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I read through some of John Gabriel's the new calculus last night, he does seem quite arrogant but some of the things he says seems to make sense. For example is his way of taking derivatives based of parallel secant lines right? To me it just seems like rolls theorem. Is this guy correct with his new Calculus or can it be ignored?

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    $\begingroup$ Just to save others the trouble of googling: thenewcalculus.weebly.com $\endgroup$ – Hans Lundmark Oct 30 '17 at 14:32
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    $\begingroup$ And based on just the introduction, it sure looks like a crank. “The New Calculus is the first and only rigorous formulation of calculus in human history.” “Neither Newton nor Leibniz nor anyone who came after them understood calculus as well as I do. In fact, no one in the history of humans has understood calculus as well as I.” $\endgroup$ – Hans Lundmark Oct 30 '17 at 14:33
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    $\begingroup$ John Gabriel is a textbook case of delusional disorder which are often referred to as cranks but it's a serious mental illness and he doesn't have much control over it. He just doesn't have the ability to see the world clearly. en.wikipedia.org/wiki/Delusional_disorder $\endgroup$ – CyclotomicField Oct 30 '17 at 14:39
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    $\begingroup$ Even more cranky: “The New Calculus is not worth just one Abel prize, it is worth ten Abel prizes.” $\endgroup$ – Michael Hoppe Oct 30 '17 at 14:49
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    $\begingroup$ Not sure why Mr. Gabriel wants all those Abel prizes, as they're named after a man who helped lead us into all this academic ignorance and stupidity. $\endgroup$ – zhw. Oct 30 '17 at 15:09
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There are interesting alternatives to the standard formulation of calculus; here I am thinking of Abraham Robinson's nonstandard analysis (see http://mathworld.wolfram.com/NonstandardAnalysis.html) and Errett Bishop's constructive approach (see e.g. https://books.google.dk/books/about/Foundations_of_constructive_analysis.html?id=Z7I-AAAAIAAJ&redir_esc=y). Robinson and Bishop were accomplished mathematicians.

However, anyone who makes the claim that

The New Calculus is not worth just one Abel prize, it is worth ten Abel prizes. Of course you will never know unless you study my work.

of his/her own work (cited from http://thenewcalculus.weebly.com) and writes that

Neither Cauchy sequences nor Dedekind cuts are valid constructions of real numbers.

is speaking the language of crackpots.

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  • $\begingroup$ I'm interested in how he's getting correect results with this other theory or is it because he is starting from things already established in calculus and picking and choosing as he likes? $\endgroup$ – jake walsh Oct 30 '17 at 14:40
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    $\begingroup$ With sufficient geometric intuition you can get correct calculus results even if you can't justify them rigorously. The inventors of calculus (Newton, Leibniz and others) did that well before rigor came to mean what it does today. $\endgroup$ – Ethan Bolker Oct 30 '17 at 14:43
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    $\begingroup$ Is his lack of rigor why he says thinks are just obvious and that there are no axioms because they are so obvious then? $\endgroup$ – jake walsh Oct 30 '17 at 14:45
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    $\begingroup$ Here is a real life quote from this guy: "Dedekind was an idiot next to me." $\endgroup$ – AlexanderJ93 Oct 30 '17 at 14:50
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    $\begingroup$ If I ever had to stand next to that guy, I, too, would feel like an idiot. $\endgroup$ – Hans Hüttel Oct 30 '17 at 14:51

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