(DEDICATED TO HERMAN HUSTON HAYS (1874-1954) WHO GAVE ME MY FIRST DICTIONARY)
"Everything" you "wanted" to know about math, but I wasn't allowed to teach"

The title is a paraphrase of the book, Everything You Wanted Know About Sex But Were Afraid to Ask, by Dr. David Reuben, made into a fitfully funny film in 1972 by Woody Allen. I put the first word in quotation marks because I may not have covered everything and the other word in quotation marks allows for the fact that you may not want some or any of this.

Many items of this Dictionary (in particular, "The Hays Agenda") are intended to be provocative. For, as any Terrible Two-er can tell you, that's the way to get attention. If any one can academically correct me, I "win". For my primary purpose is to learn and to abet the dissemination of learning.

More than half of my original mathematical concepts or emendations of existing ones began in the years 1955-1970, when I was teaching in Puerto Rico and the United States. I had constant opposition in this from my colleagues. An anecdote exemplies my problem.

Irving Plaum was a foreign correspondent for The Chicago Sun Times, covering the Spanish Civil War (where he knew Ernest Hemingway), and other story-locales. In the 1960's he was a professor at our school, Inter American U. of Puerto Rico, San Germán, P.R, and lived up the campus road from our family. He invited Esther and me to a cocktail party for Roger Baldwin, founder of The American Civil Liberties Union (he's one of the "talking heads" in Warren Beatty's fascinating film, Reds). After my introduction to him, Baldwin asked me if I had ever been "censored" by any college president or dean. I said, "No", but my teaching had frequent interference from my colleagues, and I asked him what I could do about this. He seemed surprised; said he'd have to think about; rushed away and never came near me the rest of the evening. The next year, Irv invited us to another party to see Baldwin. As soon as I came through the front door, Baldwin saw me from across the room and shouted, "I'm still thinking about it!" But he has never contacted me, since. Alerted to this problem with the ACLU, I've never heard of any case involving this problem which the ACLU has considered.

I have also tried to get many of these ideas published. Some were published as abstracts in the old Notices of The American Mathematical Society. But no articles. I became disturbed around 1972 when I would get back a paper with the comment that I did not "show" something, whereas I had specifically developed this in several pages of the paper. Suspicious, I began then a practice I followed for years in submitting a paper to a journal. After, say, the third page, I would glue the pages together. Just enough glue to stick them together, but not enough to sustain evaporation if they were pulled apart. I always got the paper back with pages glued together. Either the paper was not read or the reader went to the trouble of regluing them.

From the 70's on, I frequently gave talks on my work before the DC-Virginia-Maryland Section of The Mathematical Association of America. The Mathematical Monthly published summaries of talks before this and other sections throughout the country. My talks never appeared in the listings. I began commenting on this to other talkers at these gatherings. They complained of the same problem, and of being rejected without explanation. So I am not alone in this.

I note in particular my attempt to publish my derivations (cited in my Dictionary) of the three multivector products (which unifies more than 25 vast fields of math under one common language). One rejection of my derivations had the comment that this explication was "too difficult" for this magazine for college teachers of mathematics, although I showed that these derivations are on the level of high school algebra. Suspicious again, I spent my lunch hours at NRL, munching a sandwich, and leafing through all issues of The Mathematic Monthly from its first issue to that date in 1989. Nothing on "Clifford Algebra" was every published!

The only attention I've received from an editor occured when I sent my fable, "The Battle of the Fog and the Mouse" (available at this Website) to the Monthly. The editor at that time, Paul Halmos, sent it on (after consulting me) to Mathematical Intelligencer where it was published in 1984. (I am very grateful for this courtesy.) Later, my fable was reprinted in Pi in the Sky (pp. 223-6), by John D. Barrow, 1992. At that time, I sent a letter to the Monthly, asking that readers be notified, but this never took place.

