Dividing by zero is mathematically undefined because it leads to contradictions and meaningless results. When the denominator approaches zero, the quotient tends toward infinity, which contradicts intuitive understanding of division. The discussion highlights that division is only defined for nonzero denominators, and attempting to divide by zero produces nonsensical expressions. Some participants argue that exploring division by zero could reveal deeper mathematical insights, but the consensus remains that it is not a valid operation within standard mathematics. Ultimately, division by zero is recognized as an essential limitation in mathematical definitions.