On May 25, 2018, the European Union’s General Data Protection Regulation (GDPR) came into force. EU citizens are granted more control over personal data while companies and organizations are charged with increased responsibility enshrined in broad principles like transparency and accountability. Given the scope of the regulation, which aims to harmonize data practices across 28 member states with different concerns about data collection, the GDPR has significant consequences for individuals in the EU and globally. While the GDPR is primarily intended to regulate tech companies, it also has important implications for data use in scientific research. Drawing on ethnographic fieldwork with researchers, lawyers and legal scholars in Sweden, I argue that the GDPR’s flexible accountability principle effectively encourages researchers to reflect on their ethical responsibility but can also become a source of anxiety and produce unexpected results. Many researchers I spoke with expressed profound uncertainty about ‘impossible’ legal requirements for research data use. Despite the availability of legal texts and interpretations, I suggest we should take researchers’ concerns about ‘unknowable’ data law seriously. Many researchers’ sense of legal ambiguity led them to rethink their data practices and themselves as ethical subjects through an orientation to what they imagined as the ‘real people behind the data’, variously formulated as a Swedish population desiring data use for social benefit or a transnational public eager for research results. The intentions attributed to people, populations and publics – whom researchers only encountered in the abstract form of data – lent ethical weight to various and sometimes conflicting decisions about data security and sharing. Ultimately, researchers’ anxieties about their inability to discern the desires of the ‘real people’ lent new appeal to solutions, however flawed, that promised to alleviate the ethical burden of personal data.