White matter hyperintensities (WMH) are a hallmark of cerebrovascular disease and multiple sclerosis. Automated WMH segmentation methods enable quantitative analysis via estimation of total lesion load, spatial distribution of lesions, and number of lesions (i.e., number of connected components after thresholding), all of which are correlated with patient outcomes. While the two former measures can generally be estimated robustly, the number of lesions is highly sensitive to noise and segmentation mistakes – even when small connected components are eroded or disregarded. In this article, we present P-Count, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner. Using computational geometry, P-Count takes the persistence of connected components into consideration, effectively filtering out the noisy WMH positives, resulting in a more accurate and robust count of true lesions. We validated P-Count on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding. Our code will be made publicly available upon acceptance.