

Stanisław Ulam Stanisław Marcin Ulam ( ; 13 April 1909 – 13 May 1984) was a Polish and American mathematician, nuclear physicist and computer scientist. He participated in the Manhattan Project, originated the History of the Teller–Ulam design, Telle ...

recounts that the tables of the café had

marble Marble is a metamorphic rock consisting of carbonate minerals (most commonly calcite (CaCO3) or Dolomite (mineral), dolomite (CaMg(CO3)2) that have recrystallized under the influence of heat and pressure. It has a crystalline texture, and is ty ...

tops, so they could write in pencil, directly on the table, during their discussions. To keep the results from being lost, and after becoming annoyed with their writing directly on the table tops,

Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an original ...

's wife provided the mathematicians with a large notebook, which was used for writing the problems and answers and eventually became known as the '' Scottish Book''. The book—a collection of solved, unsolved, and even probably unsolvable problems—could be borrowed by any of the guests of the café. Solving any of the problems was rewarded with prizes, with the most difficult and challenging problems having expensive prizes (during the

Great Depression The Great Depression was a severe global economic downturn from 1929 to 1939. The period was characterized by high rates of unemployment and poverty, drastic reductions in industrial production and international trade, and widespread bank and ...

and on the eve of

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

), such as a bottle of fine

brandy Brandy is a liquor produced by distilling wine. Brandy generally contains 35–60% alcohol by volume (70–120 US proof) and is typically consumed as an after-dinner digestif. Some brandies are aged in wooden casks. Others are coloured ...

. For problem 153, which was later recognized as being closely related to Stefan Banach's " basis problem", Stanisław Mazur offered the prize of a live goose. This problem was solved only in 1972 by Per Enflo, who was presented with the live goose in a ceremony that was broadcast throughout Poland.Mauldin, ed.; Kaluza. The café building now houses the Szkocka Restaurant & Bar (named for the original Scottish Café) and the Atlas Deluxe hotel at the street address of 27

Taras Shevchenko Taras Hryhorovych Shevchenko (; ; 9 March 1814 – 10 March 1861) was a Ukrainian poet, writer, artist, public and political figure, folklorist, and ethnographer. He was a fellow of the Imperial Academy of Arts and a member of the Brotherhood o ...

Prospekt.

Participants

The following mathematicians were associated with the Lwów School of Mathematics or contributed to ''The Scottish Book'': *

* Karol Borsuk * Mark Kac * Stefan Kaczmarz * Bronisław Knaster *

Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. He worked as a professor at the University of Warsaw and at the Ma ...

* Stanisław Saks * Juliusz Schauder * Hugo Steinhaus *

References

* *

External links

The Scottish book
an
Memories from the Scottish Café
MacTutor History of Mathematics Archive
Scottish book Web page
a

at Adam Mickiewicz University in Poznań website *
Manuscript of Scottish book (PDF)
*
Typescript of English version of Scottish book (PDF)

review by Sheldon Axler {{Lviv History of Lviv History of mathematics Education in the Second Polish Republic Coffeehouses and cafés in Poland Buildings and structures in Lviv