## The Word Version of my free eBook is available to any who wish to translate the most important mathematics book ever written into their language. Any translation must be precise, not include any other information and must be correctly attributed to (c) John Gabriel, Discoverer of the New Calculus. You may sell the book if you wish and keep the profits. However, I would prefer that you make it available free to all.

You might first want to learn why mainstream calculus is a fraudulent formulation. In my article, I explain a full geometric derivation of a general derivative formula for all functions - this is historic because it is the first and only rigorous formulation using the geometry of the Ancient Greeks and the first flawless solution to the tangent line problem.

The Big Lie: "Calculus was made rigorous..."

The phrase “calculus was made rigorous...” or its equivalent has appeared in thousands of textbooks and has been repeated ad nauseam by thousands, if not millions of academics and their sycophant followers and students alike. Today, it is considered to be the cornerstone of mainstream doctrine. The truth however, is very different to a lie that repeated so many times comes to be doctrine accepted by the majority.

Let's consider just a few main points concerning the significance of this knowledge I revealed to the world:

1. It could never have been realised from your mainstream mathematics which is based on ill-formed concepts. It was realised from the New Calculus which is the first and only rigorous formulation in human history.

2. What the geometric identity proves is that calculus works because of sound geometry and does not require any theory of limits, infinity or infinitesimals. The Ancient Greeks had all the mathematics they needed to produce a rigorous formulation of calculus. They failed, but I succeeded.

3. Last, but not least: The geometric identity proves that your mainstream formulation of calculus is entirely bogus, meaning a **fraud**. Why? Because, your definitions include ill-formed concepts that cannot be reified in any logical way whatsoever. Both your derivative and integral definition are stated in terms of the slope function:

[f(x+h)-f(x)]/h = f'(x) + Q(x,h)

which with a lot of help from the New Calculus, such as rigorous definition of area, volume, etc, make it possible to connect your derivative to the integral in a seamless way, although not nearly as simple and elegant as the New Calculus.

**Read and download my free e-Book called ***An introduction to the single variable New Calculus*. My free ebook is available in 4 languages with several other translations currently in progress: English, German, Chinese and French. The most recent translation is in French. The entire New Calculus is stated in the leading graphic on this page. My free eBook is the most important mathematics book ever written. There are 13 videos produced, one for each chapter of the book:

Lecture 1: A brief history of the most relevant events

Lecture 2: What it means for a concept to be well defined

Lecture 3: Mainstream misconceptions about mathematics

Lecture 4: There are no axioms or postulates in mathematics

Lecture 5: How we got numbers

Lecture 6: How we got algebra

Lecture 7: The arithmetic mean

Lecture 8: The lack of rigour in the mainstream calculus and its flaws

Lecture 9: The Mean Value Theorem

Lecture 10: The ideas that led to the discovery of the New Calculus

Lecture 11: The New Calculus derivative

Lecture 12: The New Calculus integral

Lecture 13: Gabriel Polynomial

The New Calculus is the greatest feat of human intellectual accomplishment. It is the first and only rigorous formulation of calculus in human history. Not worth one, but ten Abel prizes, given that no one before me was able to realise it. You can be certain that if the Church Of Academia (mainstream academia) has its way, I shall never receive any prizes, never mind one Abel prize. Mainstream academics hate me passionately and are pathologically jealous of my work. They have persecuted me in many ways: on five occasions they have shut down my previous sites through libel (falsely claiming I am an anti-semite) reports and lies and through actual death threats. They have tried to shut down my YouTube channel and have set up countless web sites libeling and defaming my character, whilst at the same time casting doubt on my brilliant work through lies and misrepresentation on many forums.

Mainstream calculus is a flawed formulation as explained in this 30 minute video.

While the New Calculus is my primary work, I have debunked and exposed mainstream ignorance and stupidity in many other respects: In my 5-part series, I prove that there are no axioms or postulates in Greek mathematics. You can also watch my fine videos in which I prove that the so-called "postulates" of Euclid are not postulates at all, but can be derived from nothing and each follows from the previous. The first short video derives the straight line and extended line, while the remaining requirements are elucidated in subsequent videos also available at my YouTube channel. In case my channel is shut down again in future, all the videos have been backed up here and here.

Perhaps the most damning evidence of mainstream ignorance and stupidity is the fact that their foundations of mathematics are all wrong. I was the only human (and proud Greek!) after Euclid to write down completely the perfect derivation of the abstract concept of number - without flawed set theory and real analysis. Euclid tried but did not succeed.

There have been many objections to the New Calculus by mainstream academic orangutans in the Church of Academia. I refute all of these in my article and video. Most telling is how stupid are these "erudite" priests of academia. Don't make the mistake of assuming I am a crank. I challenge anyone to find an error in my formulation. Good luck!

