The university affiliations in this list are all official academic affiliations such as official employment and degree programs, and non-academic positions (e.g., advisory committee, administrative staff, etc) are generally excluded. The official academic affiliations fall into three categories: 1) Graduate and Attendee, 2) Long-term Academic Staff, and 3) Temporary Academic Staff. Graduates are defined as those who hold Bachelor's, Master's, PhD, or equivalent degrees from a university, while attendees are those who formally enrolled in a degree-program at a university for at least one day but did not complete the program or obtain a degree (thus, honorary degrees, summer attendees, exchange students, and auditing students are generally excluded). The category of "Long-term Academic Staff" consists of tenure/tenure-track and equivalent academic positions, while that of "Temporary Academic Staff" consists of lecturers (without tenure), postdoctoral researchers, visiting professors/scholars (visitors), and equivalent academic positions. At any university, the specific title of academic staff solely determines the type of affiliation, regardless of the actual time the position was held by a medalist.
Further explanations on "visitors" under "Temporary Academic Staff" are presented as follows. 1) All informal/personal visits are excluded from the list; 2) all employment-based visiting positions, which carry teaching/research duties, are included as affiliations in the list; 3) as for award/honor-based visiting positions, this list takes a conservative view and includes the positions as affiliations only if the medalists were required to assume employment-level duty (teaching/research) or the medalists specifically classified the visiting positions as "affiliation/appointment/work" in their Curriculum Vita or reliable websites. To be specific, some award/honor-based visiting positions such as the "Shiing-Shen Chern Visiting Professorship" in UC Berkeley are awards/honors/recognition without requiring employment-level duty; in particular, attending meetings and giving public lectures, talks or non-curricular seminars is not a form of employment-level duty. Finally, summer visitors are generally excluded from the list (unless summer work yielded significant end products) since summer terms are not part of formal academic years; the same rule applies to extension schools of universities.
The number following a person's name is the year he/she received the Fields Medal; in particular, a number with asterisk (*) means the person received the award while he/she was working at the institution (including emeritus staff) containing that asterisk. A medalist with his/her name underlined implies that this person has been counted for a same institution in previous category. If a person had multiple positions under one category, only the position with highest rank is considered.
This list, together with List of Nobel laureates by university affiliation and List of Turing Award laureates by university affiliation, presents the university affiliation (with similar criteria) of people who have won highest honors in fundamental academic disciplines.
According to Wikipedia policies on no original research and objectivity/neutrality, it is impossible in Wikipedia to assign various weights to different types of affiliations. Hence, all types of affiliations count equally in the following table and throughout the whole page.