I survey some examples of materials whose recent discovery was based in an essential way on mathematical ideas. The main idea concerns compatibility, the fitting together of the phases of a material. Some of the emerging materials have the ability to change heat directly into electricity without the need of a separate electrical generator.
Bibliographical noteFunding Information:
This work was supported by ONR (N00014-14-1-0714), AFOSR (FA9550-15-1-0207), NSF (DMREF-1629026), and the MURI program (FA9550-18-0095, FA9550-16-1-0566).