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To be listed, an account must have at least 1,000 Twitter followers and belong to an individual as opposed to a group.
Generally, a Ph.D. in mathematics or a closely related field is required. Exceptions to the Ph.D. rule are made in some cases, e.g., for current Ph.D. students and/or individuals who work in the field and have a substantial following among list members.
Individuals who meet the Ph.D. and follower criteria, but who no longer work in the list field, typically are included in the list. This aids the list in serving as a sort of window on career possibilities.
The list is not necessarily comprehensive. In particular, coverage outside the communities of most existing list members may be poor. Suggestions for additions, including self-nominations, are welcome via Twitter DM. Inclusion of links to Google Scholar pages is helpful.