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Nov 6 at 19:56 comment added Stanley Yao Xiao @SamHopkins I just read the statement again and it is indeed missing the key adjective "non-trivial". Thanks for the catch!
Nov 6 at 12:50 comment added Sam Hopkins @StanleyYaoXiao Is Conjecture 1.2 in your preprint stated correctly? I mean, it seems you implicitly want to rule out the "trivial" case where the squares are consecutive, but the statement of Conjecture 1.2 doesn't seem to contain this proviso. Apologies if I am being dense and misreading something.
Nov 5 at 19:00 comment added Stanley Yao Xiao @mr_e_man no, there is no contradiction. That question asks for whether it is possible to decide whether a single quadratic equation in arbitrarily many variables is decidable over $\mathbb{Q}$, and this is indeed possible, and solved by Siegel. However, when you restrict to integers and allow arbitrarily many equations (all of which are degree $2$), then it is expected that this is not decidable.
Nov 5 at 18:56 comment added mr_e_man I haven't read either answer carefully, but you seem to contradict math.stackexchange.com/questions/3767695/… . Is there a difference I'm missing?
Nov 5 at 16:52 comment added Timothy Chow On the topic of Hilbert's tenth problem, Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field by Alpöge, Bhargava, Ho, and Shnidman might also qualify. The statement that Hilbert's tenth problem is unsolvable for rings of integers of a number field is understandable to undergraduates.
Nov 5 at 4:43 comment added D.R. Wow, I watched your talk. The number of algebraic miracles/"simplifications"/"alignments" that need to happen are just staggering. Syzygy rivaling that of the heavens! At the very edge of human-comprehensible algebraic manipulation. Thanks for sharing :)
Nov 5 at 0:18 history edited Stanley Yao Xiao CC BY-SA 4.0
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S Nov 4 at 23:43 history answered Stanley Yao Xiao CC BY-SA 4.0
S Nov 4 at 23:43 history made wiki Post Made Community Wiki by Stanley Yao Xiao