The main idea of The Devil's Arithmetic is expressed through main character Hannah Stern. Hannah is a Jewish girl who lives in New York, but she is not religious nor devout to her faith and traditions. In fact, Hannah shows no interest whatsoever in the stories of World War II and concentration camps that are told by her grandparents. This is significant as a "problem of the story" because it shows how, as early as a second generation of Jews, the young ones were already beginning to forget even something as macabre and history-changing as the holocaust.
The book then solves the main character's issues by using the supernatural as the agent that moves the story forward. This is done during the celebration of the Jewish celebration of Passover Seder, which Hannah reluctantly attends. Wishing that she would rather be with her friend celebrating the Christian Easter, Hannah inadvertently opens the door to none other than the prophet Elijah himself and he teleports Hannah to 1942 Poland during World War II, at a time where the Jews were suffering the most. Not only does she travel in time, but she is also given the persona of Chaya Abramowicz; a sick girl who can speak and understand Yiddish.
The whole idea of the time travel is to have Hannah, under the perspective of Chaya, learn about the vicissitudes and tragedies that her ancestors endured during the War. Moreover, Chaya witnessed hunger, starvation, mistreatment, persecution, and finally, death. The realities of what her people had to survive would instill in Hannah a clear understanding of why "forgetting" and not caring are such dangerous exterminators of the human experience; especially when you are the product of survivors. Those who have in any way, shape, or form sacrificed or become sacrificed, should always be honored and kept alive in our memories. Like she said herself, describing it as the brutal, evil, "devil's" arithmetic, the formula is simple:
"As long as we breathe, we can see and hear. As long as we can remember, all those gone before are alive inside us."