Superultramodern Science (SS) and The Millennium Problems in
Mathematics
In this article I address 3 of the 7 millennium problems in
mathematics announced by the Clay Mathematics Institute (CMI),
USA. I propose solutions (not all of which are meant to be
conclusive) to the problems using the ideas in Superultramodern
Science (SS), which is my foremost creation. (The remaining 4
problems seem to be outside the scope of SS.) It is of utmost
importance to note that the nature of the ideas and consequently
of the solutions is very radical and it would take painstaking
efforts to fully understand and appreciate the solutions
proposed. Also it has to be considered that according to
Conmathematics (Conceptual Mathematics) : the superultramdoern
mathematical science, the superultramodern scientific solutions
to the problems are, though apparently philosophical, in fact,
mathematical. Virtually all of the 3 problems are such that they
demand revolutionary changes in the current (modern/ultramodern)
sciences. And SS is thought to be an appropriate change. I shall
state the problems exactly as they are stated on the website of
the CMI. However, the statements are the ones which are brief
and not the ones that are official and descriptive. This choice
is out of the revolutionary nature of the solutions which makes
it senseless to consider the conventional or orthodox symbolic
patterns which essentially make the (official) statements look
complicated and descriptive.
1. Yang - Mills Theory The laws of quantum physics stand to the
world of elementary particles in the way that Newton's laws of
classical mechanics stand to the macroscopic world. Almost half
a century ago, Yang and Mills introduced a remarkable new
framework to describe elementary particles using structures that
also occur in geometry. Quantum Yang-Mills theory is now the
foundation of most of elementary particle theory, and its
predictions have been tested at many experimental laboratories,
but its mathematical foundation is still unclear. The successful
use of Yang-Mills theory to describe the strong interactions of
elementary particles depends on a subtle quantum mechanical
property called the "mass gap:" the quantum particles have
positive masses, even though the classical waves travel at the
speed of light. This property has been discovered by physicists
from experiment and confirmed by computer simulations, but it
still has not been understood from a theoretical point of view.
Progress in establishing the existence of the Yang-Mills theory
and a mass gap and will require the introduction of fundamental
new ideas both in physics and in mathematics.
SS solution : I suppose that light, for example, is a classical
wave and photon, for example, is a quantum particle. It's an
assumption in modern/ultramodern science (relativity theory)
that no massive entity travels at (or above) the speed of light.
>From the Superultramodern Scientific perspective [in particular,
the NSTP (Non - Spatial Thinking Process) theoretical
perspective] space is a form of illusion, mass is bulk or
quantity of matter, wave and particle are two conceptually
distinct entities existing in the form of non-spatial states of
consciousness/feelings. To sum up, wave -particle behaviour is
an orderly governed illusion where the massive quantum particles
do not really travel in space but are presented at the time of
wave collapse.
2. Poincare Conjecture If we stretch a rubber band around the
surface of an apple, then we can shrink it down to a point by
moving it slowly, without tearing it and without allowing it to
leave the surface. On the other hand, if we imagine that the
same rubber band has somehow been stretched in the appropriate
direction around a doughnut, then there is no way of shrinking
it to a point without breaking either the rubber band or the
doughnut. We say the surface of the apple is "simply connected,"
but that the surface of the doughnut is not. Poincar