How does Google Maps use maths?
Google Maps knows your position via the Global Positioning System. Co-ordinate geometry is used.
How does Google Maps find a route from your current position to a particular destination?
The mathematics behind any map which intends in suggesting routes starts with finding the shortest path. There are many simple but powerful algorithms such as the Dijkstra’s algorithm that was developed for this cause.
The algorithm works by considering the map as a graph and by finding its shortest path by calculating the weights between the edges. Weights are an arbitrary value that is assigned for each node. In the simplest case, for the road map, weights are nothing but the distance between two road intersections (nodes).
Video explaining Dijkstra’s Algorithm