It came up with a way to efficiently evaluate the reliability of certain types of complex system using generating functions (https://en.wikipedia.org/wiki/Generating_function) to split the computation, which was far to large to solve with existing methods, into many embarrassingly parallel smaller problems and then reduce it back to a final result. The solution involved several distinct new ideas for it to work, really mind-blowing it was able to come up with it. The other cool thing was that, in the process and unprompted, it implemented code to validate and benchmark against existing approaches and known results just from the pdfs of the published papers (none of which gave reference implementations). In my research it would often take weeks just to replicate a single result from a paper.