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For example, one that brains appear to be able to solve in polynomial time but computers can't, or one optimized for the brain's innate capabilities - like language learning, or different possibilities computed at once.

I've found some things about the brain's computational abilities, like a "predictive coding hierarchy" that helps it learn languages and Joe Z. Tsien's Theory of Connectivity in which neurons group into cliques and motifs to process complex concepts, but I haven't really found anything from an algorithmic perspective. My ultimate goal is to see if there's an encryption algorithm that can be done by a person with pencil and paper, but that can't be easily cracked by a computer.

Has any research been done on this? Thanks for any lead you may have.

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    $\begingroup$ You can find a lot of problems that human brains are better at than computers when looking for CAPTCHAs. $\endgroup$
    – Jan Johannsen
    Nov 21 at 10:17
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    $\begingroup$ I don't see a formal -- or formalizable -- question here. Not appropriate for this forum. $\endgroup$
    – Aryeh
    Nov 21 at 13:46
  • $\begingroup$ This is more a question about (meta)physics or biology. It turns out that most computing machines that exist in the physical universe are "roughly" like a finite-memory Turing machine. But actually, nature gives us a seemingly more powerful computational primitive, namely quantum computers. Of course, it is not proven that these are really more powerful than regular Turing Machines. So what you are asking is whether the universe gives us a primitive more powerful than quantum computers, or alternatively whether the brain is a quantum computer. Both are unknown despite centuries of research. $\endgroup$
    – JoJoModding
    Nov 28 at 2:01

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One example of such an "algorithm" is finding proofs for theorems. Regarding encryption — there's no inherent problem with a human using an SPN, for example, but it just requires a lot of computation, and if you remove too much you make it susceptible to bruteforcing. Generally humans wouldn't be that good at encryption, because it has to be deterministic and can't rely on creativity. For asymmetric encryption I can't think of anything practical for a human which isn't easily breakable, and looking at tables of runtime and keysize of known algorithms I don't imagine there is one.

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