Comment by Gro-Tsen on Examples for the use of AI and especially LLMs in...
Are the proofs isomorphic (for a certain definition of “isomorphic”)?
View ArticleComment by Gro-Tsen on What are the mathematical implications of the claimed...
Re your comment about not wanting answers from a chatbot: do not hesitate to share and reuse this sign if you find it useful.
View ArticleAnswer by Gro-Tsen for What should be the editorial policy of a journal...
Let me offer the following partial thought:If a journal chooses to become more selective because of the increase in the number of submissions it receives, I believe it should not become more selective...
View ArticleComment by Gro-Tsen on certifying a proof without publishing it
@TimothyChow You know this of course, but just to be clear to everyone in the audience: there cannot be an information-theoretic secure notion of zero-knowledge proof for mathematical theorems. Indeed,...
View ArticleComment by Gro-Tsen on Examples for the use of AI and LLMs to autonomously...
IIUC, as mentioned in the comments below this answer, the existence proof of a complex structure on $S^6$ incidentally showed that there were errors in a paper by Campana-Demailly-Peternell, even the...
View ArticleComment by Gro-Tsen on Interesting anti-classical purely logical (e.g.,...
@NoahSchweber Are you saying there's a way to turn a statement about natural numbers and/or reals into a constructively equivalent one in second-order propositional logic? If so, this is highly...
View ArticleExamples of dense pointless sublocales of $\mathbb{R}^m$, or other ways to...
(Experts can immediately jump to the ‘❦’ sign below, or even directly to the question, skipping the following 3 paragraphs, which are included for completeness of MathOverflow, for the benefit of those...
View ArticleWhat is the Jarlskog invariant, conceptually?
Let $U$ be a $3\times 3$ unitary matrix, and call $(u_{ij})$ its coefficients. For $i,j,k,\ell$ in $\{1,2,3\}$ with $i\neq j$ and $k\neq\ell$, consider the quantity:$$J_{ij,k\ell} :=...
View ArticleIs every nowhere dense closed set contained in the boundary of a regular open...
(TL;DR version: is it true that every nowhere dense closed set in $\mathbb{R}^m$ is contained in the boundary of a regular open set?)Definition: In a topological space $X$, let's call a (closed) subset...
View ArticleComment by Gro-Tsen on Is every nowhere dense closed set contained in the...
Slight nitpick: I think you need to modify the statement of your claim just a little bit to say that the set of accumulation points of $C$ is exactly $X$ (which is indeed what your proof gives)....
View ArticleComment by Gro-Tsen on Ways in which $\Omega$ (the set of truth values) is...
@AndrejBauer You decide. Any answer of the form “properties in this-or-that form are of this sort” which is useful in practice, is welcome.
View ArticleComment by Gro-Tsen on What could be “Kleene's third algebra”?
@JeanAbouSamra If you wish to learn about $\alpha$-recursion the quick way, I recommend Stephen G. Simpson's “Short Course on Admissible Recursion Theory”, p. 355–390 in Fenstad, Gandy & Sacks...
View ArticleComment by Gro-Tsen on What could be “Kleene's third algebra”?
Remark: if $\mathbb{N}^{(\mathbb{N}^\mathbb{N})}$ is what it is classically, then in a certain sense LPO must hold (because we can consider the function taking $0$ on the identically $0$ function and...
View ArticleComment by Gro-Tsen on "Maximally irrational" members of...
You seem to be rediscovering a lot of Diophantine approximation theory in your recent questions. Did you try reading standard references on the subject? It is a standard fact that the golden ratio (and...
View ArticleComment by Gro-Tsen on Examples of problems that current AI models fail to...
@SamHopkins Indeed, but I'm not particularly interested in trying to shield various parts of mathematics from the reach of AI, nor do I believe discussing them here will have significant effect: either...
View ArticleComment by Gro-Tsen on Constructing the surreal numbers as iterated Hahn series
This later question, also by me, is possibly a better and more precise formulation of the present one.
View ArticleComment by Gro-Tsen on Chameleon population dynamics
PPS: Of course, the thing that we really should be looking at is the various ratios of winning probabilities in function of the starting distribution (plotted as equiratio lines in the red-green-blue...
View ArticleComment by Gro-Tsen on What missing examples, other than counterexamples,...
Do the objects have to be not known to exist? A computably enumerable Turing degree $\mathbf{d}$ such that $\mathbf{0} < \mathbf{d} < \mathbf{0}'$ is known to exist, and “examples” are known in a...
View ArticleWhich topos (or topoi) most accurately reflect Brouwer's ideas on intuitionism?
Let me first clarify that I am not expecting the titular question to have a single well-defined answer (or it would probably have to be a useless one like “the topos freely generated by the following...
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