What is the New Calculus?

The derivative is found in a systematic way in the New Calculus. There is no systematic way to find the derivative in the bogus mainstream formulation. The method known as "first principles method" is riddled with errors, including illegal arithmetic, ill-formed limit theory and real analysis. In mainstream calculus you need to guess the derivative using the bogus first principles method and then verify it is true using epsilonics arguments.

In December 2019, I revealed a rigorous method of finding the derivative in mainstream calculus, but it is inferior to the New Calculus.

The definite integral is defined without using any ill-formed concepts in the New Calculus, unlike Riemann's ill-formed definition of the definite integral.

What no mainstream moron has ever been able to understand is what the mean value theorem is all about, yet all calculus works solely because of the mean value theorem.

So what is the New Calculus in one paragraph? The New Calculus is formulated using analytic geometry. No unsound concepts such as infinity, infinitesimals or limits are used. The New Calculus can be learned and mastered by a high school student, without years of useless university courses. But it is much more than just a reformulation - there are new theorems and features not possible using the flawed mainstream calculus. The first you will encounter is the Auxiliary equation. The New Calculus makes sense in every respect. This cannot be said of Newton's bogus calculus whose results are generally true, but the formulation thereof ill formed. 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. This may sound cranky but you'll agree once you learn the New Calculus.

Initially students of the New Calculus might be overwhelmed, because it requires a sound knowledge of geometry, algebra and trigonometry - all subjects one studies in high school. A high school student can master the single variable new calculus in just 2-4 weeks.

The first constructive proof of the mean value theorem was produced by me. I am also the first human since Euclid to produce the perfect derivation of number. Before you continue reading, please take a few minutes to watch these short videos as they set the tone for the rest of this web page:

Part 1: Why the New Calculus is the first and only rigorous formulation in human history.

Watch this video only if you haven't studied Euclid's Elements.

Part 2: Why the New Calculus is the first and only rigorous formulation in human history.

A short comparison between the mainstream calculus and the New Calculus. This comparison is only about the derivative definition, but there is much more wrong with mainstream calculus ideas.

There is no valid construction of real number.

Euler's Blunder has infected almost all of mainstream mathematics. For the article, go here.

History:

The New Calculus (NC) was conceived in the early part of the second half of the twentieth century. It's quite possible more advanced alien civilisations might have discovered it a long time ago. Based only on well-formed concepts, the new calculus does not use any ill-formed concepts such as limit, infinity or infinitesimals. The derivative as defined in mainstream calculus is flawed as I demonstrate on page 19-27 of the article containing my Quora debate with Anders Kaesorg, a graduate of MIT.

**Due to persecution from mainstream academia, this is the sixth time this site has been rebuilt. **In fact, Weebly once took down the site due to false reports of spamming from Google Inc. Weebly subsequently apologised, but I had already created a new site on Wix. As of 9/17/2016, the owners of Wix succumbed to pressure from mainstream academics to take the site offline. It is unbelievable that in this day and age, such Nazi tactics are used by the supposedly enlightened, educated and open-minded academic mainstream community. These efforts were driven by Prof. Gilbert Strang (aka Port563 on sci.math) of MIT and Prof. Jack Huizenga, a Harvard alumnus. Both these academics did not like the comments I made about them. You can read these comments here and here. Neither of the previous two links are on Weebly. The efforts of these academics were much complemented by a Python programmer and purported math lecturer in France called Jean Pierre Messager (JPM) who is a regular on sci.math. JPM goes by numerous aliases: YBM, JPM, Python (latest). You can find all of JPM's nonsense on sci.math and learn how this despicable pawn of Gilbert Strang verbally abuses many others far more educated than he.

The purpose of this site is to expose the flaws of mainstream calculus and elaborate on the beauty and light of the New Calculus which contains many features that are not possible using the flawed mainstream formulation:

1. The Auxiliary equation is the first and most powerful feature that a student learns. Not possible in the flawed formulation, this feature has been used by thousands of STEM professionals worldwide in fields as varied as technology, computer aided design, statistics and last but not least, education. Some important uses of the auxiliary equation include:

a. Non-linear regression

b. Finite difference estimation

c. Solution without iteration

and much more. There is no similar or equivalent possible in the flawed mainstream formulation.

2. Systematic integration is possible for any function in the New Calculus.

3. The Gabriel polynomial (single and multivariable forms) far surpasses the Taylor analog in mainstream calculus. It contains a varied number of fixed terms and is always a closed form.

4. Solution of differential equations and use of superior numeric integration techniques.

The entire single variable New Calculus is summarised in the leading graphic on this page.

Finitism, Infinitism and "Axioms".

