**[I've now revised and expanded what had been a hastily-written Friday post, because I feel it makes for a good (though longish) 'Sunday reflection,' and so, with that purpose in mind, I re-present it below... even if you read it earlier, I hope you'll re-read for the additional material. Thanks.]:**

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A beautiful, touching, scrumptious essay this week from Keith Devlin, on the beauty of mathematics... a somewhat tiresome phrase that he breathes life into here, focusing on calculus, or, as he quotes William Blake, "

*infinity in the palm of your hand*":

http://devlinsangle.blogspot.com/2015/10/letter-to-calculus-student-sequel.html

It deals with a student's recent response to a piece Keith had written almost 10 years earlier. I heartily commend it to all mathematicians, math teachers, math majors, and students in general, and all those, who like myself, simply love math from the sidelines. It almost has a fractal quality, as a beautifully-crafted essay, about beautiful ideas, about the beauty of beauty! ;-)

[p.s... Dr. Devlin suggests "

*if you are a math instructor at a college or university, maybe print off this blog post and pin it somewhere on a corridor in the department as a little seed waiting to germinate.*" I'll second that suggestion, which derives, NOT from Keith's ego, but from his infectious love of math teaching/learning.]

Actually, half the post is simply a verbatim letter Dr. Devlin received from a math student who had previously read another of Keith's essays, and now was writing to say how much he

*finally*appreciated that earlier piece. Is there anything more rewarding to a teacher than to hear from a student (and in this case not even Keith's own student) how much something you said or did in the past has affected that student years later!? Keith's earlier piece was about the deep, deep beauty of calculus, or again from Blake,

*seeing*

*"an infinite (and hence unending) process as a single, completed thing.*"

All of us who've taken calculus will probably freely admit that, no matter what our grade or ability in a first-year course, we lacked any deep grasp of the subject at that point. To a lesser degree maybe that even holds for algebra, geometry, trig… the student can't fully appreciate these subjects 'til s/he has taken in much more mathematics for context, depth, nuance. The "inner beauty" of math requires persistence and commitment to fully access.

Dr. Devlin's post reminded me slightly of the well-known Richard Feynman blurb that I've placed below (and am sure most of you have already seen), wherein he speaks of the "

*beauty of a flower*," and how, despite what an artist friend thinks, he as a physicist also has access to seeing that beauty; perhaps even perceiving it at a deeper level than does the artist.

I

*I could see the beauty of math the way Keith, and Ed Frenkel, and Steven Strogatz, and others see it (seeing it, as Keith has previously written, from a treetop overlooking the vast but inter-connected forest below). But alas, as a rank-amateur, my vision is far more limited, far more myopic than theirs. Yet even from my lowly vantage point mathematics resounds in beauty, in "*

**WISH***excitement, mystery, and awe*" as Feynman refers to.

Some of course call mathematics the language of science, or even the language of God. But at base, I think its beauty lies in being a pure, grand, and almost inexplicable creation (or discovery) of the human mind... the pinnacle of that which our brains are capable. In a day when our lives, politics, and society, seem inundated with violence, intolerance, and irrationality, mathematical thinking stands out as a beacon for the future, if we as a species are to have a future.

Growing up, I watched my grandfather (and other seniors) become increasingly cynical about the world as they aged, and swore to myself I would never be like that. But I do now find myself saddened each day when I turn on the news… cynicism is hard to repress. My hope today though, is that every teacher out there, at least once in your lives, receives a letter like the one Dr. Devlin has shared, or if you're not a teacher, that you hear from some young person, when you're not expecting it, what a difference you made in their lives.

The oddball Count (and father of General Semantics), Alfred Korzybski wrote that we humans are a "time-binding" species (different from all other species that only "space-bind") because of the way we routinely transfer our increasing knowledge across generations. That, in part, is what I see going on in Dr. Devlin's piece, "time-binding" with a younger generation... and, as always, the younger generation is our real hope for the future... and, our shield against cynicism!

Finally, as I was completing this post a new blogpost from Megan Schmidt crossed my webfeed. If you need a reminder that teachers impact young lives (or even if you don't) I hope you will read it as well, (be sure to click on and read the student exposition she provides):

**http://mathybeagle.com/2015/10/03/where-do-we-go-from-here/**

Lastly, enjoy Dr. Feynman:

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