TITLE: How much time per day to mathematicians usually spend working?
QUESTION [8 upvotes]: 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?

REPLY [2 votes]: 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).