## Conmathematics (Conceptual Mathematics) : The Superultramodern Mathematics (SM)

Written by Dr Kedar Joshi

Continued from page 1

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 ).

http://superultramodern.blogspot.com

## The Superultramodern Principia : The Foundations of Superultramodern Science (SS)

Written by Dr Kedar Joshi

Continued from page 1

So far philosophers/scientists have argued too much regarding nature of mind, self, space, time, and, in general, reality. Now they should understand that truth on these matters might be known not through too much thinking and debate, but through more or less self-evident propositions, straightforward reasoning, and possibilities. Either, if they are smart enough, they would appreciate it or dismiss it and thus fail to see light forever.

- Dr Kedar Joshi, BSc MA DSc DA, PBSSI Cambridge, UK.

The Founder and President of 'British Superultramodern Scientific Institution' (BSSI). http://superultramodern.blogspot.com

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