Depends what you mean by ‘know more math’. In a sense, anybody as fast as you who spent more time studying knows more than you, for how could it be any other way? But that could be because they have more depth in some areas whereas you might have a broader purview. (E.g. you might know more high-level theory about algebraic curves but lose to Newton on a details-oriented question on most cubic curves.)
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.
Depends what you mean by ‘know more math’. In a sense, anybody as fast as you who spent more time studying knows more than you, for how could it be any other way? But that could be because they have more depth in some areas whereas you might have a broader purview. (E.g. you might know more high-level theory about algebraic curves but lose to Newton on a details-oriented question on most cubic curves.)
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.