Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A proof of impossibility, sometimes called a negative proof or negative result, is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or centuries of work attempting to find a solution. Proofs of impossibility are usually expressible as universal propositions in logic. One of the oldest and most famous proofs of impossibility was the 1882 proof of Ferdinand von Lindemann showing that the ancient problem of squaring the circle cannot be solved, because the number is transcendental and only algebraic numbers can be constructed by compass and straightedge. Another classical problem was that of creating a general formula using radicals expressing the solution of a polynomial equation of degree 5 or higher.

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