There are many beautiful proofs in Mathematics and one cannot say that any particular proof is the most elegant. But if I had to choose one, it would definitely be the proof that's associated with the Gödel's Incompleteness Theorem. It is Mathematics at its best. Read more about it from the related link given just below.
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Mathematics begins with arithmetic.
You most likely mean "Are Shinigami real?". There is no proof that says they aren't, but no proof that says they are.
As one of the sciences astronomy is most closely related to mathematics, physics and chemistry.
A statement in maths is true only if it is proved by a series of mathematical manipulations and logic for any GENERAL number for which the statement should satisfy. Otherwise, it is only a conjecture. This is the beauty of mathematics and it is proof which differentiate mathematics from all other fields.
Security is not fool proof.