Essay:John Gabriel
“”Yes, my feeble Jew, and your point in this comment? I see, you don't have one, yes?

—John Gabriel, on the feebleness of Jews^{[1]} 
John Gabriel, a computer programmer and mathematics educator, believes he is responsible for the first and only rigorous version of calculus, which he calls "the New Calculus".^{[2]}
A man of modesty, Gabriel openly implores the public on his green ink website that he should be nominated for the Abel Prize in mathematics already.^{[3]}
Unfortunately, he does not seem to understand the concepts of a limit, an innumerable set, and irrational numbers,^{[4]} which one learns about in an introductory course on real analysis. Before dissecting and criticizing the mathematical ideas of John Gabriel, some background information is in order.
For whatever reason, Gabriel sometimes decides to write about himself in the third person.^{[5]}
His debating tone is — unironically, no less — nearidentical to that of Newman from Seinfeld.^{[6]}^{[7]}
Exemplifying Gabriel's educational method of pedagogythroughabuse is The New Calculus derivative for absolute morons — a video intended to introduce people to his brilliant New Calculus. For just over the first two minutes of the video (a fifth of its total length), Gabriel calls nonbelievers people who don't get what he's driving at either "stupid" or "moron" at a rate of once every 13.5 seconds, on average.^{[8]}^{[note 1]} These same two words ("stupid" and "moron") also feature four times in the video title and description alone.
Contents
A brief history of calculus[edit]
On the validity of Gabriel's claims[edit]
“”As I predicted, all we have are stretched anuses  very red, swollen and hurting.

—John Gabriel, proud theorist and mature adult^{[6]} 
General Math[edit]
According to Gabriel,
 Some examples [of nonsense] are: ^{[9]}
 Irrational numbers
 Infinitesimals
 Limits
 Infinity
 Einstein's theories
 Hawking's theories
 Definitions that are selfreferential
Like all rational thinkers, Gabriel goes on to seemingly contradict himself two pages later:
 Not even "God" can measure 𝜋 or √2, because neither of these concepts require anyone to think of them. They have existed inanimately as perfect concepts, in past perpetuity and continue to exist indefinitely. ^{[10]}
Presumably he can prove √2 and 𝜋 are rational.
He discusses how mathematicians before him didn't understand numbers:
 The most serious misconception is that of number. Before me, there was no definition of number, only vague ideas of what is meant by the concept of number. ^{[11]}
He continues this rant for almost three pages, but unfortunately never defines numbers during the rant, or anywhere in the remainder of the document. However, he goes on tangents on several occasions, defining what isn't a number. Unfortuantely, this leaves the true, rational definition of numbers as a mystery. Or perhaps, as an exercise for the reader. Rational thinkers will mourn this unfortunate oversight.
New Calculus[edit]
The New Calculus definition of a derivative (which is essentially the secant method, known for centuries) indeed works for polynomials, eg.
 Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): f(x) = x^2 f'(x) = \frac {(x+n)^2  (xm)^2} {m+n} f'(x) = \frac {x^2 + 2xn + n^2  (x^2  2xm + m^2)} {m+n} f'(x) = \frac {2xn + n^2 + 2xm  m^2} {m+n} f'(x) = \frac {2(m+n)x + (m+n)(mn)} {m+n} f'(x) = 2x + mn \mathrm{let m = n} f'(x) = 2x
However, just like standard calculus, it has to resort to using concepts of infinity when it's convenient, directly contradicting the quote:
 "Based only on wellformed concepts, the new calculus does not use any illformed concepts such as limit, infinity or infinitesimals."^{[12]}
It goes on to use infinite series for sine and cosine:
 "Let's take a look at the derivative of sin(x)... [using Newton's] sine and cosine partial sum series..." ^{[13]}
Using ellipses which, according to the author, indicate the equality is not exact and is merely an approximation:
 "A number describes the measure of a size or quantity exactly, not partially or approximately, or with a rational approximation followed by an ellipsis, e.g 0.333..."^{[14]}
So much for rigor. Presumably it would use Taylor series for ln(x) and exp(x) as well, but these are not mentioned, presumably because they require calculus, which is beyond the scope of the New Calculus.
John Gabriel and RationalWiki[edit]
“”These people don't deserve to live, in my opinion. I hate them with a perfect hatred.

—John Gabriel, on the people who frequent RationalWiki^{[15]} 
Concluding remarks[edit]
—John Gabriel (writing in the third person), on the idiocy of being the wrong race^{[5]} 
Much of An Introduction to the Single Variable New Calculus is Gabriel reinventing the wheel, proving theorems known for centuries, interspersed with rants about how he is the first to discover them, how academics are out to get him, etc.
Footnotes[edit]
 ↑ 135 (seconds) / 10 (stupid/moron) = 13.5 (seconds per 1 stupid/moron)
References[edit]
 ↑ http://mathforum.org/kb/message.jspa?messageID=9832652
 ↑ John Gabriel: the New Calculus course.
 ↑ John Gabriel's home page.
 ↑ Mark ChuCarrol: Debating John Gabriel
 ↑ ^{5.0} ^{5.1} http://rationalwiki.org/w/index.php?title=Essay_talk:John_Gabriel&diff=1728752&oldid=1728545
 ↑ ^{6.0} ^{6.1} http://rationalwiki.org/w/index.php?title=Essay_talk:John_Gabriel&diff=1728798&oldid=1728778
 ↑ http://rationalwiki.org/w/index.php?title=Essay_talk:John_Gabriel&diff=1728757&oldid=1728756
 ↑ https://www.youtube.com/watch?v=ZCxaVtvGIQM
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 13
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 15
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 16
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 10
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 115
 ↑ Gabriel, John. An Introduction to the Single Variable New Calculus, p. 6
 ↑ https://www.youtube.com/watch?feature=player_detailpage&v=L0HmxyqRm2A#t=963