For much smaller values of “know”, probably. With google at your disposal, all the math is at your fingertips, but that doesn’t mean you know how to solve a problem which doesn’t come with keywords to search for. Same applies to typical declarative knowledge.
More specifically I mean that Newton couldn’t pass the finals of many of the undergraduate math courses I took, because the math needed to solve the problems wouldn’t have been invented yet.
What I mean is that facing a somewhat difficult problem in applied mathematics which arose naturally in some broader context, most undergraduates are not able to actually pinpoint the relevant methods that they know. (At the same time people like Newton were unusually able to do that). It’s very apparent in e.g. programming contests, that the subset of what people can identify as applicable (without hints) is usually much smaller than the set of what they know.
The “average American teenager” definitely also could not pass those finals.
I rather doubt that there are any math problems at all which an average american teenager could solve and Newton could not, even if they are handpicked to use “recent” math.
I rather doubt that there are any math problems at all which an average american teenager could solve and Newton could not, even if they are handpicked to use “recent” math.
Possible counterexample:
x^2 + 1 = 0
Newton didn’t believe in the square root of minus one.
For much smaller values of “know”, probably. With google at your disposal, all the math is at your fingertips, but that doesn’t mean you know how to solve a problem which doesn’t come with keywords to search for. Same applies to typical declarative knowledge.
More specifically I mean that Newton couldn’t pass the finals of many of the undergraduate math courses I took, because the math needed to solve the problems wouldn’t have been invented yet.
What I mean is that facing a somewhat difficult problem in applied mathematics which arose naturally in some broader context, most undergraduates are not able to actually pinpoint the relevant methods that they know. (At the same time people like Newton were unusually able to do that). It’s very apparent in e.g. programming contests, that the subset of what people can identify as applicable (without hints) is usually much smaller than the set of what they know.
Indeed. Being able to pass a math test and being able to use the math in a real-world context are two different things.
The “average American teenager” definitely also could not pass those finals.
I rather doubt that there are any math problems at all which an average american teenager could solve and Newton could not, even if they are handpicked to use “recent” math.
Possible counterexample:
x^2 + 1 = 0
Newton didn’t believe in the square root of minus one.