In particular, one thing which got me in trouble with my colleagues in math and science was telling my students about the Schaum Outline Series. When I started at Columbia U., I found Schaum's Outline of Chemistry and Schaum's Outline of Physics very useful. The Calculus book came out too late to help my class work, and so did all the others (Differential Equations, etc.). But when I became a teacher, I found it useful to tell my student about these books, which solve hundreds of problems or answer hundreds of questions in mathematics, the sciences, engineering, languages, etc. However, telling my students about these frequently got me in trouble with my colleagues, in PR and in universities of the "mainland". Why? I discovered that my colleagues were so damn lazy, they were taking their homework problems -- even test problems -- from these books, because it saved them the solution work. But their students would hear about the books from my students and challenge their teachers.

Censorship by colleagues is a critical matter. I call it "The Trujan Horse Syndrome". Who could better know how to interfere with the work of one professional except some one in the same profession? In the 1980's, I found an article agreeing with this in the Library at the Naval Research Laboratory, DC, where I was employed as mathematician and computer programmer (UNIX and C). The author declared that the greatest censoring in science, especially physics, had come -- contrary to general belief, not from Church or State -- but from within Science itself.

The author gave as an example Heinrich Hertz's inducing radio waves, which has changed our civilization. The literature claims that Hertz was encouraged in this by his superior, the great physicist, Hermann von Helmholtz (x-y). But the author of this article contradicted this claim, citing how Helmholtz interfered with Hertz's research. The author also mentioned something in the literature, but not played up very much. The leading physicist of this time was Lord Kelvin (William Thompson, x-y), knighted for supervising the laying of the Atlantic cable. When Kelvin heard the story of Hertz's experiment, Kelvin denounced this as a "fraud". This disturbed other physicists so much that they stayed away from this research, which was mostly left to amateurs. Fortunately, Guiseppe Marconi (x-y) was not only an able technician but a well-educated physicist. His persistence and achievements made radio research respectable. (This article appeared in one of the two publications of The American Association for The Advancement of Science. One was Science, still published; I've forgotten the name of the other, no longer published. I had a copy of this article, but lost it. I've been unable to find it on the Web.)

My professor for Laplace Transform Theory in Graduate School of New York University, 1954, was a visitor from Cambridge Univerity in England. A student in the class asked him if Laplace Transform Theory covered all useful functions used in mathematical physics. Saying, "No", he gave as an example the Heaviside step function, explaining that it turns out to be the derivative of the Dirac "function", so useful in quantum mathematics. Then he said, with a laugh, "At Cambridge, we are not allowed to teach the Heaviside function or even to mention it." And he reminded us of Oliver Heaviside's comment about his critics: "When mathematicians die, they go to teach at Cambridge."

I think that much opposition and interference with my teaching and writing arises because of my outspoken attitude about mathematics and science.

I regard magic, the paranormal, and "alternative science" as cheating, often weird, and elitist. But I argue that mathematics and science -- properly described and taught -- are democratic, in that every capable person can join in consensive understanding and use. Yet, as Sagan noted, this is not the way scimath is presented.

As I note elsewhere, I am not a wimp but a wamp (wary ass medial positioner). The popular illusion is that to take the middle position in an argument is to be a wimp. Not true! You get banged on by both extremes.

In particular, I regard constructive mathematics as "first class mathematics" and nonconstructive mathematics as "second class mathematics". I note evidence that a constructive proof often provides more information than a nonconstructive one, hence, is to be desired. However, history shows that a nonconstructive proof often inspires development of a constructive one, so nonconstructivism serves a useful purpose. But this attitude of mine has gotten me banged on by both sides -- by the pure constructivists and the nonconstructivists, particularly the Platonists. (Ow!)

In Spring, 2001, I sent an e-mail to the Editor of an MAA newsletter, asking that my URLs be listed in this newsletter for members to see. I also commented upon the fact that Clifford algebra had never been written up in the MAA Mathematical Monthly. This mathematician contacted me to say that he too had not found any article on it in the ONLINE archive of the magazine. This was his only communication with me. The listing was not placed in the newsletter.

Soon after this, I explained to a person phoning from MAA that I decided not to renew my 43-year-old membership in MAA in protest about my second-class MAA membership and the second-class mewmbership imposed upon other MAA members I've encountered in this area.

Other teachers not allowed to teach.