The phrase "hopeless quest" means a task or mission that is unlikely to succeed or achieve a positive outcome. It implies that there is little or no hope of accomplishing the goal. Full definition
Tiger Woods, with the way things are going for the nearly 40 - year - old fading superstar, is likely to add a 15th ailment to his injury count before he gets to that number in his increasingly hopeless quest to top 14 major championship titles. (sbnation.com)
It is the vision of something which stands beyond, behind and within, the passing flux of immediate things; something which is real, and yet waiting to be realized; something which is a remote possibility, and yet the greatest of present facts; something that gives meaning to all that passes, and yet eludes apprehension; something whose possession is the final good, and yet is beyond all reach; something which is the ultimate ideal, and the hopeless quest. (religion-online.org)
«Religion is the vision of something which stands beyond, behind, and within, the passing flux of immediate things; something which is real, and yet waiting to be realized; something which is a remote possibility, and yet the greatest of present facts; something that gives meaning to all that passes, and yet eludes apprehension; something whose possession is the final good, and yet is beyond all reach; something which is the ultimate ideal, and the hopeless quest.» (religion-online.org)