Thread:Matthew Schroeder/@comment-38729545-20190724212729/@comment-38729545-20191005043835

“Okay... So I just decided to reread the new thread and quite frankly I now seeing why people are forgetting something.

Remember when I say that theories can happen to science?

Same can applies to the studies of math itself.

So let me explain the error in the logic Ultima is using in such a situation to this as this goes back into the studies of mathematics and no... I not kidding. There is literally a study of mathematics itself to the point I have to taken into consideration about the views regarding infinity especially with the fact there are... lengthy debates surrounding the foundation of mathematics to the point there was a crisis

For instance, I gonna post this link which is gone into into depth about Hilbert’s problems that still persists to even this day

Before I got into depth about it, I will tell you that problems he has with Ultima’s logic:

https://en.m.wikipedia.org/wiki/Hilbert%27s_problems

1st The continuum hypothesis (that is, there is no set whose cardinality is strictly between that of the integers and that of the real numbers) Proven to be impossible to prove or disprove within Zermelo–Fraenkel set theory with or without the Axiom of Choice (provided Zermelo–Fraenkel set theory is consistent, i.e., it does not contain a contradiction). There is no consensus on whether this is a solution to the problem. 1940, 1963

2nd Prove that the axioms of arithmetic are consistent. There is no consensus on whether results of Gödel and Gentzen give a solution to the problem as stated by Hilbert. Gödel's second incompleteness theorem, proved in 1931, shows that no proof of its consistency can be carried out within arithmetic itself. Gentzen proved in 1936 that the consistency of arithmetic follows from the well-foundedness of the ordinal ε₀. 1931, 1936

3rd Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that can be reassembled to yield the second? Resolved. Result: No, proved using Dehn invariants. 1900

4th Construct all metrics where lines are geodesics. Too vague to be stated resolved or not.[h] —

5th Are continuous groups automatically differential groups? Resolved by Andrew Gleason, depending on how the original statement is interpreted. If, however, it is understood as an equivalent of the Hilbert–Smith conjecture, it is still unsolved. 1953?

6th Mathematical treatment of the axioms of physics

(a) axiomatic treatment of probability with limit theorems for foundation of statistical physics

(b) the rigorous theory of limiting processes "which lead from the atomistic view to the laws of motion of continua" Partially resolved depending on how the original statement is interpreted.[9] Items (a) and (b) were two specific problems given by Hilbert in a later explanation.[1] Kolmogorov's axiomatics (1933) is now accepted as standard. There is some success on the way from the "atomistic view to the laws of motion of continua."[10] 1933–2002? 7th Is ab transcendental, for algebraic a ≠ 0,1 and irrational algebraic b ? Resolved. Result: Yes, illustrated by Gelfond's theorem or the Gelfond–Schneider theorem. 1934 8th The Riemann hypothesis ("the real part of any non-trivial zero of the Riemann zeta function is ½") and other prime number problems, among them Goldbach's conjecture and the twin prime conjecture Unresolved. —

9th Find the most general law of the reciprocity theorem in any algebraic number field. Partially resolved.[i] —

10th Find an algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution. Resolved. Result: Impossible; Matiyasevich's theorem implies that there is no such algorithm. 1970

11th Solving quadratic forms with algebraic numerical coefficients. Partially resolved.[11] —

12th Extend the Kronecker–Weber theorem on Abelian extensions of the rational numbers to any base number field. Unresolved. —

13th Solve 7th degree equation using algebraic (variant: continuous) functions of two parameters. The problem was partially solved by Vladimir Arnold based on work by Andrei Kolmogorov.[j] 1957

14th Is the ring of invariants of an algebraic group acting on a polynomial ring always finitely generated? Resolved. Result: No, a counterexample was constructed by Masayoshi Nagata. 1959

15th Rigorous foundation of Schubert's enumerative calculus. Partially resolved. —

16th Describe relative positions of ovals originating from a real algebraic curve and as limit cycles of a polynomial vector field on the plane. Unresolved, even for algebraic curves of degree 8. —

17th Express a nonnegative rational function as quotient of sums of squares. Resolved. Result: Yes, due to Emil Artin. Moreover, an upper limit was established for the number of square terms necessary. 1927

18th (a) Is there a polyhedron that admits only an anisohedral tiling in three dimensions?

(b) What is the densest sphere packing? (a) Resolved. Result: Yes (by Karl Reinhardt).

(b) Widely believed to be resolved, by computer-assisted proof (by Thomas Callister Hales). Result: Highest density achieved by close packings, each with density approximately 74%, such as face-centered cubic close packing and hexagonal close packing.[k] (a) 1928

(b) 1998

19th Are the solutions of regular problems in the calculus of variations always necessarily analytic? Resolved. Result: Yes, proven by Ennio de Giorgi and, independently and using different methods, by John Forbes Nash. 1957

20th Do all variational problems with certain boundary conditions have solutions? Resolved. A significant topic of research throughout the 20th century, culminating in solutions for the non-linear case. ?

21st Proof of the existence of linear differential equations having a prescribed monodromic group Partially resolved. Result: Yes/No/Open depending on more exact formulations of the problem. ?

22nd Uniformization of analytic relations by means of automorphic functions Unresolved. ?

23rd Further development of the calculus of variations

So basically what Ultima has just say is being put against other theories especially with LordWhis who isn’t wrong in the fact that not many mathematicians will necessarily agree with the view that Ultima is presenting per se.

https://en.m.wikipedia.org/wiki/Metamathematics

This is also goes back to the Gobel Incompleteness Theorem.

So to argue with metamathematics is a argument against itself.

As such, I would have to keep my stance as neutral regarding this as a result of the extensive argument surrounding this dilemma.”