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> 1. Why do you compare it to multiplying two 1000 digit numbers and not to factorizing a 4096-bit numbers into its 2 prime factors, when not knowing any details?

The objection is to phrasing "much harder". One should distinguish between something that is difficult for reasons stemming from a lack of computational power and something that is difficult for reasons stemming from a lack of relevant abstractions or the ability to grapple with them. If the reason that a particular problem is "hard" for a PhD student is that they have to do a long calculation, but not because of a lack of conceptual understanding, then it doesn't say much about the capabilities of generative AI if the computer solves it.

Hence the example: multiplying two large numbers is hard for the former reason, not the latter. Your example of factoring a 4096-bit semiprime is hard for both reasons (because the brute force method is too slow).

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Well, you are correct that one should distinguish the two. But we give no indication that the questions are hard because of computational tasks and we give many indications that the problems are of theorecical nature and hard for theoretical reasons. There is not a single question where a PhD student would need to do a long calculation.

I trust the judgement of respected researchers submitting the questions, I personally know them, and they publish research under their full names (and whose names are fully disclosed in the paper). And you also should trust them.

Please consider disclosing your name and your field of expertise, pick a question in your own research area and explain to me why this question is not research-level. And, best of all, solve it yourself to clarify why it was too easy.

I solve 034.

By [1, Theorem 4.1], the Neron-Severi rank of the perfectoid cover is the same as the Neron-Severi rank of the reduction. For a product E x E' of elliptic curves, it is well known that NS(E x E') = NS(E) + NS(E') + Hom(E,E'); see [2, Prop. 2.3]. Since E = E' here and E is supersingular, this number is 1 + 1 + 4 = 6.

Is it research level? It of course takes a graduate student a long time to understand, say, what a perfectoid space is. But the statement follows immediately from quoting the literature, as long as one knows what to quote.

1. https://arxiv.org/pdf/2105.05230 2. https://arxiv.org/pdf/1402.2233

You see yourself that your own solution is purely of theoretical nature and not at all what you wrote before, right? (And no, I am not commenting on your answer.)

Indeed. But I chose the problem in response to your comment:

> But we give no indication that the questions are hard because of computational tasks and we give many indications that the problems are of theorecical nature and hard for theoretical reasons.

and Question 034 seemed to be one of the few that did not have a computational component, and so would presumably be hard for theoretical reasons. I already indicated above some problems that I feel to be of a non-theoretical nature.

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