(1.) Speaking of which, here’s a kind of philosophical math question. True or false. The essence of mathematics IS the notation/symbology, e.g., the notation for derivatives and integrals.
(2.) What happens when you try to find the indefinite integral for the pdf (probability density function) of the normal random variable? Note, the graph of this pdf is the famous bell shaped curve.
(3.) The quadratic equation has the quadratic formula for its closed for solution. Does the fifth degree (quintic) polynomial also have a closed from solution? If not, why not?
(4.) Fermat’s Last Theorem argued that x^n = y^n + z^n (sorry about the carrot notation for exponents) was true only if n = 2. For example if n is a counting number greater than 2, it would always be false. This was undecided for hundreds of years, but fairly recently a proof was found. Did the proof confirm or deny Fermat’s conjecture?
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Ok Karl, here’s the dope;
(1.) Absolutely not. Indeed confusing mathematics with its symbology may well be the most common misunderstanding of mathematics. Math is what the notation is “about”, not mathematics itself, almost exactly like musical notation which is itself not music, but “directions” that tell you what to do to make music. Now of course math music is intellectual, but it can still be exceedingly beautiful.
(2.) Nothing happens because the normal pdf is a transcendental function without a corresponding indefinite integral. Said differently, there IS NO function whose derivative is that pdf. So, April Fool, not all functions can be integrated.
(3.) No, there is no closed form solution (even though there is for linear, quadratic, cubic, and quartic polynomials). The “why” question was a dirty trick, since this discovery helped to open up a vast area of abstract math called modern algebra (VERY different from ordinary algebra).
(4.) Yes, it was proved to be true a few years ago, but take a deep breath before you look at the proof, because it is a very long, convoluted monster of subtlety.
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What do you think, folks? Did “genius” Karl Rove answer even one question?
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