What’s wrong with (1) being a valid explanation? The geniuses of the 17th and 18th centuries, like Gauss and Newton, did work that today is expected of moderately bright high-schoolers. Decartes’ geometry can be understood by middle-schoolers. Even the science of the 19th century, like work of Maxwell and Rutherford is considered to be pretty much undergraduate level today.
Is it really that implausible to you that the low-hanging fruit is gone?
I think you are drastically overestimating how common it is for even “moderately bright high-schoolers” to understand the material even half so well as Gauss or Newton did, rather than merely learning techniques (which techniques, by the way, were developed over the course of considerable time, so the math students of today are taking advantage of the work of many before them…).
I think there is about a three orders of magnitude difference between the difficulties of “inventing calculus where there was none before” and “learning calculus from a textbook explanation carefully laid out in the optimal order, with each component polished over the centuries to the easiest possible explanation, with all the barriers to understanding carefully paved over to construct the smoothest explanatory trajectory possible”.
(Yes, “three orders of magnitude” is an actual attempt to estimate something, insofar as that is at all meaningful for an unquantified gut instinct; it’s not just something I said for rhetoric effect.)
What’s wrong with (1) being a valid explanation? The geniuses of the 17th and 18th centuries, like Gauss and Newton, did work that today is expected of moderately bright high-schoolers. Decartes’ geometry can be understood by middle-schoolers. Even the science of the 19th century, like work of Maxwell and Rutherford is considered to be pretty much undergraduate level today.
Is it really that implausible to you that the low-hanging fruit is gone?
I think you are drastically overestimating how common it is for even “moderately bright high-schoolers” to understand the material even half so well as Gauss or Newton did, rather than merely learning techniques (which techniques, by the way, were developed over the course of considerable time, so the math students of today are taking advantage of the work of many before them…).
I think there is about a three orders of magnitude difference between the difficulties of “inventing calculus where there was none before” and “learning calculus from a textbook explanation carefully laid out in the optimal order, with each component polished over the centuries to the easiest possible explanation, with all the barriers to understanding carefully paved over to construct the smoothest explanatory trajectory possible”.
(Yes, “three orders of magnitude” is an actual attempt to estimate something, insofar as that is at all meaningful for an unquantified gut instinct; it’s not just something I said for rhetoric effect.)