Any human being who can factor 2048 bit numbers in their head faster than a computer is almost certainly a human being who has, in effect, discovered a new algorithm to factor numbers. Which, if implemented on a computer, would be even faster.
But that doesn't rule this out.
I'm going to be a bit less than totally precise below. For example, I'll mix up decision problems and algorithms to keep terms simple.
We don't know how hard factoring numbers is really. We know it is in a complexity class BQP, which for classical computers (or a human running a classical algorithm in their head) in NP.
A problem is in NP if it is relatively cheap to verify you got the right answer. The example here is that if someone states that the factors of some number are A and B, you can check it by ... calculating A*B and seeing if it matches.
But there there isn't any proof that NP isn't the same as P. If NP=P, then every problem whose solution can be verified fast can be solved fast. (This is very hand-wavy, but true within those bounds). And if NP=P, then BQP which is in NP is also in P.
For problems in NP, we know of no classical algorithm that is much all that much faster than "just try every possibility" here for generous definitions of "all that much". (the fastest factoring algorithms are strictly sub-exponential; like O(e^(k + bits^(1/3)*ln(bits)^(2/3)) if I copied that right).
So, if someone came up with an algorithm to factor large numbers that was polynomial time, they could in theory learn how to run the algorithm in their head, and be able to factor large composite numbers faster than any computer can.
This is implausible. And, honestly, such an algorithm would probably be more valuable to share than to stuff into your head.
The Savant could find fast factorization without showing NP=P or even that BQP=P; for example, it could be that factorization of the specific kinds of primes we use for cryptography is easier than the general problem, or maybe a large percent of such composite numbers are easy to factor (but not all of them), or that there is some other "corner case" that lets it work (even sometimes) extremely faster than "try every case". Such a result would be powerful, but wouldn't be revolutionary on the scale of rewriting much of what we consider interesting mathematics (which an efficient P algorithm for NP problems would do, honestly).