Cell differentiation during development is traditionally viewed as a series of bifurcations (points at which cells can adopt one of two distinct fates) underpinned by complex gene regulatory networks. In addition to this ‘Waddington landscape’ view of cell fate decisions, cells might undergo gradual changes in the expression of a multitude of genes as one cell type transitions into another. Now, Simon Freedman and colleagues employ a branch of mathematics known as dynamical systems to analyse cell fate decisions from published single-cell RNA sequencing (scRNA-seq) data of haematopoiesis. Using pseudotime as a control parameter for the dynamical system, the researchers identify two statistical signatures that represent one-to-one transitions and one-to-many cell fate bifurcations. By combining scRNA-seq data and a mathematical toy model, the authors can identify a cell fate decision bifurcation from a progenitor cell into the neutrophil lineage. Subsequently, they reveal one-to-one transitions during neutrophil development that reflect the linear maturation of the lineage into mature neutrophils. Finally, by focusing on specific parts of dynamical systems theory (eigenvectors), they can pinpoint bifurcations in scRNA-seq datasets. Together, this work helps to produce a predictive understanding of cellular trajectories of differentiation from scRNA-seq data.