Is this LLM-generated? The style is somewhat off (long lists repeating the same thing over and over, calling random meta statements “theorems”), and the link to the repo is completely broken.
Every time I try to understand algebraic geometry I get stuck at just beyond varieties and ideals. I can't even work my way up to chain complexes and homologies to even get a hold on the content. Honestly functors and natural transformations, I dont grok either, so its greek to me.
Like whenever i'm working through definitions or content it all makes sense. But not being a working mathematician it all just blurs away into abstract nonsense that I can't organize internally.
math looks pretty legit. the only issue would come from the formulation of the category Comp and if it actually represents what it wants to. Hopefully some bigshot looks at this soon
* First, it's written in the typical style of AI slop.
* Second, a mathematician I know and trust writes "I went straight to the technical part (Sect. 3) and randomly checked one of the results (Theorem 3.14), finding that it is obviously false. (The category Comp mentioned in the theorem is formally introduced and makes sense per se, but it is certainly not additive with the proposed definition, as claimed in the statement of the theorem)."
* Third, another mathematician I know and trust writes "I spent almost an hour poking through here carefully to see where the more central claims begin to fall apart. Theorems 3.24 and 4.1 brazenly contradict each other, proving respectively that problems in P are homologically trivial and that all NP-complete problems are homologically isomorphic to all problems in NP. Even more to the point, the proof of 3.24 really shows the lie where it says "The detailed argument uses the functoriality of the computational homology construction and the fact that homology isomorphisms preserve the 'computational topology' of problems." The last claim is, naturally, not mathematically defined. The computational chain complex also appears not to be genuinely defined, as far as I can tell. I haven't compared to see what the author chucked into the formalized definition."
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[ 4.3 ms ] story [ 35.3 ms ] threadhttps://github.com/comphomology/pvsnp-formal
Like whenever i'm working through definitions or content it all makes sense. But not being a working mathematician it all just blurs away into abstract nonsense that I can't organize internally.
* Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves, An Invitation to Algebraic Geometry, Springer, Berlin, 2004.
and then this:
* Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.
* First, it's written in the typical style of AI slop.
* Second, a mathematician I know and trust writes "I went straight to the technical part (Sect. 3) and randomly checked one of the results (Theorem 3.14), finding that it is obviously false. (The category Comp mentioned in the theorem is formally introduced and makes sense per se, but it is certainly not additive with the proposed definition, as claimed in the statement of the theorem)."
* Third, another mathematician I know and trust writes "I spent almost an hour poking through here carefully to see where the more central claims begin to fall apart. Theorems 3.24 and 4.1 brazenly contradict each other, proving respectively that problems in P are homologically trivial and that all NP-complete problems are homologically isomorphic to all problems in NP. Even more to the point, the proof of 3.24 really shows the lie where it says "The detailed argument uses the functoriality of the computational homology construction and the fact that homology isomorphisms preserve the 'computational topology' of problems." The last claim is, naturally, not mathematically defined. The computational chain complex also appears not to be genuinely defined, as far as I can tell. I haven't compared to see what the author chucked into the formalized definition."