The failure of mathematics

In the late nineteenth century mathematicians established that it is not merely difficult but impossible to deduce Euclid I from Euclid I to IV. The square root of two is not rational but irrational, the sum of two odd numbers is always an even number , a polynomial quadratic equations cannot have more than two roots , it is not possible to trisect the general given angle , it is impossible to square a circle and duplicate a cube and it is not possible to draw a regular heptagon. These are all famous mathematical impossibilities. But the mathematical variation of liar''s paradox says that ¿In any logical system one can construct statements that are neither true nor false.¿ [Gödel''s first incompleteness theorem] In this work, the author re ¿ probed the parallel postulate problem and found sixteen new consistent findings which may give birth to a new field of science. Also, the author''s findings establish the above mentioned theorem.