Atiyah and Singer
One thing I find fascinating is their belief in the fundamental importance of the connection between physics and mathematics. Most famously, in recent years, this has resulted in what is apparently an extremely fruitful cross-fertilization between the high-energy physics community (especially the string theorists) and mathematicians.
I’ve occasionally wondered to what extent similar connections may appear as a result of the ongoing work in quantum information science.
These papers are ostensibly about a problem of great physical interest, namely, characterizing the possible relationships between the quantum state of a many-particle system, and the quantum state of the individual particles. This is certainly a problem of interest in quantum information, and the solution probably has implications in other areas of physics, like condensed matter physics.
Remarkably, these papers relate this physical problem to some quite sophisticated (and, occasionally, very recent) developments in mathematics. It seems pretty likely to me that the many problems of physical interest still open in this general area may in the future help stimulate the development of interesting new mathematics.