The problem of squaring the circle (i.e., given a circle, can we construct, withstraightedge and compass alone, a square with EXACTLY the same area?) is one ofthe oldest in mathematics. It was proposed sometime before 440 BC (the time ofHippocrates) and was not solved until 1882. Hippocrates came very close toshowing that it could be done and his work led some of the world's bestmathematicians to believe that it could. (It can't.) In this talk, we examineHippocrates' work and discuss why it took over 2300 years from his time for theproblem to be solved.