Can high school students know calculus better than Newton?

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SUMMARY

The discussion centers on whether contemporary high school students can understand calculus better than historical figures like Newton and Leibniz. Participants argue that modern educational tools and insights into limits and infinitesimals allow students to grasp calculus concepts more effectively than the original inventors. However, it is also emphasized that while students may know more techniques, they lack the intuitive brilliance that characterized the work of Newton and Leibniz. The consensus suggests that while understanding has evolved, the foundational insights of these mathematicians remain unparalleled.

PREREQUISITES
  • Understanding of calculus fundamentals, including limits and infinitesimals.
  • Familiarity with the historical context of calculus development by Newton and Leibniz.
  • Knowledge of modern mathematical notation and its evolution.
  • Awareness of the philosophical implications of mathematical discovery versus invention.
NEXT STEPS
  • Explore the historical development of calculus through primary texts by Newton and Leibniz.
  • Study modern calculus teaching methods and their effectiveness in conveying concepts.
  • Investigate the role of mathematical intuition in problem-solving compared to rote learning.
  • Analyze the impact of advancements in mathematical notation on student understanding.
USEFUL FOR

Mathematics educators, high school students, and anyone interested in the evolution of calculus and its pedagogical approaches.

  • #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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