Introduction
This blog aims to be the clearing house of information and queries about the resolution of the centuries-old conjecture post by Fermat in 1637 known as Fermat's last theorem (FLT) and its off-shoot: the development of the new mathematics and physics. Although the threads, articles and posts in various blogs, websites and forums across the internet already provide an overview of the subject, I shall summarize them all right now and provide details later.
1) The failure to resolve FLT for 360 years is attributed to the defects of the underlying fields, namely, foundations, number theory and the real number system.
2) Critique-rectification of these fields was undertaken starting 1992 that yielded:
a) Identification of defects of foundations, particularly, present mathematical reasoning and their remedy.
b) The requirement for contradiction-free mathematical space, since any contradiction or inconsistency reduces a mathematical space to nonsense, and the remedy.
c) Identification of the defects of the real number system and the remedy.
d) The remedy for the major flaw of number theory: lack of valid axiomatization of the integers.
e) The remedy for the present flaw in extension of mathematical space.
f) Characterization of undecidable propositions.
g) The reconstruction of the real number system into the contradiction-free new real number system.
g) The countably infinite counterexamples to FLT.
3) The development of the new non-standard calculus whose base space is the new real number system.
4) Implications of the characterization of the characterization of undecidable propositions
for mathematical physics and the remedy for the flaw of present methodology called mathematical modelling.
5) That remedy is called dynamic modelling. While mathematical modelling EXPLAINS nature in terms of numbers, equations, functions, inequalities and statistical trends, dynamic modelling EXPLAINS nature in terms of its laws. Then the task of the physicists is to discover the laws of nature.
6) The discovery of the basic constituents of matter called superstring.
7) The solution of the 200-year old gravitational n-body problem in 1996.
8) The development of the flux theory of gravitation that now qualifies as grand unified theory or the theory of everything.
For background materials and references visit my website:
http://home.iprimus.com.au/pidro/
Comments, contributions, criticism, contrary opinions and debate are welcome.
E. E. Escultura
1) The failure to resolve FLT for 360 years is attributed to the defects of the underlying fields, namely, foundations, number theory and the real number system.
2) Critique-rectification of these fields was undertaken starting 1992 that yielded:
a) Identification of defects of foundations, particularly, present mathematical reasoning and their remedy.
b) The requirement for contradiction-free mathematical space, since any contradiction or inconsistency reduces a mathematical space to nonsense, and the remedy.
c) Identification of the defects of the real number system and the remedy.
d) The remedy for the major flaw of number theory: lack of valid axiomatization of the integers.
e) The remedy for the present flaw in extension of mathematical space.
f) Characterization of undecidable propositions.
g) The reconstruction of the real number system into the contradiction-free new real number system.
g) The countably infinite counterexamples to FLT.
3) The development of the new non-standard calculus whose base space is the new real number system.
4) Implications of the characterization of the characterization of undecidable propositions
for mathematical physics and the remedy for the flaw of present methodology called mathematical modelling.
5) That remedy is called dynamic modelling. While mathematical modelling EXPLAINS nature in terms of numbers, equations, functions, inequalities and statistical trends, dynamic modelling EXPLAINS nature in terms of its laws. Then the task of the physicists is to discover the laws of nature.
6) The discovery of the basic constituents of matter called superstring.
7) The solution of the 200-year old gravitational n-body problem in 1996.
8) The development of the flux theory of gravitation that now qualifies as grand unified theory or the theory of everything.
For background materials and references visit my website:
http://home.iprimus.com.au/pidro/
Comments, contributions, criticism, contrary opinions and debate are welcome.
E. E. Escultura
posted by E. E. Escultura at 3:43 AM
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