Tomorrow would have been American writer David Foster Wallace's 53rd birthday. Over 7 months ago I posted this as a "Sunday Reflection" over at

*MathTango*. I re-post it again today, here at

**Math-Frolic,** in his honor and for his many fans:

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*"Here
is a quotation from G.K. Chesterton: 'Poets do not go mad but chess
players do. Mathematicians go mad, and cashiers; but creative artists
very seldom. I am not attacking logic: I only say that this danger does
lie in logic, not in imagination.' Here also is a snippet from the flap
copy for a recent pop bio of Cantor: 'In the late nineteenth century, an
extraordinary mathematician languished in an asylum… The closer he came
to the answers he sought, the further away they seemed. Eventually it
drove him mad, as it had mathematicians before him.'*

*"The
cases of great mathematicians with mental illness have enormous
resonance for modern pop writers and filmmakers. This has to do mostly
with the writers'/directors' own prejudices and receptivities, which in
turn are functions of what you could call our era's particular
archetypal template….*

*"Chesterton
above is wrong in one respect. Or at least imprecise. The danger he's
trying to name is not logic. Logic is just a method, and methods can't
unhinge people. What Chesterton's really trying to talk about is one of
logic's main characteristics -- and mathematics'. Abstractness.
Abstraction."*

-- From "**Everything and More**" by David Foster Wallace

I've lately been re-reading parts of

David Foster Wallace's "

**Everything and More: A Compact History of Infinity**."

I
don't read fiction, but that doesn't stop me from sometimes being
intrigued by fiction writers, or in this instance one who additionally
wrote non-fiction. And I have other reasons to be fascinated by Wallace:

He
spent much of his childhood in Champaign/Urbana, Illinois, very near my
own hometown, and died tragically in 2008 while teaching at my alma
mater, Pomona College, in Claremont, California. In-between, his brain seemed to gallop effortlessly all over the place.

Of course it's
not his widely-acclaimed, award-winning fiction that interests me; it's
his, slightly-lesser-known, non-fiction. That a person of the humanities
with an English degree, who poured himself into long, involved, complex
novels and wordplay, was capable of also writing about deep mathematics
is fascinating. It's a little less strange given that Wallace did
deeply study philosophy, logic, and mathematics at the college level...
but still amazing to me that "

**Everything and More**" could be born in the same mind that authored "

**Infinite Jest**"(…interesting that "infinite" makes its way into this title as well).

Wallace called his 300+ page volume ("

**Everything and More**")
on infinity a "booklet," and he no doubt genuinely considered it but an
introduction to the whole subject; scratching the surface of a
topic that so often baffles undergraduates, even leading to
incredulity or heated arguments, amongst young math majors. Yet the book
is a meticulous parsing of the subject as virtually never found in a
popular work. In fact, I suspect it falls into that category of
'widely-bought, least-read books ever,' with a large percentage of
buyers never completing it; purchasing it solely based on the author's
reputation, and
then abandoning it after the first 30-50 pages.

The book
received a number of favorable reviews upon release, but several
professional mathematicians also harshly critiqued it, finding it
peppered with technical errors… I s'pose that I, as a non-professional,
tend to be more forgiving, spellbound as I am by Wallace's ability to
even approach these strenuous subjects innovatively… not that that justifies
inaccuracies, but just that my joy with the volume stems not simply from
the mathematics/philosophy entailed, so much as from the sheer
audacity of a renowned novelist crossing boundaries to tackle such
matters. I can't even imagine who this book was intended for… surely not
the same audience who loved Wallace's fiction; but nor for professional
mathematicians who would find faults in it. And not just for me, an
audience of one ;-) Somewhere out there must be other "mees," I guess, who
stand almost in awe of what Wallace accomplished: the mix of language
and math, of thought and meta-thought, of narrative and
cerebral-wrestling, while attempting to communicate it all to a mass(?)
audience. As I wrote once before, this volume is "

*written
in an informal and conversational tone about ideas that are utterly
UN-informal and UN-conversational (...and the multitudinous footnotes
are virtually as fascinating as the main text).*"

And
Wallace's prose isn't just deep, but in some ways, prescient...
anticipating something we now commonly hear about high school math education, here's
what he said in 2003 about college-level math:

*"The
trouble with college math classes -- which classes consist almost
entirely in the rhythmic ingestion and regurgitation of abstract
information, and are paced in such a way as to maximize this reciprocal
data-flow -- is that their sheer surface-level difficulty can fool us
into thinking we really know something when all we really 'know' is
abstract formulas and rules for their deployment. Rarely do math classes
ever tell us whether a certain formula is truly significant, or why, or
where it came from, or what was at stake. There's clearly a difference
between being able to use a formula correctly and really knowing how to
solve a problem, knowing why a problem is an actual mathematical problem and not just an exercise."*

This
remains one of the quirkiest, both convoluted and semi-profound, volumes on my math bookshelf, from one of
the quirkiest, most imaginative minds America has produced. Possibly
there is some irony, some stinging irony, that Wallace, a long-time
sufferer of depression, died tragically at his own hands, via hanging at
the young, fertile age of 46... possibly even suffering mental demons
not altogether dissimilar from Georg Cantor, a century earlier; died
perhaps an example of the same stereotype or "archetypal template" he
points to in the opening passage above

(*"the closer he came to the answers he sought, the further away they seemed"*).
One of the endorsement blurbs on the back of my copy of the volume says, "

*...David
Foster Wallace is the perfect parachute buddy for a free fall into the
mathematical and metaphysical abyss that is infinity*." I
think "abyss" may be too strong a word, but I do like the imagery of
'free-falling' into infinity... with an English major no less!

This
volume won't suit a lot of people's taste, but reading it more as a
treatise on human thought/genius and psychology, than a math treatise, I
return to it... in wonderment and reflection... each year.

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