Scottish Café
Encyclopedia
Lviv
Lviv is a city in western Ukraine. The city is regarded as one of the main cultural centres of today's Ukraine and historically has also been a major Polish and Jewish cultural center, as Poles and Jews were the two main ethnicities of the city until the outbreak of World War II and the following...
(now Lviv) where, in the 1930s and 1940s, mathematicians from the Lwów School
Lwów School of Mathematics
The Lwów School of Mathematics was a group of mathematicians who worked between the two World Wars in Lviv, then known as Lwów and located in Poland, but now located in western Ukraine. The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the...
collaboratively discussed research problem
Mathematical problem
A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's...
s, particularly in functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and topology
General topology
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
.
Stanislaw Ulam recounts that the tables of the café had marble
Marble
Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite.Geologists use the term "marble" to refer to metamorphosed limestone; however stonemasons use the term more broadly to encompass unmetamorphosed limestone.Marble is commonly used for...
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
Stefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
'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
Scottish Book
The Scottish Book was a thick notebook used by mathematicians of the Lwow School of Mathematics for jotting down problems meant to be solved. The notebook was named after the "Scottish Café" where it was kept....
. 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
Great Depression
The Great Depression was a severe worldwide economic depression in the decade preceding World War II. The timing of the Great Depression varied across nations, but in most countries it started in about 1929 and lasted until the late 1930s or early 1940s...
and on the eve of World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
), such as a bottle of fine brandy.
For problem 153, which was later recognized as being closely related to Stefan Banach's "basis problem", Stanislaw Mazur
Stanislaw Mazur
Stanisław Mazur was a Polish mathematician and a member of the Polish Academy of Sciences....
offered the prize of a live goose. This problem was solved only in 1972 by Per Enflo
Per Enflo
Per H. Enflo is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years:* The basis problem and the approximation problem and later...
, who was presented with the live goose in a ceremony that was broadcast throughout Poland.
The café building now houses the Universal Bank at the street address of 27 Taras Shevchenko Prospekt.
See also
- Stefan BanachStefan BanachStefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
- Karol BorsukKarol BorsukKarol Borsuk was a Polish mathematician.His main interest was topology.Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts , and the cohomotopy groups, later called Borsuk-Spanier cohomotopy groups. He also founded the so called Shape theory...
- Marek Kac
- Stefan KaczmarzStefan KaczmarzStefan Kaczmarz was a Polish mathematician. His Kaczmarz method provided the basis for many modern imaging technologies, including the CAT scan....
- Bronisław Knaster
- Kazimierz KuratowskiKazimierz KuratowskiKazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.-Biography and studies:...
- Stanisław Mazur
- Stanisław Saks
- Juliusz SchauderJuliusz SchauderJuliusz Paweł Schauder was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equation and mathematical physics.Born on September 21, 1899 in Lemberg, he had to fight in World War I right after his graduation from school...
- Hugo SteinhausHugo SteinhausWładysław Hugo Dionizy Steinhaus was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics...
- Stanisław Ulam
External links
- Scottish book
- Scottish book Web page at Home Page of Stefan Banach at University of Gdańsk website
- Kawiarnia Szkocka at the MacTutor archive
- http://www.axler.net/Banach.htmlSheldon AxlerSheldon AxlerSheldon Jay Axler is an American mathematician, professor of mathematics and the Dean of the College of Science and Engineering at San Francisco State University. He has made contributions to mathematics education, publishing several mathematics textbooks....
's review of "The Life of Stefan Banach"]