I am an academic mathematician, who (like most) is an expert in a sub-subfield in my discipline. Outside my specialty I certainly have some knowledge, but I usu

I am an academic mathematician, who (like most) is an expert in a sub-subfield in my discipline. Outside my specialty I certainly have some knowledge, but I usually can't distinguish a major breakthrough from incremental progress. Meanwhile, I've been asked to evaluate hundreds of other mathematicians, on hiring committees and grant panels. Most of the applications are in specialities bordering mine, but not squarely in my area of expertise. Usually I can get a sense of what they've accomplished, but in most cases I can't reliably evaluate its depth or importance. Unfortunately, external markers of quality are needed.