These are all nonsensical concepts that have no place in any rational thought because infinity is itself a 100% junk concept that is not required at all in any mathematics and in particular calculus. The New Calculus is proof of this fact. There are no axioms in sound mathematics.

Resources:

Articles.

LinkedIn Articles (I was banned from LinkedIn).

Interactive and dynamic applets.

The 10 lesson NC course.

The 9 lesson NC Applet course.

YouTube Videos.

Advanced students and educators of mathematics:

The new single variable calculus is described in these abstracts:

Differentiation

Integration

**Objections from the BIG STUPID (mainstream academics):**

There have been numerous objections that are very quickly dismissed as nonsense. Read about these objections to make up your own mind.

High School Students:

Learn about the New Calculus derivative.

Learn about the New Calculus integral.

See how the formula for arc length is easily derived in the New Calculus.

It is easy to derive the new calculus integral definition using the new derivative definition.

Understand why the standard integral is a product of two arithmetic means using one of the following applets:

Applet 1. The New Calculus uses no ill-formed concepts such as infinite sums, limits or infinitesimals.

Applet 2. This applet explains the new calculus integral in great detail.

The Future.

This is the only official site of the New Calculus and one of its goals is to expose the fallacies in mainstream mathematics.

The ideas that added zero rigour to calculus.

The video and this applet explain the ideas that added no rigour to calculus, but in fact made it more obscure and complicated.

In the applet, you can click on the check box called "Show Information" to see why it is an ill-formed definition. It fails for many reasons, but the two most important are:

i. There is no valid construction of real numbers.

ii. Circular definitions are invalid.

The 13 fallacies of mainstream mathematics.

What's kind of sad and also kind of funny is how mainstream academics always ask for sources, usually printed or peer reviewed. The greatest mathematicians never had their work reviewed because they had no peers on their level. It is the same with me. In order for my work to be reviewed, my "peers" (I have none) would need to possess my intelligence and not to be infinitely ignorant like Prof. Gilbert Strang from MIT.

There is no such thing as an instantaneous rate of change.

So, courtesy of the internet, I am able to share some of my ideas and educate those aspiring young mathematicians with knowledge that is well formed.

Read what it means for any concept to be well defined.

What is pseudo mathematics?

The 13 fallacies that form the foundation of mythmatics (mainstream mathematics):

1. Infinity is not a well-formed concept.

2. There is no such thing as an infinite set. Proof by Prof. W. Mueckenheim using mainstream theory that a contradiction exists in set theory. Mueckenheim does a great job of showing how infinite set theory invalidates itself. The video is an eye opener.

3. Non-terminating radix representation cannot be used to represent "real" numbers. Much of the source for such confusion goes back all the way to Newton and the Dutch engineer Simon Stevin. It can be shown that multiplication is not distributed over infinite series. Newton experienced some really dull moments in his life and thoughts.

4. There are no irrational numbers. Hence no real numbers also.

5. An infinite sum is not possible. It is impossible to sum an infinite series according to mainstream academics. The mean value theorem is the reason calculus works and the fundamental theorem (which does not have two parts) is derived directly from it. The single variable New Calculus can be explained in under 25 minutes.

6. 1/3 =/= 0.333... Newton never used infinite series. Most of his misguided ideas came from manipulating partial divisors. This fallacy is easily debunked. In fact, the very idea of limit is flawed. Find out 5 reasons why Cauchy's derivative definition is flawed.

7. 1 =/= 0.999... It's hard to find a more controversial topic than the fallacy that 0.999... is anything but a sequence and that it's a very bad idea to define it as a limit. Irrational numbers do not exist and the worthless (not to mention absolutely useless) idea that 0.999... can be well defined as 1 is easy to dismiss. 0.999... is not well defined as 1 in this universe or any other. An article describing many reasons why it's a bad idea. My debate on SpaceTimeAndTheUniverse debunks each and every fake proof of this fallacy.

8. The integral is not the limit of an infinite sum. The definite integral is a product of arithmetic means and has nothing to do with non-existent infinite sums. The mean value theorem is the reason we can evaluate definite integrals. Riemann's ideas in this regard are completely misguided.

9. Numbers cannot be derived using sets. The von Neumann ordinal approach is a joke. The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means *number*, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of magnitudes? Of course you don't. Unless you have read my article, you don't have a clue what it means to be a *number*. Thousands of worthless books on numbers and history of numbers have been printed - all of them worthless rot.

After reading that article, ask yourself, does set theory require the natural numbers to be in place? Hint: YES

Does the von Neumann ordinal approach make any sense at all? Hint: NO

Is there any valid construction of irrational number? Hint: NO

Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO

10. The derivative is not a limit and does not require the limit concept. The nonsense of limit theory is trivially debunked.

