It's like a cache level issue.
In the old world, you had your wet brain memory. You needed to fill it with the order of the alphabet, so that you could make use of paper reference works. You also needed some arithmetic and some English style notes, in case you wanted to express yourself. You had to remember things like there/their/they're and that kind of thing. You needed a small encyclopedia so that you could have a clue about where general knowledge could be found.
On top of this, you were expected to layer on your professional knowledge. If you were a doctor, a huge number of Latin terms. A more detailed understanding of how the body works that you got from the base installation. Something about how the profession works. You would get a sense for what was likely through experience. A BS detector, in some ways.
All because your brain ain't gonna get bigger, and paper information technology was what it was: found in a library, limited in size, hard to search, slow to update.
Nowadays, the brain cache is no different in capability. But the external memory system you are accessing is completely different. It's massive, it can update in real time, and it's very searchable.
So you need to keep different things in your brain cache to take advantage of this.
But what do you need?
The only component that really matters is the BS detector.
Not only do I not need to be able to do long division, I don't even need to know that a calculator exists for calculating my tax, a calculator containing the Haversine formula is out there somewhere, and a so on. I just assume something like epochconverter exists, and that I can plug a timestamp into it and get something readable out.
I just assume that I will be able to find things that I want, the tradeoff being that I don't have sit there and refresh my math knowledge to calculate distances on a sphere, type out a program, and run it for a single output. The other side of this coin is of course, I don't know whether the guy whose work I am borrowing did it correctly, whether he has some sort of interest he's not disclosed, and whether it's safe. I also have to compromise on any variation between what he built and what I wanted.
I do this with almost everything now. I can't help it, having grown up and been educated before the internet exploded, and having started work just as the explosion was happening.
So I'd say you actually don't have to remember everything, but you do have to use your judgement in everything.