How can one sail against the direction of the wind? Intuitively, it would seem like one could only move in the direction of the wind. Terry Tao at UCLA dissects this problem in a very interesting post. From the analysis, it is the rudder of the boat that allows one to sail against the wind.
Using some assumptions about the effect of tacking the sail (exploiting the crosswind direction) and the use of keels (sails in water), different achievable boat velocities are analyzed. Through the use of both tacking and keels, one can theoretically achieve arbitrary directions and speeds.