The 1001 Inventions traveling exhibition (London, Istanbul, New York, Abu Dhabi, Los Angeles, and now Washington DC) displays a representative sample of popular myths about medieval science and technology in Muslim lands. A prominent example is its claims about human muscle-powered flight achieved through wings constructed by the 9th century Andalusian Ibn Firnas and the 17th century Ottoman Hezarfen Ahmet Çelebi. These feats have very poor historical documentation, and a simple scaling argument shows the virtual physical impossibility of such achievements. Yet not only are beliefs about the flights of Ibn Firnas and Hezarfen common among Muslim populations today, they have been endorsed by the engineers and historians associated with the 1001 Inventions project. The myth of medieval Muslim flight serves as a case study illuminating how the history of science in Muslim lands has been fashioned into a narrative supporting present needs for technological modernization. This narrative, however, also supports a revival of medieval ways of thinking about nature, and is an obstacle to improving the poor state of natural science in Muslim-majority countries.