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It entails some flaws in modern pure mathematics and ultramodern reconstruction of pure mathematics, free of those flaws. Some of flaws are mentioned below.
a) Flaw in 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 ontology of general relativity. ii. Four or higher dimensional space cannot justifiably be imagined. ) ] implies that concept of hyperspace is invalid. And flaw in concept of hyperspace has following implications :
i. The Riemann hypothesis ( which asserts that all interesting / non - trivial solutions of zeta function equation lie on a straight line Re (z) = 1 / 2 ) shall never be proved as it is based on concept of four - dimensional space. ( Then still how Riemann hypothesis turns out to be correct for first 1,500,000,000 solutions is in same category as mathematical / experimental success of general relativity, despite of background physics of NSTP theory. )
ii. The Poincare conjecture [ if 3 dimensional sphere ( set of points in 4 dimensional space at unit distance from origin ) is simply connected ] shall neither be proved nor be disproved as it is based on 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 ( theorem that there are no whole number solutions to equation x^n + y^n = z^n for n greater than 2 ) is flawed as it is also based on concept of four - dimensional space.
b) Flaw in concept of irrational number - An irrational number ( e.g. Ö 2 ) is not really a number at all as no number can be a square root of 2. 'Ö 2', for example, is a mere symbolic way of saying square root of 2 without actually presenting it, as any way it does not exist.
4. Conmathematical Foundations of Pure Mathematics -
These are in contrast with symbolic or, in particular, set theoretic foundations of pure mathematics ( as laid out in Bertrand Russell's Principia Mathematica ). The conmathematical foundations are conceptual ( though symbolism itself is a concept ) which attempt to define number, for example, as a symbolic representation of quantity and justify equality a + b = b + a on reason that in scalar addition order is irrelevant ( and, if possible, to decompose this concept or a group of concepts further ).