  The Newton-Sabatier method for solving inverse scattering problem with
fixed-energy phase shifts for a sperically symmetric potential is discussed. It
is shown that this method is fundamentally wrong: in general it cannot be
carried through, the basic ansatz of R.Newton is wrong: the transformation
kernel does not have the form postulated in this ansatz, in general, the method
is inconsistent, and some of the physical conclusions, e.g., existence of the
transparent potentials, are not proved. A mathematically justified method for
solving the three-dimensional inverse scattering problem with fixed-energy data
is described. This method is developed by A.G.Ramm for exact data and for noisy
discrete data, and error estimates for this method are obtained. Difficulties
of the numerical implementation of the inversion method based on the
Dirichlet-to-Neumann map are pointed out and compared with the difficulty of
the implementation of the Ramm's inversion method.
