Most people, on coming to know that I do research in pure math, respond with a nod or a wide-eyed, “Ohh, that must be so hard!” Occasionally however, someone goes further and asks me what my research is really about. And then, I am usually in a fix.
How do I respond? There’s no way to explain that I study special values of L-functions for automorphic forms to a person who is not already familiar with all these words. So I usually take refuge in generalities like “Prime numbers”. Sometimes when I am in the mood, I explain to them what Fermat’s last theorem says (if I am lucky they already know this) and add that I work with methods ‘related to’ how Fermat was proven.
It was therefore a source of great joy to me to read Barry Mazur’s excellent article in the Bulletin on error-terms in number theory and the Sato-Tate conjecture. While the article isn’t quite about what I do research on, it comes fairly close. More importantly, it is engrossing, beautifully written, mathematically solid and accessible to anyone who knows some college-level mathematics and statistics. Perhaps, I should start carrying a copy of it in my pocket for exigencies like described above.