11. Natural numbers did not come first. The real story of numbers is very different to anything ever published on thousands of worthless books on the same. The understanding of mainstream academics is based entirely on that mythical object called a *real number line. *It is absurd how they imagine numbers correspond to indistinguishable points on a number line.

12. There are no axioms in real mathematics.

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

A review by Ricardo Otero who studied the New Calculus:

*An introduction to the single variable New Calculus*. My free ebook is available in 4 languages with several other translations currently in progress: English, German, Chinese and French. The most recent translation is in French. The entire New Calculus is stated in the leading graphic on this page. My free eBook is the most important mathematics book ever written. There are 13 videos produced, one for each chapter of the book:

*Today's calculus explanations are so unbelievable, that they discourage a lot of students from learning calculus and mathematics in general. Take for example the concept of 'limit', which is based on the concept of infinity with respect to convergence. Infinity and limit theory are controversial topics, requiring more than a couple of semesters to study. Regardless of the controversy, it is clear that one argument has gained a stronger position over the other, as now limit theory is taught in every school and almost standard in most popular calculus textbooks. It is important to take notice of this situation, because even if you disagree with controversial topics such as limit theory, without alternatives, there is no choice but to memorize and push through 'by force', without really understanding calculus.*

The New Calculus is an exact formulation of calculus. By exact I mean, unlike calculus, which was derived by Newton empirically through approximation methods, the NC is derived strictly from geometry and has exact - unique algebraic solutions, with precise definitions of derivative and integral. There is no approximation and no limit theory used. This is an important point which confirms that the NC is not a rewrite of calculus. The NC derivation is new, ingenious and unrelated to the derivation of mainstream calculus. The ramifications are many. For example, differentials are now defined rigorously, and in reality nothing more than a fixed ratio. You don't need to think twice on how to work with them because they are standard ratios. There are many more ramifications, but the end-result is a very simplified and elegant calculus. A formulation that is easy to learn and will eradicate any doubts or questions in your mind, in particular if you already know calculus or (a formulation that) will make sense from the beginning if you are new to calculus.

The NC is an ingenious derivation of calculus, and I don't say this lightly. If you learn the NC, you are in for a treat, because from an aesthetic/intellectual point of view, the NC is beautiful. Remember that feeling you experienced when you first begun to learn calculus?

The New Calculus is an exact formulation of calculus. By exact I mean, unlike calculus, which was derived by Newton empirically through approximation methods, the NC is derived strictly from geometry and has exact - unique algebraic solutions, with precise definitions of derivative and integral. There is no approximation and no limit theory used. This is an important point which confirms that the NC is not a rewrite of calculus. The NC derivation is new, ingenious and unrelated to the derivation of mainstream calculus. The ramifications are many. For example, differentials are now defined rigorously, and in reality nothing more than a fixed ratio. You don't need to think twice on how to work with them because they are standard ratios. There are many more ramifications, but the end-result is a very simplified and elegant calculus. A formulation that is easy to learn and will eradicate any doubts or questions in your mind, in particular if you already know calculus or (a formulation that) will make sense from the beginning if you are new to calculus.

The NC is an ingenious derivation of calculus, and I don't say this lightly. If you learn the NC, you are in for a treat, because from an aesthetic/intellectual point of view, the NC is beautiful. Remember that feeling you experienced when you first begun to learn calculus?

Ricardo Otero

Software Developer

Bachelor degree in CS, Mexico

**John Gabriel**

Age: 60

Favourite Original Quotes:

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"

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"

"

The above quote is understood more profoundly as follows:

Age: 60

Favourite Original Quotes:

"

*Whatever I imagine is real because whatever I imagine is well defined*""

*The objects that arise from concepts in a mathematician's mind are only as appealing as they are well defined*""

*All well-formed knowledge is discovered, never invented*""

*Future inventions have always existed, only we cannot realise them all*""

*A number describes the measure of a magnitude*"The above quote is understood more profoundly as follows:

**My old LinkedIn explains what is a number and how we got numbers. There is no such thing as an "irrational number" - it's a myth.**

A NUMBER is a NAME given to a MEASURE that describes a commensurable MAGNITUDE (length, area, mass, etc).

We say a magnitude is commensurable (really means rational number) when it has a common measure with a magnitude other than itself.

A NUMBER is a NAME given to a MEASURE that describes a commensurable MAGNITUDE (length, area, mass, etc).

We say a magnitude is commensurable (really means rational number) when it has a common measure with a magnitude other than itself.

**Contact:**

**thenewcalculus AT gmail DOT com**

Photos of me in the last 3 decades:

The first image is me at age 41. It is a photograph taken at my US naturalisation ceremony.

Photos of me in the last 3 decades:

The first image is me at age 41. It is a photograph taken at my US naturalisation ceremony.