THE ZIPPER THEOREM.

THE ZIPPER THEOREM. PROOF is a very moving play about a father and daughter. The father is a great mathematician who has lapsed into madness. The daughter has some of his mathematical talent and fears that she will share his fate. They are close. The daughter has devoted years of her life to caring for him. We just watched a wonderful local production of PROOF. Our daughter Annalisa did the poster and the program cover. The design superimposes the information about the production over a page from a mathematical notebook (important to the plot). Prominent on the notebook page are the words “Zipper Theorem” and the beginning of the statement of the Zipper Theorem. The Zipper Theorem deals with the interweaving of a series a1, a2, a3…. and a series b1,b2,b3…. so that the new series is a1,b1,a2,b2,a3,b3…—just like the intermeshing of two sides of a zipper. In the Zipper Theorem, if both series converge at the same place (the limit), the intermeshed series converges at the same place (the limit). The daughter fears that the events (a1,a2,a3…) in her series (her life) will be similar to the events in her father’s life (b1,b2,b3…), and she will wind up in the same place. And the lives of father and daughter are interwoven like a closed zipper. As mathematicians would say, elegant.