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

I found the following comment for Modern Algebra: A Logical Approach, Book One by Helen R. Pearson &Frank B. Allen (at Amazon) of interest:

I especially like the last paragraph about living in an anti-intellectual world so dominated by politics that only the most vulgar displays of superficial mechanical proficiency are ever even noticed while everyone frantically attempts to "Beat the Joneses" with whatever latest gimmick they can get their hands on ...

A still born child of New Math the loss of which has left us with little hope

I have an MS in Math from Ohio State, and my wife and I home school our three children. We've been home schooling now for several years and it is approaching time for us to figure out our algebra/geometry/trig (or the equivalent) program. As a former graduate student in math, I know about this thing out there lurking under the surface of college math. It is the proof, of course. Somehow what a "proof" is, what "math" is, and what it is all good for has all gotten extraordinarly lost in a way that goes far beyond even the scope of secondary school education.

This basic problem can be heard reverberating in ancient videos of Feynman lecturing to the public on the role of mathematics in physics (and how rigor is not particularly useful). It can be seen in the mathematics curricula of undergraduate programs all over the nation that pander to other departments' needs. cutting out most of the actual math content and reducing the math major to a generalist in the mathematical sciences rather than a specialist in mathematics. At any rate, it is much, much bigger than even math ed or math ed reform and will stop any meaningful progress in math ed reform, for that matter, since it is a basic disagreement on the necessity and/or intellectual value of rigor (and, in many cases, what "rigor" even is for that matter).

At any rate, it's too bad these books are out of print -- victims of a war far greater in magnitude than even the math wars. The New Math of the 60s was as close as it gets to mathematics being handed down to society by its mathematicians, and we threw it all away. Frank Allen's books are not just books written to pay lip service to the movement, but truly written in the spirit of the times by a real advocate of the New Math. In any case, these books are probably the very best algebra books I have ever seen as of this writing. If you put them together with a good geometry program that at the very least proves the Pythagorean Theorem, you will have youself one first class high school education.

Unfortunately, Frank Allen will never receive the vindication he deserved. But, perhaps he imagined that there might be people like me that would happen upon his work and find it immeasurably valuable in an anti-intellectual world so dominated by politics that only the most vulgar displays of superficial mechanical proficiency are ever even noticed while everyone frantically attempts to "Beat the Joneses" with whatever latest gimmick they can get their hands on.

This may be why I feel like some kind of "mental patient".

Not only am I considered "disabled" (via a mood disorder), which means I would be seen as someone who may not work well with others, maybe not obey orders, report to work on time, etc.,

More than this though, the things I find to be so impressive, such as those old textbooks by Frank Allen or Mary Dolciani, this world ignores.   When I witness such things, I really feel in my heart, WHY BOTHER?

Why bother with anything?

I'll just continue smoking tobacco, drinking coffee, and studying, knowing full well that I am living the life of a second-class citizen, practically a ward of the State ...

It's so strange to consider oneself "crazy" or even having some kind of "mental disorder" when deep down inside I feel "intellectually superior" to many of those who serve society in some kind of administrative or managerial capacity.

I am simply resigned to being depressed and just have to get used to being generally disappointed with life.  Seeking a cure or a way out may only make us feel worse.

So, I am reading Frank Allen's book ... which was wrtten before I was born.

I was not the target audience, but happen to be one of the few who is interested.

It is what it is.