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Jul 21, 2023 at 11:22 comment added Damiano Mazza A related question has two answers which contain some possibly useful explanations. In short, there has been some interesting work but it's too soon to see if Durov's thesis will have remarkable applications. This was nearly 4 years ago, I am not sure whether things have changed in the meantime (I am not an expert of this field at all). At any rate, I think that we may exclude for sure that any mistake has been found.
Jul 16, 2023 at 13:42 comment added user473423 This is the definition of a classic: everybody mentions it, but no one ever reads it.
Jul 15, 2023 at 22:15 comment added Geoffrey Irving It is surprising to me that anything can be often mentioned but almost forgotten!
Jul 15, 2023 at 19:05 comment added Gro-Tsen My gut feeling about many approaches to $\mathbb{F}_1$ is that they are technically correct (in the sense that the theorems follow from the definitions by the proofs), and I have no reason to doubt this of Durov's thesis in particular, but on the other hand none of the approaches is “right” in the sense that “this is not the $\mathbb{F}_1$ we are looking for”, i.e., they don't capture the properties which are expected or hoped of $\mathbb{F}_1$. But maybe this is like chasing unicorns.
Jul 15, 2023 at 18:25 history edited Carlo Beenakker CC BY-SA 4.0
less offensive title
Jul 15, 2023 at 18:25 comment added Carlo Beenakker I took the liberty to rephrase the title in a less offensive way.
Jul 15, 2023 at 18:23 comment added Carlo Beenakker why "almost forgotten" ? the arXiv paper [ arxiv.org/abs/0704.2030 ] has been cited 125 times (Google Scholar); the author has many other interests [en.wikipedia.org/wiki/Nikolai_Durov], and only a few publications, but that by itself should be no reason to dismiss the thesis.
Jul 15, 2023 at 18:07 comment added Stopple This question would be improved if you included some links to where the thesis has been mentioned.
Jul 15, 2023 at 17:17 history asked manifold CC BY-SA 4.0