In this research, we examine the hypothesis that gender disparities in international research collaboration differ by collaboration intensity, academic position, age, and academic discipline. The following are the major findings: (1) while female scientists exhibit a higher rate of general, national, and institutional collaboration, male scientists exhibit a higher rate of international collaboration, a finding critically important in explaining gender disparities in impact, productivity, and access to large grants. (2) An aggregated picture of gender disparities hides a more nuanced cross-disciplinary picture of them. (3) An analysis of international research collaboration at three separate intensity levels (low, medium, and high) reveals that male scientists dominate in international collaboration at each level. However, at each level, there are specific disciplines in which females collaborate more than males. Further (4), gender disparities are clearly linked with age. Until about the age of 40, they are marginal and then they begin to grow. Finally, we estimate the odds of being involved in international research collaboration using an analytical linear logistic model. The examined sample includes 25,463 internationally productive Polish university professors from 85 universities, grouped into 27 disciplines, who authored 159,943 Scopus-indexed articles.