P ≠ NP Provable in PA

Ad hominem attacks, especially in mathematics should not stand but still I would give a heads up to laypeople: be very very cautious about just accepting this until further reviews are done because this is not the first time he submitted a paper with absolutely bombastic results which has been proven flawed. <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1712.09678" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1712.09678</a> is withdrawn and <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1812.03837" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1812.03837</a> is still being revised and from what I read about the latter the chances of it being salvaged is very low. Here&#x27;s one of the easiest to understand comments about it:<p>&gt; I have attempted to read through the paper, and there are several places where it states that construction can be done, and provides evidence that the construction can be done, but never outright does the construction.<p>It then rapidly devolves into higher mathematics which the author later acknowledged with &quot;Thanks. That does seem like a good objection&quot;.

This should probably have a &quot;(2020)&quot; in the title.<p>Also, I agree with the 8yo comment here: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=5785787" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=5785787</a><p>&gt; ArXiv has many &quot;proofs&quot; that P=NP and that P!=NP. ArXiv does not do any vetting of correctness (it is beyond their scope.) We don&#x27;t need a HN submission for this and the title is inaccurate&#x2F;clickbait.

For anyone wondering what PA stands for, after a few minutes digging I came across a subsection of this P versus NP Wikipedia Article [1] which lead to this article about Peano Axioms[2].<p>My guess would be it stands for Peano Axioms or Peano Arithmetic, which is a formalized system of reasoning about natural numbers -- if I understand the first couple sentences of the Wikipedia article.<p>1. <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;P_versus_NP_problem#Results_about_difficulty_of_proof" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;P_versus_NP_problem#Results_ab...</a><p>2. <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Peano_axioms" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Peano_axioms</a>

I don&#x27;t know why the authors can&#x27;t define any of these, but the complete mapping of capital letter soup to actual words is:<p>PA: Peano Arithmetic<p>EFA: Elementary Function Arithmetic<p>ZFC: Zermelo-Frankel set theoretic axioms plus the axiom of Choice

Note that this paper was first submitted to arXiv in May 2020. I haven&#x27;t been able to find any previous discussion by an expert, though.

I didn&#x27;t know and I&#x27;m sure others are wondering too: PA probably means Peano Arithmetic.<p>See <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Peano_axioms" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Peano_axioms</a> and <a href="https:&#x2F;&#x2F;math.stackexchange.com&#x2F;a&#x2F;213264" rel="nofollow">https:&#x2F;&#x2F;math.stackexchange.com&#x2F;a&#x2F;213264</a>.

Does anyone have a suggestion of a more engaging explanation of P != NP, its history and significance for the neophyte reader of popular math&#x2F;sci subjects?<p>On the lines of, Aczel, Amir D. The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (2001) or whatever.

Okay, I&#x27;ll bite. PA probably isn&#x27;t Pennsylvania, so what is it?

what is PA?