  We identify new, rather serious, physical and axiomatic inconsistencies of
the current formulation of string theories due to the lack of invariant units
necessary for measurements, lack of preservation in time of
Hermiticity-observability, and other shortcomings. We propose three novel
reformulations of string theories for {\it matter} of progressively increasing
complexity via the novel iso-, geno- and hyper-mathematics of hadronic
mechanics, which resolve the current inconsistencies, while offering new
intriguing possibilities, such as: an axiomatically consistent and invariant
formulation on curved manifolds, the reduction of macroscopic irreversibility
to the most primitive level of vibrations of the universal substratum (ether),
or the treatment of multi-valued biological structures. We then identify three
corresponding {\it classical} formulations of string theories for {\it
antimatter} via the novel anti-isomorphic isodual mathematics. We finally
outline the intriguing features of the emerging new cosmologies (including
biological structures, as it should be for all cosmologies), such as: universal
invariance (rather than covariance) under a symmetry isomorphic to the
Poincar\'e group and its isodual; equal distributions of matter and antimatter
in the universe (as a limit case); continuous creation; no need for the missing
mass; significantly reduced dimensions; possibility of experimental
identification of matter and antimatter in the universe; and identically null
total characteristics of time, energy, linear and angular momentum, charge,
etc.
