"Prof.
Paul Halmos died of pneumonia early in the morning of October 2, 2006.
He was 90 years old. He is survived by his wife, Virginia Halmos. An
obituary may be found at the website of the Mathematical Association of America...."

-- Halmos's home page
at Santa Clara University

For a memorial of sorts, see
Lovely, Dark and Deep. 

Update of 8 PM Oct. 4 --

From Google Book Search:
 

This is the source of the
"Halmos tombstone" symbol,
which has been described in a
different form at Wikipedia:

"The tombstone, or halmos--
symbol ∎ (Unicode U+220E)--
is used in mathematics to denote
the end of a proof." 

This Unicode character is rendered
as an empty square in Explorer
and as a black square in Firefox.

Related material:

The Unity of Mathematics
and
Monolith

"Hard lessons lately."
 
-- Bruce Springsteen

A belated meditation for Yom Kippur, which ended at sundown yesterday:

"Whatever
the shatterings Hopkins felt threatened his and other sacred selves,
perhaps precisely because of that threat, he composed the greatest
passage on the God-relation of identity since Galatians 2:20....

The
aesthetics of truth form alliances, profoundly elective affinities,
that the intellect stripped of feeling inclines to reject....
Intellection must address the matter of its feeling."

-- Philip Rieff,
    Sacred Order/Social Order, Vol. 1:
    My Life among the Deathworks:
    Illustrations of the
    Aesthetics of Authority,
    University of Virginia Press, 2006.
    256 pages.

Serious

"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."

-- Charles Matthews at Wikipedia, Oct. 2, 2006

"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of
the mathematical ideas which it connects. We may say, roughly, that a
mathematical idea is 'significant' if it can be connected, in a natural
and illuminating way, with a large complex of other mathematical
ideas."

-- G. H. Hardy, A Mathematician's Apology

Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:

Affine group‎
Reflection group‎
Symmetry in mathematics‎
Incidence structure‎
Invariant (mathematics)‎
Symmetry‎
Finite geometry‎
Group action‎
History of geometry‎

This would appear to be a fairly large complex of mathematical ideas.

See also the following "large complex" cited, following the above words of Hardy, in Diamond Theory:

Affine
geometry, affine planes, affine spaces, automorphisms, binary codes,
block designs, classical groups, codes, coding theory, collineations,
combinatorial, combinatorics, conjugacy classes, the Conwell
correspondence, correlations, design theory, duads, duality, error
correcting codes, exceptional groups, finite fields, finite geometry,
finite groups, finite rings, Galois fields, generalized quadrangles,
generators, geometry, GF(2), GF(4), the (24,12) Golay code, group
actions, group theory, Hadamard matrices, hypercube, hyperplanes,
hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman's
schoolgirls problem, Latin squares, Leech lattice, linear groups,
linear spaces, linear transformations, Mathieu groups, matrix theory,
Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads,
the octahedral group, orthogonal arrays, outer automorphisms,
parallelisms, partial geometries, permutation groups,
PG(3,2), polarities, Polya-Burnside theorem, projective geometry,
projective planes, projective spaces, projectivities, Reed-Muller
codes, the relativity problem, Singer cycle, skew lines,  sporadic
simple groups, Steiner systems, symmetric, symmetry, symplectic,
synthemes, synthematic, tesseract, transvections, Walsh functions, Witt
designs.

From Wallace Stevens
On His Birthday

"Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word...."

-- Notes Toward a Supreme Fiction

The Joy of Six

Yom Kippur begins on the East Coast
at about 6:38 PM today.

Recommended holiday reading list
from Robert Langdon, Harvard author
of "the renowned collegiate texbook
Religious Iconology" --

Elegance

Gerard Manley Hopkins on parallelism

Figures of Speech

Hamlet's Transformation and the four
Log24 entries that preceded it

Finite Geometry of the Hexahedron
(Alternate title for the Christmas, 2005, entry)

Happy Six

Recipe for Disaster
 
according to Jerome Kagan,
Harvard psychologist emeritus 

From Log24 --
The Line	The Cube
From Harvard's Jerome Kagan --
"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world.'"	"People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise-- to entertain the possibility that life is not black and white, but variously shaded in gray-- is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."
Black and White: Log24 in May 2005	Shades of Gray: An affine space and  Harvard's Jerome Kagan

The above Kagan quotes are taken
from a New York Times essay by
Judith Warner as transcribed by
Mark Finkelstein on Sept. 29.

See also Log24 on
Sept. 29 and 30.

Related material:

Kagan's book

Surprise, Uncertainty,
and Mental Structures

(Harvard U. Press, April 2002)

and Werner Heisenberg--
discoverer of the
uncertainty principle--
as Anakin Skywalker
being tempted by
the Dark Side: