Or, to write the question in slightly fuller form: Assuming a sufficient level of interest and competence, and very good teachers, could a high school student today understand the calculus better than Newton or Leibniz ever did in their lifetimes? And if not a high school student, then maybe an undergrad university one? The trigger for this question comes from Sean Carroll's blog, The Alternative-Science Respectability Checklist, and specifically his comment: In at least one respect, a high school student today can understand the calculus better: she can get a handle on limits and infinitesimals that is far better than Newton's was. So, I'm not all that interested in whether the answer is "yes", or "no", but rather in what respect, which aspects, can we say that a dozen years' or so of dedicated study can give you a better understanding of the calculus than that which either of the geniuses who first discovered (invented?) it ever had?