The genesis of this work was a fault-injection study on fault-tolerant matrix multiplication. Because of the way we injected the faults, all injections should have resulted in observable error. Instead, we were surprised to find that in some of the trials, the output was completely correct. The fault injector was mature and well-validated, and the code we were testing was simple; still, we examined both suites carefully and found no bugs. When we finally turned to the mathematics beneath the code, we found the unexpected theoretical resilience of the multiplication operator that we discuss here.

source: grugq