Scottish Book

Part of the Scottish Book with notes of Stefan Banach and Stanislaw Ulam.

The Scottish Book (Polish: Księga Szkocka) was a thick notebook used by mathematicians of the Lwów School of Mathematics in Poland for jotting down unsolved problems. The notebook was named after the Scottish Café, where it was kept.

Originally, the mathematicians who gathered at the cafe would write down the problems and equations directly on the cafe's marble table tops, but these would be erased at the end of each day, and so the record of the preceding discussions would be lost. The idea for the book was most likely originally suggested by Stefan Banach's wife, Łucja Banach.

History

The building of the Scottish cafe where the book was recorded and stored
1972: Mazur (left) acknowledges Per Enflo with the promised "live goose", the prize for having solved problem 153.

The Scottish Café (Polish: Kawiarnia Szkocka) was the café in Lwów (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in functional analysis and topology.

Stanisław Ulam recounted that the tables of the café had marble tops, so they could write directly on the table in pencil during their discussions. To keep the results from being lost and after becoming annoyed with their writing directly on the table tops, Stefan Banach's wife Łucja provided the mathematicians with a large notebook, which was used for writing down 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 and on the eve of World War II), such as a bottle of fine brandy.

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 in 1972 by Per Enflo, who was presented with a live goose by Mazur in a ceremony that was broadcast throughout Poland.

The café building used to house the Universal Bank [uk] at the street address of 27 Taras Shevchenko Prospekt.[clarification needed][citation needed] The original cafe was renovated in May 2014 and contains a copy of the Scottish Book.

Problems contributed by individual authors

A total of 193 problems were written down in the book. Stanisław Mazur contributed a total of 43 problems, 24 of them as a single author and 19 together with Stefan Banach. Banach himself wrote 14, plus another 11 with Stanisław Ulam and Mazur. Ulam wrote 40 problems and additional 15 ones with others.

During the Soviet occupation of Lwów, several Russian mathematicians visited the city and also added problems to the book.

Hugo Steinhaus contributed the last problem on 31 May 1941, shortly before the German attack on the Soviet Union. The problem involved the probability distribution of matches within a matchbox, a question motivated by Banach's habit of chain smoking cigarettes.

Continuity

After World War II, an English translation annotated by Ulam was published by Los Alamos National Laboratory in 1957. After World War II, Hugo Steinhaus at the University of Wrocław revived the tradition of the Scottish book with The New Scottish Book from 1945 to 1958.[citation needed]

The tradition of the Scottish Book continues to inspire not only mathematicians but also educators in other fields. Piotr Kowzan proposed a "goose method" as a pedagogical tool for marking open problems and encouraging future research. Inspired by the eccentric rewards in the Scottish Book, this approach aims to foster curiosity and knowledge-building across generations.

Associated people

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

References

  1. 1 2 3 4 Raikhel, Yuri (January 2010). "Scottish Book: Lviv's mathematical relic". День. Retrieved November 17, 2011.
  2. 1 2 Visser, Jan; Visser, Muriel (2003). "Talking about the unknown" (PDF). TechTrends. 47 (1): 5–8. doi:10.1007/BF02763324. S2CID 62646372.
  3. ↑ Mauldin, ed.
  4. ↑ Mauldin, ed.; Kaluza.
  5. ↑ "Stanislaw Mazur". The MacTutor History of Mathematics archive. School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved November 17, 2011.
  6. ↑ "Manuscript of Scottish book (PDF)" (PDF). Archived from the original on April 28, 2018. Retrieved October 12, 2016.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  7. ↑ Ulam, page=88
  8. ↑ Ulam, Stanislaw. The Scottish Book (PDF). pp. I–II. (sent by Stan Ulam from Los Alamos to Professor Copson in Edinburgh on January 28, 1958)
  9. ↑ Kowzan, Piotr (2023). "The Pedagogy of Geese Sent into the Future: On the Theory of Value". Ars Educandi. 20 (20): 57–68. doi:10.26881/ae.2023.20.03.

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