It takes a lot less time to learn calculus from a textbook than it does to invent it; it would presumably be accurate to say that Einstein knew more physics than Newton. I don’t know if there are any problems in my 3-semester introductory calculus textbook that Newton would have choked on, but he’d definitely have a problem the first time he saw a complex number, let alone something like “e^(a+bi)= a cos(b) + ai sin (b)” that dates to Euler.
Ahhh yeah I forgot discovery was a thing. I guess even going through the process to invent something is its own kind of learning, but that seems tenuous with respect to the original intent of what you said.
Edit: But I think there is a meaningful sense (even if not the only one) in which, say, Euclid or Archimedes probably know more classical geometry than you. And perhaps its meaning comes from their internalisation of a greater depth (even if you could use a theorem prover or theory to quickly derive all their knowledge), which would make those deeper facts accessible to their intuition when solving other problems or developing theory.
It takes a lot less time to learn calculus from a textbook than it does to invent it; it would presumably be accurate to say that Einstein knew more physics than Newton. I don’t know if there are any problems in my 3-semester introductory calculus textbook that Newton would have choked on, but he’d definitely have a problem the first time he saw a complex number, let alone something like “e^(a+bi)= a cos(b) + ai sin (b)” that dates to Euler.
Ahhh yeah I forgot discovery was a thing. I guess even going through the process to invent something is its own kind of learning, but that seems tenuous with respect to the original intent of what you said.
Edit: But I think there is a meaningful sense (even if not the only one) in which, say, Euclid or Archimedes probably know more classical geometry than you. And perhaps its meaning comes from their internalisation of a greater depth (even if you could use a theorem prover or theory to quickly derive all their knowledge), which would make those deeper facts accessible to their intuition when solving other problems or developing theory.