A business or social networking method is operative in a server. The method enables mobile device users to meet one another, on a permission basis. The determination of whether a given pair of mobile device users are introduced depends on whether the server determines they are in intellectual or "cognitive" proximity, which is typically a function of one or more factors, such as: each user's reciprocal networking objective, the nature of the industry in which the user works, the user's level within the management hierarchy of his or her company, any specialty function the individual may possess, and so on. Individuals who are matched in one or more of such attributes to a given degree or threshold are said to be in intellectual proximity. According to the invention, when given mobile devices users are within physical proximity of one another during an overlapping time window, the server determines whether the users are also within a given intellectual proximity. If so, and if both users have opted to receive new introductions, the server issues a mutual collaboration opportunity message to each of the mobile device users to determine whether they desire to be introduced to one another. Preferably, the mutual collaboration opportunity message masks personally identifying information. If the mobile device users agree to be introduced, the server establishes a direct private messaging session between them.