{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

Last night I was reading The new math : a political history, circa 2015, by Christopher Phillips.

The more I think about it, the more I think that movement ought to have been called "Novel Math" rather than "New Math".

novel - original or striking especially in conception or style

It's hard to believe that the Federal Government of the United States actually funded this program, School Mathematics Study Group, where mathematicians were placed in charge of writing a series of experimental textbooks, mostly focused on secondary schooling.

I won't go into details as I have written about my obsession with texts written by Mary Dolciani or Frank B. Allen or Bechenbach, Donnelly, Wooton, Sorgenfrey, Graham, Myers, or even Swanson, Sharron, Kane, Brown, Jurgensen ... You know the texts I mean, the ones that presented the material in a very novel and formal manner grounded in set theoretic notation.

This strange event is like science fiction to me.  That movement came and went rapidly.  It was strong for maybe 10 years and was rejected, replaced by a "Back to Basics" revolt.

But, for that brief period, mathematicians wrote some textbooks for high school mathematics, presenting in a manner that might prepare the minds for pure mathematics.

The revised editions of the Dolciani texts which appeared in the 1980's and even the ones from the 1990's which contained computer programming exercises using BASIC or PASCAL are really awesome, I think.

What I keep pointing out is that even if the "New Math" movement is seen as a failed experiment, I, for one, appreciate many of the textbooks from that period and I have hunted them down, along with any solution manuals I could find.

I even located a couple obscure texts by Frank B. Allen, one which experimented with presenting Linear Algebra to high school students (from 1961) which made it all the way to Germany.  I found a rare inexpensive copy at abebooks.com along with teacher's commentary.  I don't know why I am so fascinated and obsessed with such texts.   Maybe it has to do with the fact that there was a long decade between when I graduated high school (1985) and when I attended university, finally studying Linear Algebra, Multivariable Calculus, and Mathematical Reasoning (writing proofs) in the year 2000. 

The material is presented in a novel way, and those texts bridge a certain gulf between computational mathematics (algorithms) and the more abstract mathematics involved more with reasoning and less with "plug and chug" rote learning.  I feel these texts offer an extremely rare presentation of "school mathematics" from the perspective, not of educators, but of "pure mathematicians".   It had never been done before, and I doubt it will ever be presented this way again, not at that level, anyway.

The book I linked to, The new math : a political history,  is interesting.  It explains the political climate in which the project was funded.  What a unique event in the history of textbook publishing!   

Maybe my life's work might be intimately tied up with this phenomenon. 

They thought they were writing those texts for high school students and high school teachers (back in the 1960's).  In this science fiction saga, it turns out that a 50 year old Steppenwolf ends up being the unexpected receiver of the mind treasure, the gong-ter.

It is for this reason that, whenever I hear this phenomenon referred to as "The New Math" (used in a derogatory manner), I will refer to it as "A Novel series of mathematics textbooks created by the School Mathematics Study Group back in the mid-twentieth century".

 The "New Math" may have been mocked and rejected by popular culture, but I am one who appreciates those efforts, and I will treasure going through their texts, filling in the gaps and bridging the gulf between the technical computational math hacker and the elite "pure mathematician" ... The buzz word "new math" is misleading.   It's now so old school, and I might go as far as to use the term, "uncanny," to describe the feeling I get when I approach a textbook older than I am that presents "modern mathematics".

What was called "modern algebra" is now called "abstract algebra".

What was "modern analysis" is now called "real analysis" even though NJ Wildberger has some nasty things to say about so-called real numbers, like the fact that there is no way to represent them as a decimal number?  or is his gripe that there are an infinite number of real numbers between two points on the real number line?