The key advantage that a #polymath holds is their ability to develop mental models from different fields and apply them to solve problems in a unique way.
A brilliant scientist, Galileo Galilei was also master of perspective drawing (chiaroscuro) and his obervations of the moon got him in trouble because he debunked the perfect sphere myth by speaking of mountains and valleys before telescopes proved him right.
Combining principles of music and science, Hollywood icon Hedy Lamarr invented frequency hopping (based on the principles of how pianos work) which paved the way for Bluetooth, WiFi and GPS.
More recently, Daniel Kahneman, an Israeli psychologist was awarded the Nobel Prize in Economic Sciences for challenging the assumption of human rationality prevailing in modern economic theory. 
