Which navigational method relies solely on mathematical computations?

Dead reckoning is the navigational method that relies solely on mathematical computations to determine the aircraft's position. This method involves calculating one's current position based on a previously determined position, known as the last known position, along with estimating speed, heading, and time. By applying these elements, a pilot can calculate how far they will travel over a specific period, allowing for navigation without external references.

In contrast, pilotage involves navigating by referencing visible landmarks on the ground, which does not rely on mathematical computations. Visual navigation similarly involves using visual cues and aids to guide the aircraft, again moving beyond computations. Flight planning encompasses a broader range of navigation aspects, including route selection, fuel calculations, and time estimations, but it does not specifically denote the act of navigating purely through mathematical means. Dead reckoning stands out because it consistently uses calculations to determine current and future positions while in flight.