When I was a student in Lvov in 1970-s, I've heard many legends about Banach, so let me add a few points. Once Steinhaus was walking in a park, and he accidentally heard a conversation of two young people sitting on a bench. The words "Lebesgue integral" were pronounced. At that time very few people in Lvov had heard of the Lebesgue integral. So Steinhaus was curious, and introduced himself... Banach was an engineering student at that time. (Who was the other person on the bench, the story does not tell).
According to the legend, Banach worked most of his time in the Scottish cafe. Students and colleagues joined him for conversation. (One of the results of this was the famous "Scottish book" of unsolved problems. Prizes were offered sometimes and recorded to the book together with the problems. For example, in 1970-s, when Per Enflo solved the "basis problem" from the Scottish book, he won a prize, a live goose, which was delivered by Mazur). He used to write on the table cloth. The owner of the cafe never complained. At the end of the day, he changed the tablecloth for a new one. And the old one he sold to students.
Banach drunk a lot (and there are many stories about this, which I omit). Frequently he was short of money, and had to drink in credit. At some time, the debt grew large, and there was an argument with the owner of the Scottish cafe. Finally the owner proposed that Banach writes a calculus textbook to make money to pay for his drinks. (Some version of the legend says this was suggested by students). Indeed, he wrote a calculus textbook:-) But I have never seen his high school textbooks.
The Scottish cafe still existed in 1990-s, but under a different name, and in 1970-s this was a simple cantina. Then the rooms passed to some financial institution.
P.S. Wikipedia, http://en.wikipedia.org/wiki/Scottish_Caf%C3%A9 has somewhat different details of doing math in the Scottish cafe, based on Ulam's recollections.
