Can high school students know calculus better than Newton?

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Discussion Overview

The discussion centers on whether high school students today can understand calculus better than historical figures like Newton or Leibniz, considering advancements in education, understanding, and teaching methods. Participants explore various aspects of calculus, including its historical context, the evolution of mathematical understanding, and the implications of modern education.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that modern students can grasp concepts like limits and infinitesimals more effectively than Newton did, due to advancements in teaching and understanding.
  • Others suggest that while students today may know more mathematics, they lack the brilliance and intuition that historical figures possessed, which allowed them to make groundbreaking discoveries.
  • One participant mentions that calculus has transformed significantly over the years, implying that contemporary understanding is deeper than that of its founders.
  • Concerns are raised about the ability of modern students to teach or convey complex ideas, with some asserting that many students focus on memorization rather than true understanding.
  • Some participants highlight the historical challenges faced by early mathematicians, such as the lack of notation and peer support, which modern students do not encounter.
  • There is a contention about the general capabilities of college students, with some expressing skepticism about their understanding and ability to explain concepts compared to historical figures.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement. While some believe modern students can understand calculus better in certain respects, others maintain that the brilliance and intuition of figures like Newton and Leibniz cannot be matched, leading to an unresolved debate.

Contextual Notes

Limitations include varying definitions of "understanding," the subjective nature of brilliance, and the historical context that influenced the development of calculus. The discussion does not resolve these complexities.

  • #61
the 1000000$$ dollar question is.. if Einstein and others were sooo smart why are there still unsolved problem in physics ??.. I'd be also a genius if i had mathematician like Hilbert Poincare or similar working on my side ¡¡¡ .. Newton and Einstein were the LUCKIEST (at least speaking from scientific point of view) men in the history easy problems --(except GR of course but with a good mathematician you can understand almost everything) and easy solutions.

The main problem for us (physicist) is the vast complexity of actual theories.. you can deduce the Uncertainty relations for (x,p) and (t,E) from Fourier Analysis, but 'Standard Model' of particles need heavy courses of Group theory not to mention that 'Functional integrals' are impossible to solve and so on NO way :(
 
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  • #62
There still are unsolved problems in physics because the mathematics to solve those problems is not (yet) created. I think.
 
  • #63
Of course we know more than he did. We have the shoulders of a bigger giant than he had.
 

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