Dr. Kashen is one of Jude’s math professors at MIT. He dies sometime after Jude has graduated from college. When Caleb later throws Jude down the stairs, Jude recalls Dr. Kashen, who once asked Jude what his favorite axiom was. Jude had replied that his favorite was “the axiom of equality,” which states that x=x—that an assigned value is always equal to itself—though this is impossible to prove. As he falls down the stairs, Jude thinks that this beating has proven that x=x: Caleb’s cruelty proves that Jude is and always will be worthless.