Honest question here - does anyone actually still believe a single algorithm can solve general problems? Certainly the human mind doesn't work that way - we are fairly compartmentalized with a lot of communication between compartments.
AIXI is a single algorithm that can solve every problem, given enough time, which is enough to prove that they do exist, however uselessly long it would take AIXI to solve any actual problem.
The book "On Intelligence" does a decent job explaining for non-neuoroscientists a theory where all parts of the brain (imaging, hearing, speach, cognition, etc) use the same pattern matching algorithm.