XPost: comp.theory, sci.math
From: user7160@newsgrouper.org.invalid
On 11/29/25 5:50 PM, olcott wrote:
> On 11/29/2025 7:37 PM, dart200 wrote:
>> On 11/29/25 4:38 PM, Richard Damon wrote:
>>> On 11/29/25 5:12 PM, dart200 wrote:
>>>> On 11/29/25 1:15 PM, Richard Damon wrote:
>>>>> On 11/29/25 3:48 PM, dart200 wrote:
>>>>>> On 11/29/25 12:24 PM, Richard Damon wrote:
>>>>>>> On 11/29/25 1:57 PM, dart200 wrote:
>>>>>>>> On 11/29/25 6:26 AM, olcott wrote:
>>>>>>>>> On 11/29/2025 2:33 AM, dart200 wrote:
>>>>>>>>>> On 11/29/25 12:00 AM, wij wrote:
>>>>>>>>>>> I just found that Goldbach conjecture may be a (A)NP problem
>>>>>>>>>>> if stated:
>>>>>>>>>>>
>>>>>>>>>>> Q: Given an even integer n, n>2. Is n the sum of two prime
>>>>>>>>>>> numbers?
>>>>>>>>>>>
>>>>>>>>>>> Proof Q∈ANP:
>>>>>>>>>>> v= AKS Primality Test // Ptime algorithm
>>>>>>>>>>> C= {| n=a+b } // card(C)∈ O(|Q|)
>>>>>>>>>>>
>>>>>>>>>>> bool gbf(int n) { // n is an even number
>>>>>>>>>>> int a,b;
>>>>>>>>>>> for(a=3; a>>>>>>>>>> b=n-a;
>>>>>>>>>>> if(v(a)&&v(b)) return true;
>>>>>>>>>>> }
>>>>>>>>>>> return false;
>>>>>>>>>>> }
>>>>>>>>>>> Thus, Q∈ANP (ANP=NP).
>>>>>>>>>>>
>>>>>>>>>>> Goldbach conjecture is likely a NPC problem.
>>>>>>>>>>> If so, from the ℙ≠ℕℙ result of
>>>>>>>>>>> https://sourceforge.net/projects/cscall/files/MisFiles/PNP-
>>>>>>>>>>> proof- en.txt/download
>>>>>>>>>>>
>>>>>>>>>>> We can conclude that no formal proof can solve Goldbach
>>>>>>>>>>> conjecture, if formal
>>>>>>>>>>> proof is a Ptime algorithm.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> boring semantic paradox variant
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>> I have always assessed that the Goldbach conjecture
>>>>>>>>> to be proven true requires an infinite proof. It seems
>>>>>>>>> best dismissed as insignificant.
>>>>>>>>>
>>>>>>>>
>>>>>>>> i fully believe the goldbach conjecture is a premise about
>>>>>>>> natural numbers that can be proven at some point one way or
>>>>>>>> another,
>>>>>>>>
>>>>>>>> i believe the same is true about the collatz conjecture,
>>>>>>>>
>>>>>>>> and rienmann hypothesis.
>>>>>>>>
>>>>>>>> when we do prove them, it will increase the totality of machines
>>>>>>>> we can compute halting in regards to
>>>>>>>>
>>>>>>>
>>>>>>> Fine thing to beleive, but we do know that there do exists true
>>>>>>> propositions that can not be proven.
>>>>>>
>>>>>> unless you can prove something undecidable, then it cannot just be
>>>>>> supposed to be so
>>>>>>
>>>>>
>>>>> Which Godel did.
>>>>>
>>>>> It may be a highly artificial statement, but he showed that it
>>>>> existed.
>>>>
>>>> it is an incredibly artificial ...
>>>>
>>>> "a truth that exists as true without proof" is mind numbingly
>>>> artificial construct that in fact has a proof, just not in a formal
>>>> system ...
>>>
>>> It is without proof IN THAT SYSTEM.
>>>
>>> It IS proven in a system with extra knowledge, knowledge that was
>>> used to build thee particular form of the relationship that we use to
>>> test the number.
>>>
>>> The key point is that relationship uses only operations in the base
>>> system
>>>
>>>>
>>>> like maybe we just didn't find the formal system robust enough to
>>>> describe what we're doing in godel's proof
>>>
>>> His system is totally formal.
>>>
>>> The point is that the interprestation can't be made in the base
>>> system the statement is expressed in, only a meta-system derived by
>>> adding choices to that original system.
>>>
>>> The point that is made is that in ANY sufficiently expressive system,
>>> there are statements which are true in it that can't be proven.
>>>
>>> Adding certain axioms/knowledge to that system to make it "higher
>>> order" can allow some to be proven and resolved.
>>>
>>> No matter how finitely high you go with this, you will ALWAYS end up
>>> with some statements that can't be proven.
>>>
>>> Only by adding an infinite number of these axioms/knowledge might it
>>> be possible to prove every statement, but then the system doesn't
>>> meet the initial requirements of a Formal Logic system of having a
>>> finite number of axioms.
>>
>> or we just haven't found a robust enough set of axioms to deal with it
>>
>
> The axioms are simply the currently existing
> finite set of basic facts of general knowledge
> of the actual world.
well sure axioms are just the set of premises we accept because of what
we can do with them
>
> It took me 28 years to this come up this idea
> it shouldn't take 28 more years for another
> human to understand it.
>
it is kinda crazy how people assert incompleteness is certainly innate
vs an indication we haven't found all necessary axioms yet
idk where the certainty comes from
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis
please excuse my pseudo-pyscript,
~ nick
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