In any sport or human endeavor, coaches regularly state “play to your strengths.” One might not guess that a land-locked, mountainous country like Switzerland would have strengths that would give them a chance at winning the oldest, most competitive sailing competition in the world, the America’s Cup. But it does! In 2003, in the Harukai Gulf of New Zealand, a Swiss yacht called Alinghi was the surprise winner of the America’s up. And in 2007, in the Mediterranean sea near Valencia, Alinghi confirmed its dominance by defeating the New Zealand Team 5 to 2 in a breathtaking final match race. Mathematics and computational science were involved in Alinghi’s first successes in 2003, when it won the Louis Vuitton Cup and then the America’s Cup by defeating the defending Black Magic Team of New Zealand. Mathematics helped create the design of the boat which brought the defender Alinghi its second triumph in Valencia in 2007. Mathematical models were used in the design phase and again during the competition. Of course mathematical models alone are not enough to guarantee success in a race as competitive as the America’s Cup: a great team and much luck are needed. We know that people and explorers have been sailing literally since the stone age. It may seem astonishing that, with all the technological progress that has been achieved, sailing is still such a challenge. Alinghi has shown that part of the progress that will likely be made in the future rests on mathematical models and their numerical solution.