The Critical Path Method (CPM) was developed by Morgan Walker of DuPont and James Kelley of Remington Rand in 1957–1959, originally to schedule complex plant maintenance shutdowns — the dependencies between tasks were far too many to schedule by hand.

The approach: break the project into 'activities,' note each activity's duration and the precedence dependencies between them, and connect everything into a network diagram. CPM is a deterministic method (durations are treated as known values), built to answer two core questions: How fast can this project possibly finish? Which tasks drag the whole project the moment they slip?

The other core concept is float (slack): how long an activity can be delayed without delaying project completion. Activities on the critical path have zero float — the moment they slip, the whole project's delivery date slips; activities off the critical path have positive float and can be postponed within that float without affecting the final duration.

So 'critical' does not mean the task is the hardest or the most important — it means the task has no buffer at all: move it and you move everything. Identify the zero-float activities and you have found exactly the tasks a project manager must watch like a hawk.