Final answer:
Solipsism is a philosophical belief that only one's own mind is sure to exist. It cannot be mathematically proven due to its subjective nature.
Step-by-step explanation:
In philosophy, solipsism is the belief that only one's own mind is sure to exist. It posits that there is no way to prove the existence of anything outside of one's own mind. Mathematically proving solipsism would be challenging because it involves subjective experiences and perceptions that cannot be objectively quantified.
While mathematics can provide logical deductions and proofs, it cannot prove or disprove the existence of reality beyond one's own mind. Solipsism is a philosophical concept that goes beyond the scope of mathematical reasoning.
Therefore, solipsism is not mathematically proven, as it is a philosophical belief rather than a mathematical theorem.