In his 1944 book "Practical Analytic Geometry with Applications to Aircraft," Roy Liming put forward a goal of developing a "practical system of analytic calculation techniques for direct use in the aircraft, automotive, and marine industries." He did so because, as he said, "the application of mathematical methods results in more complete control of the developments from basic conditions. Consequently, desired or intended performance characteristics are more nearly realized." At the Boeing company, we have been pursuing this goal for over 50 years with some stunning successes and a few abject failures. In this talk, I will discuss both successes and failures considered from the point of view of the practicing engineer. I will describe, using Boeing projects such as the 777 airplane, how some geometric design concepts have enabled designers to do more and how others have actually inhibited productivity. Of course, each success or failure is a learning opportunity, pointing the way to new mountains to be conquered. I will finish the discussion by describing mathematical problems in the area of geometric modeling that continue to aggravate and frustrate engineers. I promise not to provide solutions - only problems of mathematical and industrial interest.