How much time per day to mathematicians usually spend working? I was reading Poincare's wikipedia page and I noticed that Poincare only did 4 hours of hard mathematical research a day, preferring to let his subconscious have the rest of the time to attack the problems. Is this true for other mathematicians and physicists as well? 
 A: From a biographical note on the great G.H. Hardy 

In fact for most of his life his day, at least during the cricket season, would consist of breakfast during which he read The Times studying the cricket scores with great interest. After breakfast he would work on his own mathematical researches from 9 o'clock till 1 o'clock. Then, after a light lunch, he would walk down to the university cricket ground to watch a game. In the late afternoon he would walk slowly back to his rooms in College. There he took dinner, which he followed with a glass of wine. When cricket was not in season, it was the Australian cricket scores he would read in The Times and he would play real tennis in the afternoons. 

By the way, that's real tennis as in https://en.wikipedia.org/wiki/Real_tennis 
A: As answers and comments indicate, probably some four hours a day.  The rest of the typical 9 to 5 day teaching and doing random administrative tasks, on evenings and weekends sometimes grading. 
A: Success is all about hard work. Mathematicians usually don't maintain a routine like a football player or a businessman. They found their work more interesting than any other works. This interest or passion made them obsessed to their research and personal inquiry including calculations. Sometimes they work more than regular schedule. Sometimes they take leisure. 
A: Alexandre Grothendieck'work routine at some point of his life, was spanning 10pm-6am (source: https://www.lemonde.fr/sciences/article/2019/05/06/les-archives-insaisissables-d-alexandre-grothendieck_5459049_1650684.html ). Giuseppe Ludovico Lagrange, the famous mathematician better known under his (naturalized) French name Joseph-Louis Lagrange (and the well-known contributions such as the concept of lagrangian, lagrange multipliers method, etc..) used to work from 6pm to midnight every evening, except when he had guests (source: a documentary from the Henri Poincare Institute available at https://www.youtube.com/watch?v=K_tAygfZnAE ). As explained in another answer,the British mathematician G.H. Hardy used to commit four hours a day for research. It is said that this was in fact, according to him, his limit in terms of daily productive work.  
It is interesting to compare the routine of such professional mathematicians to neighboring fields such as theoretical physics: from their own account, R.P. Feynman and S. Hawking developed an extraordinary ability to perform mental calculation that could speed up the mathematical part of their work and focus more on concepts. To a certain extent,this requires a certain level of abstraction which is also aimed at by the typical mathematician (which is why I add this complementary information in the answer).
