  The new great development in Physics could be related to the excited progress
of a new mathematics: ternary theory of numbers, ternary Pithagor theorem and
ternary complex analysis, ternary algebras and symmetries, ternary Clifford
algebras,ternary differential geometry, theory of the differential wave
equations of the higher degree n>2 and etc. Especially, we expect the powerful
influence of this progress into the Standard Model (SM) and beyond, into high
energy neutrino physics, Gravity and Cosmology. This can give the further
development in the understanding of the Lorentz symmetry and matter-antimatter
symmetry, the geometrical origin of the gauge symmetries of the Standard Model,
of the 3-quark-lepton family and neutrino problems, dark matter and dark energy
problems in Cosmology.
  The new ambient geometry can be related to a new space-time symmetry leading
at high energies to generalization of the Special Theory of Relativity. We
related the future of this development with C_n numbers, n-algebras (n>2) and
corresponding geometrical objects. We will discuss the following results - C_n
complexification of R^n spaces - C_n structure and the invariant surfaces - C_n
holomorphicity and harmonicity - The link between C_n holomorphicity and the
origin of spin 1/n - New geometry and N-ary algebras/symmetries - Root system
of a new ternary TU(3) algebra - N-ary Clifford algebras - Ternary 9-plet and
27-plet number surfaces
