Harvard's Barry Mazur likes to quote Aristotle's Metaphysics.  See 1, 2, 3.

Here, with an introductory remark by Martha Cooley, is more from the Metaphysics:

The central aim of Western religion --

"Each of us has something to offer the Creator...
the bridging of
                 masculine and feminine,
                      life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy --

                 Dualities of Pythagoras
              as reconstructed by Aristotle:
                 Limited     Unlimited
                     Odd     Even
                    Male     Female
                   Light     Dark
                Straight     Curved
                  ... and so on ....

"Of these dualities, the first is the most important; all the others
may be seen as different aspects of this fundamental dichotomy. To
establish a rational and consistent relationship between the limited
[man, etc.] and the unlimited [the cosmos, etc.] is... the central aim
of all Western philosophy."

-- Jamie James in The Music of the Spheres (1993)

"In the garden of Adding

live Even and Odd...

And the song of love's recision
is the music of the spheres."

-- The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

Harvard University, Department of English:

Today's birthday: Jerry Seinfeld.
Related material:
Is Nothing Sacred? and Symmetries.

Black Moses

For an explanation of the title, see
the previous entry and
Robert P. Moses and The Algebra Project.

For another algebra project, see
Log24 entries of April 14-25 as well as
the following "X in a box" figure

from March 10, 2005 and

April 5, 2005.

Those interested in artistic rather than mathematical figures may compare this diagram with that of Samuel Beckett in Quad (1981):

Related quotations:

Barry Mazur on a seminal paper of algebraist Saunders Mac Lane:

The paper was rejected "because the editor thought that it was 'more
devoid of content' than any other he had read.  'Saunders wrote
back and said, "That’s the point,"' Mazur said.  'And in some ways
that’s the genius of it. It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else.'"

J. Peter May, a professor of mathematics at the University of Chicago quoted in the Chicago Tribune:

"There are some ideas you simply could not think without a vocabulary to think
them."

Amen.

From The Measure of a Life:

Does religion
play a role
in attitudes toward ETIs? Philip Morrison gave his considered
opinion... “Well, it might, but I think that it’s just one of the
permissive
routes; it isn’t an essential factor. My parents were Jewish. Their
beliefs were conventional but not very deep. They belonged to the
Jewish community; they went to services infrequently, on special
occasions—funerals and high holidays”....

Although Sagan did not
believe in God, he nevertheless said this about SETI’s importance... “It touches deeply into myth, folklore, religion,
mythology; and every human culture in some way or another has wondered
about that type of question. It’s one of the most basic questions there
is.” In fact, in Sagan’s novel/film Contact, described by Keay Davidson
as “one of the most religious science-fiction tales ever written”... Ellie discovers that pi—the ratio of the circumference of a
circle to its diameter—is numerically encoded in the cosmos and this is
proof that a super-intelligence designed the universe...

The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself,
you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover
a miracle—another circle, drawn kilometers downstream of the decimal point. In the fabric of space and
in the nature of matter, as in a great work of art, there is, written small, the artist’s signature.
Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an
intelligence that antedates the universe.

Mathematical Style:

Mac Lane Memorial, Part Trois

(See also Part I and Part II.)

"We have seen that there are many diverse styles that lead to success in
mathematics. Choose one mathematician... from the ones we studied
whose
'mathematical style' you find most rewarding for you....
Identify the mathematician and describe his or her
mathematical style."

From today's Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

[Saunders] Mac Lane was most famous for the
ground-breaking paper he co-wrote with Samuel Eilenberg of Columbia in
1945 which introduced category theory, a framework to show how
mathematical structures relate to each other. This branch of algebra
has since influenced most mathematical fields and also has functions in
philosophy and linguistics, but was first dismissed by many practical
mathematicians as too abstract to be useful.

Gade University
Professor of Mathematics Barry Mazur, a friend of the late Mac Lane,
recalled that the paper had at first been rejected from a lower-caliber
mathematical journal because the editor thought that it was "more
devoid of content" than any other he had read.

"Saunders wrote
back and said, 'That’s the point,'" Mazur said. "And in some ways
that’s the genius of it. It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else."

He likened it
to a sparse grammar of nouns and verbs and a limited vocabulary that is
presented "in such a deft way that it will help you understand any
language you wish to understand and any language will fit into it."

Get the Gospel Feeling
on April 24

"In my hour of weakness,

that old enemy
tries to steal my soul.

But when he comes
like a flood to surround me

My God will step in
and a standard he'll raise."

-- Jesus Be a Fence

^.

Mac Lane Memorial

In memory of Saunders Mac Lane, mathematician, who died Thursday, April 14, 2005:

From MacTutor --

"It was during these years [the late 1930's] that he wrote his famous text A Survey of Modern Algebra with G. Birkhoff which was published in 1941. Kaplansky writes in [*] about this text:-

A Survey of Modern Algebra opened to American undergraduates what had until then been largely reserved for mathematicians in van der Waerden's Moderne Algebra, published a decade earlier. The impact of Birkhoff
and Mac Lane on the content and teaching of algebra in colleges and
universities was immediate and long sustained. What we recognise in
undergraduate courses in algebra today took much of its start with the
abstract algebra which they made both accessible and attractive.

[*] I. Kaplansky, "The early work of Saunders Mac Lane on valuations and fields," in I Kaplansky (ed.), Saunders Mac Lane: Selected Papers (New York - Heidelberg, 1979), 519-524."

Mac Lane is noted for introducing, with Eilenberg, category theory.

For some remarks on the place of category theory in the history of mathematics, see Log24  entries of Dec. 3, 2002.