This talk is offered in honor of the remarkable mathematician Stephen H. Schanuel, who died last summer. It will primarily be historical and so accessible to all, including advanced undergraduates.

 

We proceed chronologically with some stories about Schanuel as a student, as junior faculty member, and as my (initially somewhat reluctant!) advisor.

 

We will give background and motivation for his formulation of the famous conjecture which remains the Holy Grail of transcendence investigations involving the exponential function. This conjecture continues to imply everything that is known to be true concerning values of the exponential function, but is much more powerful than anything now known.

 

We will say a few words about Ax's theorem on the analogue for functions. Finally, if time allows, I may attempt a few words on some recent activity related to Schanuel's Conjecture.