The work of mathematicians outside their professional environment

Mathematics differs from most other professions in that the only "resources" which are really needed are paper and pencil. (Even these are not strictly necessary, one can use sand and stick as the ancients did. Some can do even without sand, as the examples of famous blind mathematicians show).

As a result, the working habits of mathematicians widely wary. I know one study of this variety of working habits: J. Hadamard's book An essay on the psychology of invention in the mathematical field. It contains in particular the results of a poll that he made among his friends mathematicians. (For example it cites a famous story by Poincare how he invented authomorphic functions, while boarding a bus).

Many similar examples are known from the memoirs of mathematicians, or books like Littlewood's Miscellany. The idea of the uniformization theorem came to Klein when he was recuperating from asthma in a seaside resort (described in his book History of mathematics in XIX century). He was so excited that interrupted his vacation and rushed home to write a paper. Banach had a habit of working in a cafe. Feynman (not exactly a mathematician but close to it) recalls that he used to work in a topless bar at some time. If I remember correctly the so-called "tropical geometry" was invented by a group of mathematicians in a Rio-de-Janeiro beach, perhaps this is just a legend.

There is no opposition between "an office' and "home". Many mathematicians have offices at their homes, with books, computers, etc. Some of my friends have even blackboards in their home offices. A blackboard saves paper and it is more convenient for conversations. It is just a question of habit and convenience, where one prefers to work. Some people can have nicer office at home than at the university. Some people whom I know prefer home because smoking is prohibited on most US campuses:-)

Also, in some countries many mathematicians do not have convenient isolated offices. This was the case in Soviet Union, for example. Many of them also did not have convenient offices at home. In the beginning of my career, I remember proving most of my results while walking. I had regular walks with my adviser in a park near the university (my adviser shared an "office" in the university with 6 or 7 people, so we rarely discussed mathematics in his office).

When I moved to the US and obtained a convenient office, I still remember proving several theorems while walking my dog. I even think that walking stimulates mental activity, especially walking in a nice environment, in a park or a forest.

Many people used to work in a library if a library with convenient working space was available. Nowadays computers replace books, which makes the choice of a working place even more flexible.

I also know mathematicians who come to their office at 9 and work till 5, and do not work on Saturdays and Sundays. My impression is that this is a minority, but I am not aware of any statistics.

Famously, A. Wiles produced his celebrated proof of Fermat's Last Theorem after working in his attic at home (in near-total secrecy) for seven years.

This is clearly a kind of extreme example; however, doing research at home is not unusual, especially when one is looking for a quieter environment than the university.

Significant work is done by mathematicians while asleep (usually in bed). Normally, this does not happen in isolation but follows a long period of intense concentration on a problem while awake. It hardly needs to be said that this is a rare and unpredictable phenomenon.