Codes are generally deciphered via frequency analysis (which requires knowing what characters and language are encoded), via some knowledge of the coding process, and/or via having some knowledge of what statement (in what language) is encoded.people can and do decipher dead languages and codes that they have never encountered before.
Dead languages are similar. The Rosetta Stone would be a classic example.
Anyway, the point of the example of the classic Read Languages ability is that many knowledge-style checks are about recall and/or application of existing knowledge - not the "solution of problems that a person has never seen or heard of".
I think you are running together sufficiency and necessity.Not all knowledge is intelligence. When talking about a genius figuring things out, we're discussing reason coming into play. Knowledge of the sort you just described has no basis in intelligence. Any idiot can know it if taught, and the smartest person in the world won't if not taught. Your question is a distraction from what genius and idiocy mean.
Knowing that 1066 is an important date in world history is not sufficient for being intelligent. But knowing those sorts of dates is a necessary condition of being a world history genius. Geniuses in fields like history manifest that genius, in part, by operating upon a very wide range of information that has been learned. I think the same is relatively true of (say) chemistry and biology.
In 5e terms, a character with 20 INT but no skills is going to turn out to be relatively uninformed on a wide range of subjects. This is inconsistent with being a genius in a wide range of fields.
This is very obscure to me, because I don't know what "training" means here, what you are contrasting it with, and what the conception of "genius" is that you are working with.You have a 50/50 shot at int based checks that you haven't been trained in. A genius is the only one who could be right half the time under those circumstances.
In the real world, a person who does not know the significance of the year 1066 does not have a 50/50 chance of working it out by the sheer application of brain power. To make it concrete - if the sphinx asks "What year did William conquer England", no one who does not know the answer is 1066 has a 50% chance of working that out via guesswork.
A person who doesn't know the significance of that year might still come up with an interesting account of world history, but they will have to no some dates or other. (This is what European historians and social theorists did, in times before they had assimilated into their learning and traditions dates and events from non-European parts of the world.)
But D&D doesn't really have a mechanic for resolving a task like writes Economy and Society or invents the Periodic Table - which, in the real world, are the sorts of doings that manifest genius.
Again, this is odd to me. Both the mathematical phsyicists that you mention, for instance, were well-trained in sophisticated mathematical techniques. This was a necessary condition of them making the progress that they did in physics.Einstein, Hawking, and others are only as great as they are at physics because they are ALSO highly trained. Their base genius could only take them so far in physics with no training. Probably not even 50/50.
No one who is not trained in mathematics, for instance, has any chance of inventing special relativity!
Bringing this back to 20 INT: what 20 INT indicates in 5e is that the character has assimilated more-or-less as much information and technical expertise across all fields of human knowledge as has a 10 INT person trained may have done in a few fields (+2 or +3 prof bonus with Expertise).
But in any event, all the above discussion is largely orthogonal to the question I asked of [MENTION=6813615]Giant2005[/MENTION] (and others):
what does it mean to play a character as a genius, besides succeeding at INT checks?
To me the answer is there is no such meaning. Which means that, if by dint of luck, skill training or whatever, my PC whose INT stat is nothing special nevertheless ends up dominating the game in the INT check department, my PC turned out to be a clever person - perhaps even a genius - although no one might have predicted so at the outset.
This is the contrast between various forms of pre-scripting or "modelling", on the one hand, and "playing to find out what happens" on the other.