Graduate Student's Thesis Defense Lasts Eleven Hours After Committee Discovers Off-By-One Error

A doctoral thesis defense in pure mathematics extended to eleven hours yesterday after a committee member discovered that the candidate had indexed a sequence starting at one instead of zero, an error that propagated through the subsequent 200 pages of proofs. Candidate Emily Summand, who has spent six years on her thesis titled "Asymptotic Bounds for Generalized Partition Functions Over Finite Fields," was ninety minutes into a confident presentation when Professor Harold Basis raised his hand. "Page seven, Definition 3.1," Basis said. "Your sequence begins at n equals one. Should it not begin at n equals zero?" The room fell silent. Summand stared at the definition. She turned to page eight. Then page forty. Then page one hundred and twelve. The color reportedly drained from her face in stages, each stage corresponding to another theorem that depended on the initial indexing. "Everything shifts," Summand whispered. "Every sum, every bound, every asymptotic estimate. The main theorem's constant changes from seven to eight. Or maybe nine. I need a moment." The moment lasted nine and a half hours, during which Summand re-derived her principal results at the blackboard while the committee consumed three pots of coffee and two pizzas ordered by the department secretary. "The remarkable thing is that most of her results survive," noted committee chair Professor Ada Eigenvalue. "The bounds shift by a constant factor, the asymptotics remain valid, and the core methodology is sound. She essentially re-proved her thesis in real time, which is either the most impressive or the most unnecessary thing I have ever witnessed." Summand passed her defense at 9:47 p.m. Her first act as a doctor of philosophy was to write "START AT ZERO" on a sticky note and attach it to her laptop. She has since been offered a postdoctoral position by two committee members, both of whom cited "grace under pressure" as the deciding qualification.