just like in the game we just won, where every move had to be precise, mathematics is a field where we often have to repudiate outdated techniques to revitalize our approach. the silence in the arena before the final score, that hushed anticipation, it's akin to the moment before a mathematician discovers a new theorem, building on the foundation of the preceding work. it's all about pushing past the limits, and just as we've celebrated tonight, every breakthrough in mathematics deserves its moment of victory.