The problem. t-SNE (day 6) gave the field a way to see high-dimensional single-cell data, but at a cost: it’s slow on large datasets, scales awkwardly to millions of cells, and distorts global structure — distances between clusters aren’t meaningful. As cell counts exploded (see: droplet single-cell), that became limiting.

The idea. UMAP builds a fuzzy topological representation of the data — a weighted neighbour graph grounded in manifold theory — then optimises a low-dimensional layout to match it. In practice it runs much faster than t-SNE, handles large datasets gracefully, and preserves more of the global arrangement while keeping local neighbourhoods intact. The math is heavier; the payoff is speed and better structure.

Why it matters. UMAP is now the standard embedding in Scanpy and single-cell workflows — the plot I see in nearly every scRNA-seq paper. Reading it after t-SNE completes the visualisation arc: same goal (see the neighbourhoods), better engineering. And it carries t-SNE’s caution forward — it’s still a projection, so over-reading exact distances and cluster sizes remains a trap.

Verdict. Foundational for modern single-cell visualisation and dimensionality reduction, and the natural successor the t-SNE post pointed toward. Read it for the neighbour-graph framing — and keep treating the picture as a lens, not a measurement.