The Origin of the 11d World Membrane as a Pascal Conic Section of Six 1d Strings in a 5d Projective Space
The biography of David Hilbert discusses a debate concerning whether it was an intellectual faux pas to advocate advancing the 2000 year old Theorem of Pappus to the status of an Axiom. This issue is notable from a number of perspectives, one being his 1920 proposal establishing the Hilbert Program of formulating mathematics and/or geometry on a more solid and complete logical foundation conforming to inclusively greater ‘meta-mathematical principles.’
Yet at that time, he proposed this could be done if: 1. all math follows from a complete or correctly-chosen finite system of axioms, and 2. this axiom system is provably consistent through some means like his epsilon calculus. Although this formalism has been successfully influential in regard to Hilbert’s work in algebra and functional analysis, it failed to engage in the same way with respect to his interests in logic, as well as physics – not to mention his axiomatizion of geometry, given the sketchy issue of regarding Pappus’s theorem as an axiom. Likewise, a similar problem arose when Bertrand Russell rejected Cantor’s proof that there was no ‘greatest’ cardinal number, and went on to defend the ‘logicism’ of his and A. N. Whitehead’s proposition in <i>Principia Mathematica</i> that all mathematics is in some important sense reducible to logic. But both Hilbert and Russell’s support for an axiomatized mathematical system of definitive principles that could banish theoretical uncertainties “forever” would end in failure by 1931.
For Kurt Gödel demonstrated that any such non-contradictory (self-consistent) formal system comprehensive enough to at least include arithmetic, could not demonstrate