Success of Hilbert's Axioms We know Euclid's axioms were found to be having many loopholes as in there were still many assumptions which weren't being stated in his system of axioms .
Are Hilbert's axioms today completely perfect ? Is modern mathematics today completely perfect and rigorous as in there are no loopholes , everything that needs to be assumed is assumed perfectly ?
Is it true in all the various areas of mathematics ?
 A: Nice question. Mathematics, as any other science (for example physics), is done by human beings, and is similarly prone to errors and imperfections. It is true that some students are attracted to mathematics out of a search for ultimate perfection. However, none of the historians, philosophers, or practitioners of physics, for example, pursue any such "ultimate" claims for their discipline.  Rather, they view investigations in physics as gradually increasing our understanding of what are generally classified as physical phenomena.  Similarly, the historians and philosophers of mathematics, and many mathematicians as well, view mathematical investigations as gradually increasing our understanding of what are generally classified as mathematical phenomena, rather than as any search for ultimate perfection. A further indication of the futility of "ultimate" claims for mathematics comes from foundational research in 20th century mathematics.  To give an example, it has been established that it is impossible to prove that ZF (the Zermelo-Fraenkel axiom system, commonly used in modern mathematics), is consistent, without using additional foundational assumptions that go beyond ZF.  See http://en.wikipedia.org/wiki/Zermelo-Fraenkel_set_theory
