This paper discovers that current variational principle and Noether theorem for both different physics systems and (in)finite freedom systems have missed the double extremum processes of the general extremum functional that is deduced by variational principle and necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her theorem, which result in the crisis deducing all the physics laws. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle problem in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical and physical pictures for (in)finite freedom systems are discovered. The improved variational principle and improved Noether theorem are given, which are key useful to different branches of science.as key tools of studying and processing them.