Trust arises from confidence in a person or confidence in the practices of an institution. Theorists argue that institutional trust depends, to varying extents on intrapersonal trust, which is trust between people who know each other. Science rests its claim to expert knowledge on the practices of knowledge production engaged in by its institutions. Most people cannot check these practices themselves and effectively must trust the experts who explain and vouch for those practices of science, and thus, there is an element of intrapersonal trust needed if the laity is to have trust in science. Much of the sociology of science is concerned with democratic exchanges between scientists and other citizens, in which scientists are expected to show a commitment to open-mindedness and transparency, yet this may leave scientists and their knowledge vulnerable to contestation in terms that may undermine trust in their science. In this article, I draw on data generated in a study of Australian scientists to describe the ways in which trust was important in the work of these scientists and consider the consequences for a scientist who is prepared to admit to uncertainty. Drawing upon these data and from media accounts of the COVID-19 vaccination debate in Australia, I argue that science education for contemporary society must equip scientists and the laity for relationships that are more than narrowly cognitive. I argue for an education that makes explicit the ways in which the community of science interacts to produce and verify knowledge, and that equips students to recognise uncertainty and dissent as central to science and value expert knowledge. I suggest approaches that may achieve this goal.