how do we know calculus will provide the "answer" we seek? Is there any objective method to judge its accuracy? How do we know the solutions are correct and reliable? How do we know the professor is actually teaching us the correct methods for doing this stuff? Why isn't calculus taught as applied math instead of random problems? How does the student know if the grader is ignorant or if the his solution is wrong? How do we know that the person who wrote the book did so accurately according to Newton, and whether the "problem-creating algorithms" are reliable? How do we know the calculators that are programmed to "do calculus" can do it correctly? Are there different solutions to any given problem, or is there only one "right one"? How does the student or grader know that?


closed as off-topic by user137731, Ant, marty cohen, Rob Arthan, user147263 Sep 14 '15 at 22:25

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    $\begingroup$ It sounds like you are just wanting to see the proofs all the questions and such , usually the proofs are not included in first courses in calculus but will come later if you do analysis $\endgroup$ – Quality Sep 14 '15 at 21:30
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    $\begingroup$ Seems to me that you're seeing math as some kind of magical, black box that works because someone tells you to. It's not. Math is very logical, everything makes sense if you understand it. "How does the student know it?" Understand it, and you'll know. $\endgroup$ – Ant Sep 14 '15 at 21:31
  • $\begingroup$ I don't know. But do not mistake physical applications for self containing formal rule games. $\endgroup$ – zoli Sep 14 '15 at 21:31
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    $\begingroup$ If you want proofs, that's one thing. If what you're asking is "Is calculus really the right tool for describing the physical reality?", then the answer is "We don't really know, but it's worked wonders so far, so we're pretty darn certain." $\endgroup$ – Arthur Sep 14 '15 at 21:32
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    $\begingroup$ I'm voting to close this question as off-topic because this looks like trolling to me. $\endgroup$ – user137731 Sep 14 '15 at 21:32

This math moment brought to you by Calculus.

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