Mathematics is a universal language, Hale says, but there are communication barriers. For it to be universal, you have to have people who are receptive to communicating with other disciplines. There are many mathematicians who don't want to do that. They prefer to do their mathematics. On the other hand, some mathematicians would like to interact with other disciplines but encounter difficulty.
Engineers often see the role of a mathematician as that of a handbook.
Mathematicians come with tools, and the engineer wants a tool. But that's not good interdisciplinary work. In good interdisciplinary work, you complement others' way of thinking and they complement yours, so new ideas occur on both sides. On a marker-board in his office in the Skiles Building, Hale has written the equation of a mathematical model for the creation of metal alloys. Posted on the markerboard are pictures of complicated patterns in the formation of alloys.