I was searching the board for a proper place for this link, and, if you don't mind I will place it here.

Upon further research into just what Zeilberger and Wildberger have in common besides their German?Jewish sounding names, I found that

Perhaps the most prominent ultra-finitist working today is Doron Zeilberger, a mathematician at Rutgers. Zeilberger, like many ultra-finitists, believe there is a largest natural number. When asked the inevitable question about what happens when you add 1 to it, he replies that, in a very elegant circularity, you go back to 0.Zeilberger is a Finitist who insists that today’s Mathematics (capital M) is a religion.

*Its central dogma is ***thou should prove everything rigorously**.

That page links to his

Opinions page.

Mind you, I only stumbled upon his name in Wildberger's book and took notice because of the mention of RENE. I have been curious to see a computer program in action proving elementary Euclidean Geometry proofs. So ...

Also, a three dollar book I ordered from 1993 by Arthur Engel, Exploring Mathematics with your Computer, which interested me because of its uniqueness (It was all math code written in Pascal) - the wrong book arrived which shared the same "series ISBN" - New Mathematical Library.

Uncanny and strange that the WRONG BOOK has the title, Geometry Revisited by Coxeter and Greitzer, circa 1967. Why do I use my most favorite word (

*uncanny*) up there with the word

*weird*? Well, you see, the current volumes of my "mathematical diary" are called exactly that: GEOMETRY REVISITED.

Besides that, I was born in 1967.

It's just a weird coincidence. The full title of the art sketchbook I pencil in solutions in is called Geometry Revisited, Book Two, A Mathematical Diary by a disciple of The Weird.

I have a great many of such math diaries which have replaced the scribblings I once called "A Philosophical Diary".

In the preface of the WRONG BOOK, they write, "Historically, it must be remembered that Euclid wrote for mature persons preparing for the study of philosophy. Until our own century, one of the chief reasons of teaching geometry was that its axiomatic method was considered the best introduction to deductive reasoning."

Anyway, as you can see, even though my brain feels like it is ALL OVER THE PLACE, actually the chaos has a definite theme and pattern.

The one thing the professional mathematicians may not have is the leisure to think about what they may consider "high school and undergraduate" mathematics, and yet, for me, that material, along with the mathematical thinking of our ancestors, both ancient as well as prehistoric, require a great deal of leisure to explore and reflect upon.

Our brains have not changed physiologically throughout the eons.

What has changed is the unfathomable mass of information and knowledge passed down to us as well as the pace at which mass industrial society attempts to "inject" thousands upon thousands of years of thinking into our basically prehistoric brains!

No wonder we get headaches and suffer from insomnia. No wonder we become distracted, frustrated, and overwhelmed.

I suggest we continue to play dumb, for our feelings of inadequacy must be a very common response.

What can we do but space out and meditate in between our feeble efforts to think?

What is the geometric space between our thoughts?

Holden, have you considered that you just might be a heretic of this religion?

And myself, I want at all costs NOT to be a crank or a phony elitist. I apologize for responding to your "Re-Imagining Mathematics" as though I were a religious fanatic.

In reality, I most likely am some in some kind of chaotic, spontaneous, informal, unofficial cult of mathematically-oriented programming enthusiasts and hobbyists who, having found themselves marginalized and unable to keep pace with the more ambitious but less contemplative masses of the Industrial World, have latched on to LEISURE as a way of life. There are many of us who choose books over automobiles,

Whereas in the ancient world, only the aristocrats could spend their lives practicing this religion of Mathematics, now a great many "disabled" or "psychologically unemployable" would-be slaves, are taking to foraging for "information" as some kind of treasure.

You are a heretic, Holden, and I am an infidel. Also, I am moving in an opposite direction from the PhDs and graduate students ... I find I am rejuvenated by this revisiting the college-prep high school curriculum from the vantage point of an escaped slave or time-traveler from prehistoric times.

The approach taken in the 1960's, what may have appeared too formal and rigorous (i.e., RELIGIOUS) back then (which is why there was such a strong resistance, that is, "the math wars"), is now very novel to me. Yes, now that I have proven to be officially "resistant to traditional employment" and quite content living on government relief like our Ignatius Reilly from Toole's A Confederacy of Dunces, I can embrace the mathematics I only hated because we were so methodically marched through it during a period of our lives when we were experiencing emotional turbulence (adolescence).

Again, please do not let me discourage you from engaging with mathematics however the hell you want to. Myself, I am leaning in the direction of riding the wave of alternating periods of enthusiasm and depression/disgust.

Where our minds meet, I think, is in our sense of inadequacy and inferiority - due to the premium we place on honesty, clarity, and self-deprecating humor. We both may have violent resentments against obfuscation, so we are inclined to seek some balance by injecting a little humility and, if possible, even simplicity into our own personal engagement with what goes by the names of maths, math, or mathematics.

- Your Working Boy, paying homage to Ignatius J. Reilly.

PS: another excerpt from the book I did not ask for which has the same title as my (current) secret diaries,

*Geometry Revisited*.

**With a literature much vaster than those of algebra and arithmetic combined, and at least as extensive as that of analysis, geometry is a richer treasure house of more interesting and half-forgotten things, which a hurried generation has no leisure to enjoy, than any other division of mathematics.** ~ E.T. Bell

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An aside:

A not so small but mostly overlooked tragedy of living in an age of information abundance is that there are many enthusiastic young scholars who may find themselves criminalized by the representatives of capitalism, commerce, and the corporate state for say, using "Student Editions" of mathematics software or distributing digitalized literature.

What kills me about so-called student editions of products such as Mathematica, Matlab, and Maple is that the Industry is claiming to define what a student is!

In other words, you are not considered a student unless you are in the system working toward a degree. They are blatantly denying the far more prevalent practice of independent and exploratory "self-education."

My strong personal opinion is that such "Student Edition licenses" ought to be altered to include those who promise

*to use the products for educational purposes only, not commercial purposes.*