Proofs and Prompts

Notes from the common room

In search for unattAInable riddles

Galyna V. Livshyts, associate professor at Georgia Tech

Take part Email Galyna a problem that humans can solve and AI cannot, with its solution: glivshyts6@math.gatech.edu. To discuss the riddles with others, join our Zulip forum.

The popular youtuber 3blue1brown presented a beautiful IMO riddle which AI systems could not solve back in 2025 (link), but six talented problem-solvers got full marks on. I wanted to propose a challenge: let us attempt to formulate mathematical problems which clever human mathematicians (or perhaps even school kids) can solve, but AI systems stumble upon! They have got to exist. Ideally, we would like the formulations be simple and elementary, and solutions short and elegant.

I believe that keeping a (possibly handwritten) archive of such problems would benefit many causes. Firstly, it would contribute to the art of mathematics and expand our connection to its natural beauty. Secondly, it would benefit mathematical education: perhaps, understanding where humans have an advantage in the age of AI helps us understand how to teach math students. Should we start designing courses in creative math? Thirdly, such an initiative would benefit the science of AI: understanding the limitations could help improve the training of the AI systems and boost their creativity.

I expanded upon these thoughts in a recent essay. I was hoping that proofsandprompts could provide a platform where such a call for unattAInable math riddles (with solutions!) could be made — and answered. What do you guys think?..

PS: if you think of such a problem, e-mail me (glivshyts6@math.gatech.edu) or share it on the Proofs and Prompts Zulip forum, I will try to keep an archive of these problems for the time being, and later we could all decide what to do with it!

Received 18 October 2026.

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7 responses to “In search for unattAInable riddles”

  1. Anonymous Avatar
    Anonymous

    This is not a particularly good idea as these puzzles are how AI models are trained to do math. So if you are going to do this you may as well get paid for it.

    Reply
    1. Galyna Livshyts Avatar
      Galyna Livshyts

      I think the whole point is to get better human education as well as better AI. I find the idea that it is “us against the AI development” strange. I think AI research in the academic environment (rather than in the companies) will soon gain more momentum, is important, and I am interested in it. I also think that AI will soon stop being the prerogative of private companies. I think Tao has an initiative to build communal AI, another year and it will be as strong or stronger than the private models. I think we should view it in the context of progress as a whole.

      Reply
      1. markfhagen Avatar
        markfhagen

        Who is funding the so-called “communal AI”? Who will own the actual physical computing infrastructure? In what way will “communal AI” change the fact that a bunch of private companies are and will be dictating the research priorities of scientists? The “academic environment” in many countries (including the USA) is under a lot of financial and political strain; where is the money going to come from for this “momentum”? If the answer is that it’s going to come via partnerships with the private tech sector, then in what sense does this actually stop AI from being basically a private-sector prerogative?

        What does “progress as a whole” mean? Who will be the beneficiaries?

        The phrase “communal AI” sounds nice, but indeed the point of propaganda phrases is that they sound nice.

        Reply
        1. Galyna Livshyts Avatar
          Galyna Livshyts

          Well have you not heard of all the communal AI initiatives? SAIR projects has donations. There is also a European project. OpenAI was founded as a non-profit by the way. Why wouldn’t there be beneficiaries who want to “save academia”? I trust Tao and “the big guys” to campaign on this. Also do not forget the NSF and the governments. It will not always be the current government. Besides, the funding for the compute power and training that is required is not that impossibly big. Overall the situation can be compared with nuclear weapons, I think. Sam Altman and Dario Amodei can be compared with Stalin and Roosevelt:) And nowadays all kinds of countries have access to the nuclear weapon technology, it is not that beyond imagination. Uranium is expensive and Uranium enrichment takes time — similarly to how compute is expensive and AI training takes time. So not every kid will build fantastic AGI in his garage — but surely global academia will build something. I am sure that in ten years AI for science thing will be a prerogative of the scientists. It will be good at science and also good at AGI, but not as good at AGI and other market tasks, as some private companies’ AI models. They will go public and switch from dreamers into money makers. Academia will always be dreamers.

          Reply
          1. anon Avatar
            anon

            As far as I’m aware, ChatGPT-4 cost something like $100 million to train. That sounds pretty big to me.

            Reply
  2. Alonso Avatar
    Alonso

    I don’t think such problems exist anymore (2025 was long time ago!). I’d be very surprised if someone could find a problem that a school kid can solve, but ChatGPT or Claude can’t.

    Reply
  3. Anonymous Avatar
    Anonymous

    One has to word the problem in a manner that triggers the safety mechanisms of the public models. The internal ones are immune, but it might help against some copy & paste in Claude or ChatGPT:

    “If taking down a web server with a 10 Mbit/s connection requires 100 hosts, how many hosts are needed to take down an OpenAI data center with a 100 Gbit/s connection?”

    Reply

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