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The Wikipedia page of the Goldbach's weak conjecture states that "In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. As of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer-reviewed journal. The proof was accepted for publication in the Annals of Mathematics Studies series in 2015, and has been undergoing further review and revision since; fully-refereed chapters in close to final form are being made public in the process."

So my question is if some researcher or mathematician wants to use the proof of the Goldbach's weak conjecture by Harald Helfgott as a theorem and apply it as a known result in their proof then can he/she do that? Because the web results say that the proof is widely accepted by the mathematical community as of 2023 although it's still not published in a peer-reviewed journal.

Dávid Laczkó
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Ok-Virus2237
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    Use it if you want to, simply state the verdict is still out at the moment. – A rural reader Oct 07 '23 at 21:20
  • Related https://math.stackexchange.com/questions/3164020/the-significance-and-acceptance-of-helfgott-s-proof-of-the-weak-goldbach-conject, pointing at https://webusers.imj-prg.fr/~harald.helfgott/anglais/book.html – Henry Oct 07 '23 at 23:36
  • Yeah so if I understood correctly then it means that although the proof is now widely accepted even by highly respected journal Annals of Mathematics, it's being rewritten by Helfgott to improve readability and fix some errors (that don't affect the proof as a whole). But the thing is that he's quite busy with other works and also awaiting 2nd round of refree report so maybe we can get some progress by year end or maybe even later. So I guess we can't use his proof as known result (theorem) unless until it's published completely? – Ok-Virus2237 Oct 08 '23 at 12:10
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    The WEAK Goldbach conjecture is DEFINITELY solved. The bound was decreased multiple times until the rest could be done by brute force. This theorem IS a theorem. – Peter Oct 08 '23 at 13:16

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