Conmathematics (Conceptual Mathematics) : The Superultramodern
Mathematics (SM)
The term Conmathematics [ invented by Kedar Joshi (b.1979),
Cambridge (England), i.e. myself ] means Conceptual Mathematics.
It is a meta - mathematical system that defines the structure of
Superultramodern Mathematical Science. (Conmathematics means
that modern/ultramodern mathematics is not as conceptual as it
should be.)
It has four main components.
1. Conmathematical Definition of Mathematics :
a) Conmathematical definition of pure mathematics - Pure
mathematics is a system of 100% precise propositions believed to
be 99.999...% certain ( the 0.00...1 % margin in the belief
being for the sake of universal doubt : the principle that
'anything may be possible.'). Precise means every term of a
proposition is absolutely clarified, and every non - axiomatic
proposition is supported on the basis of axiomatic one/s leaving
no doubt, except the universal doubt. It is very possible that
some of the mathematical propositions are not clear ( or
understandable ) to some persons. And, some of the propositions
are less than 99.999...% certain to some persons. This
possibility effectively gives rise to the possibility of
multiple mathematical systems according to the nature of the
individuals concerned, though truth is believed to be existing
independent of individual minds. The principle of universal
doubt makes it necessary to review the mathematical systems
continuously so that in future they may not be seen to be
mathematical at all.
b) Conmathematical definition of applied mathematics - Applied
mathematics is a system of propositions constructed by applying
some or all of the pure mathematical propositions to deal with (
i.e. to explain and / or predict ) phenomena that are believed
to be less certain than the phenomena expressed by pure
mathematical propositions. For example, I cannot believe the law
of gravity ( the law that every matter, in principle, attracts
every matter out of some force or curvature of space - time ) to
be 99.999...% certain, as I can imagine a universe where the law
of gravity is invalid ( i.e. where every matter distracts every
matter out of some force or absence of space - time curvature ).
2. Philosophy as Mathematics :
According to the conmathematical definition of mathematics, the
core ideas in ultramodern science / philosophy, though appearing
to be philosophical, are, in fact, mathematical. For example,
the axiomatic component of the NSTP ( Non - Spatial Thinking
Process ) theory is pure mathematical, while its hypothetical
component is applied mathematical.
3. Conceptual Reconstruction of Pure Mathematics :
It entails some flaws in modern pure mathematics and the
ultramodern reconstruction of pure mathematics, free of those
flaws. Some of the flaws are mentioned below.
a) Flaw in the concept of hyperspace - The Joshian conjecture of
3 dimensional space [ that space, whether appearance or reality,
can have 3 and only 3 dimensions ( The conjecture is based on
two grounds : i. The NSTP theory implies falsehood of the
ontology of general relativity. ii. Four or higher dimensional
space cannot justifiably be imagined. ) ] implies that the
concept of hyperspace is invalid. And the flaw in the concept of
hyperspace has following implications :
i. The Riemann hypothesis ( which asserts that all interesting /
non - trivial solutions of the zeta function equation lie on a
straight line Re (z) = 1 / 2 ) shall never be proved as it is
based on the concept of four - dimensional space. ( Then still
how the Riemann hypothesis turns out to be correct for the first
1,500,000,000 solutions is in the same category as the
mathematical / experimental success of the general relativity,
despite of the background physics of the NSTP theory. )
ii. The Poincare conjecture [ if 3 dimensional sphere ( the set
of points in 4 dimensional space at unit distance from the
origin ) is simply connected ] shall neither be proved nor be
disproved as it is based on the concept of four - dimensional
space as well.
iii. Andrew Wiles' proof ( entitled : Modular elliptic curves
and Fermat's last theorem ) of Fermat's last theorem ( the
theorem that there are no whole number solutions to the equation
x^n + y^n = z^n for n greater than 2 ) is flawed as it is also
based on the concept of four - dimensional space.
b) Flaw in the concept of irrational number - An irrational
number ( e.g.