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4
I would like to use this as an opportunity to make an important distinction.
Proof by contradiction is an argument of the form:
Assume $\neg p$
Argue a contradiction under this assumption.
Conclude $p$.
Proof of negation is an argument of the form
Assume $p$
Argue a contradiction under this assumption.
Conclude $\neg p$
I learned about the difference ...
1
Your question prompted me to reread a comment that John Tukey wrote in the March 1979 edition of the Journal of the American Statistical Association (pp. 121-122).
He referred to what he calls "the whole data analyst-statistician." Such a person is able to "take quite different views and adopt quite different styles as the needs change." ...
4
they can just run a simple simulation
Simulations outside the classroom are often anything but simple. Brute force simulations are often a lot of work to set up, take a long time to calculate, and take even more computational resources to make sufficiently accurate. It is therefore necessary to have more advance tools in one's toolbox.
Here is a very nice ...
5
Your question could apply generally to why should anyone learn the math "behind" anything, if they can easily compute the answer on a computer. I don't think they ALWAYS should. There should be a reason. For example, I had an old professor who said that when calculators first became common, some professors insisted that students should still learn ...
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