In yet another attempt to show how this is not irrational, here goes:
There are every year about 100,000 new math theorems produced. To learn each of these theorems would require learning them at a rate of about 1 every minute when sleeping is taken into account. This is excluding all of the theorems needed to understand those theorems. Further this is just math and doesn’t included every other field of human endeavor as well as on the job knowledge.
It should be clear from the above that is physically impossible to have all the knowledge in the world, let alone the problem of being able to remember it all. There are no “heros” and it is impossible to have such “heros”. This is more then about gains in specialization (which are great and the only reason we can have this discussion in the first place) but the bounds of learning.
Now, going back to my earlier response on specialization and gains from trade there arises the question of does it make sense to try and have answers to every problem?
There is a reason that specialization works well, people become better at doing what they are currently doing. So even assuming one were able to “know” everything they would still not be as good at doing any particular task as someone that had specialized in that task. I may know how to read a recipe and how to make bread but I am not going to be a master bread maker and make amazingly good bread unless I practice making bread for some amount of time.
So assume for a minute that you have specialized in mayan epigraphy and someone brings you an Egyptian hieroglyph, as they are both ancient writing systems so they must have some common skill sets, is it rational to say “I have no idea and I am going to drop working on finding the meaning of all of these other glyphs that I am working on deciphering to figure out what most likely any master level Egyptologist knows off of the top of their head ” or to say “I have no idea, here is the number to my colleague that specializes in reading Egyptian hieroglyphs”? in the one you have filled in a blank in your knowledge, but at a cost to adding new knowledge to the world, while in the other the blank remains but you continue working on what you are paid to do. What appears to be advocated here is the first response which has a huge opportunity cost for extremely low reward.
In economics it is known as specialization and there are gains associated with specialization and trade. In a marriage generally each party specializes which tasks they perform to bring about an overall net gain in the work done with in the marriage. So my comparative advantage may be in doing the dishes and the laundry while the other party to the marriage may be in cooking dinner and vacuuming. Soon I no longer know where all the spices are but the other party no longer knows where all the dinner dishes go, not that we can’t find out but it is cheaper to just ask the other person when we need that knowledge then to maintain constantly the current knowledge on what the other has specialized in.
So rewriting the question to “does specialization bring about benefits?” should make it obvious that the answer is a resounding yes. To give two examples, in the wealth of nations there is the example of a pin factory, not going to quote exact but give the basic argument: a skilled blacksmith making the pin by himself may be able to make say 100 pins a day. Three laborers working in a manual pin factory however can make 100 pins an hour while as they are relatively unskilled blacksmiths may not be able to make a whole pin in a day by themselves. Second example: there isn’t any one person in the entire world that knows how to make a pencil from the basic materials, that is no one person that knows which trees to cut, how to mill the tree, which rocks to mine, how to mine them, how to smelt them, how to shape the graphite, how to combine everything (not even including how to make and operate all the machines needed for each step). This should give you a decent understanding of how specialization is extremely beneficial to everyone involved.