I’m curious to know in what scenarios or situations a professional mathematician can to get more chances to get a good achiviement in his/her work. In this introductory paragraph I explain what I know about the work of mathematicians, I know that professional mathematicians have many activities related to their academic work: for example I evoke when professors attend as public to a math conference or teach in a worshop to young professional mathematicians, or when they write an email to a coauthor or collaborator, or when they teach lecture notes in his/her universities to an advanced group of researchers, when they have a meeting in an congress with a specialist in his/her field of knowledge and can to discuss ideas in person from which they were able to continue their research from another point of view, or exchange ideas with other group or mathematicians of a far country, when they are advisors of an exceptional PhD student, or when they daily study and expand the articles of other mathematicians.

Question.I would like to now if it is possible to say something interesting and helpful about when, and if it possible what are the factors/circumstances involved in such academic situations and that benefit a good work, professional mathematicians can get a good feedback and chances to develop a successful achiviement of their investment of time and work in the activities related to their profession with other professional mathematicians.Many thanks.

With my question and the words *a good achievement/work* I evoke those professional situations that are virtually excellent in contrast to other situations that I, as ignorant of the academic world, might think that are a wasting time (another boried conference, another day of unsuccessful work after a contact with a research group,…*). In other words I believe that the work of mathematicians is very subtle, it seems to me more subtle than for example the work of an experimental physicist than can to work with instruments and schedule his/her work using the scientific method, while I think that dedicating of professional mathematicians can be compared to a full time job. I would like to know if it is possible to add tips about what factors or circunstances play a role improving the chances or opportunities to get efficiency in the work of professional mathematicians in special with their relationships to other colleagues.

If there is literature about this (how the mathematicians do a good work as professionals in their daily or scheduled (conferences/congress ispiring new ideas,…) activities, and in relation with other group of mathematicians) feel free to answer my question as a reference request adding the reference of the article as companion of your reasonings, that I try to search and read it from the literature.

*I add these words just to emphasize the discussion here, I think that the professional mathematicians do the best possible in their works, and I respect them.