A classic of mathematical history in this week's New Yorker begins,

"On the evening of June 20th, several hundred physicists, including
a Nobel laureate, assembled in an auditorium at the Friendship Hotel in
Beijing for a lecture by the Chinese mathematician Shing-Tung Yau."

The story, by Sylvia Nasar and David Gruber, is now online.

Related material

Log24 on June 20th
(morning in New York,
 evening in Beijing)--

Beijing String begins,

"Oh, do not ask, 'What is it?'
Let us go and make our visit."
-- T. S. Eliot

Same Time
Last Year:

"'Once upon a time' used to be a gateway to a land that was inviting precisely because it was timeless, like the stories it introduced and their ageless lessons about the human condition."

-- Dorothea Israel Wolfson, Claremont Review of Books, Summer 2006

"It's quarter to three..." --Sinatra

Introductions

In talks at Valencia, Spain, in May through August of 2004, Alexander Borisenko, of Kharkov National University in the Ukraine, provided a detailed introduction to the topic of today's opening lecture at ICM 2006 in Madrid:

An Introduction to Hamilton and Perelman's Work on the Conjectures of Poincare and Thurston (pdf, 155 pages).

For a less detailed introduction, see an ICM 2006 press release (pdf, 3 pages) on Fields Medal winner Grigory Perelman.

Related material: The previous entry, "Beginnings," and an introduction to the second-simplest two-dimensional geometry (Balanchine's Birthday, 2003).

"How much story do you want?"
-- George Balanchine

Beginnings

"Nothing ever begins.

There is no first moment; no single word or place from which this or any other story springs.

The
threads can always be traced back to some earlier tale, and to the
tales that preceded that; though as the narrator's voice recedes the
connections will seem to grow more tenuous, for each age will want the
tale told as if it were of its own making."

-- Clive Barker, Weaveworld

"No mathematical subject lies closer to intuition than the geometry of two and three dimensions."

-- Robert E. Greene, beginning an April 1998 review of Three-Dimensional Geometry and Topology, by William P. Thurston

Thurston's book provides some background for today's opening lecture by Richard Hamilton, "The Poincare Conjecture," at the beginning of the International Congress of Mathematicians in Madrid.

Hamilton is likely to discuss the Poincare conjecture in the wider context of Perelman's recent work on Thurston's geometrization conjecture.

In "The Eight Model Geometries," section 3.8 of his book, Thurston provides yet another beginning--

Special Topics

From a review by Liesl Schillinger in the Aug. 13 New York Times of a new novel by Marisha Pessl:

"... Special Topics in Calamity Physics
tells the story of a wise newcomer who joins a circle of students who
orbit a charismatic teacher with a tragic secret. The newcomer, a
motherless waif named Blue van Meer, spent most of her life driving
between college towns with her genius poli-sci professor father,
Gareth....  Gareth is fond of making oracular statements, which
his daughter laps up as if they were Churchill's: 'Everyone is
responsible for the page-turning tempo of his or her Life Story,' he
tells her. And, he cautions, 'never try to change the narrative
structure of someone else's story.'

.... Heeding Gareth van
Meer's dictum that the most page-turning read known to man is the
collegiate curriculum, with its 'celestial, sweet set of instructions,
culminating in the scary wonder of the Final Exam,' Pessl structures
Blue's mystery like a kind of Great Books class.... A professor is
all-powerful, Gareth liked to tell his daughter, he puts 'a veritable
frame around life,' and 'organizes the unorganizable. Nimbly partitions
it into modern and postmodern, renaissance, baroque, primitivism,
imperialism and so on. Splice that up with Research Papers, Vacation,
Midterms. All that order-- simply divine.' Blue's syllabus also
includes a murder or two. Her book's last pages are a final exam. You
will be relieved to learn it is mostly multiple choice, and there is no
time limit."

Multiple choice:
The examination below, taken from a page by a scholar at a Jesuit university, is on the Borges story "The Garden of Forking Paths"-- a classic of multiple choice.

No time limit:
See the first question.

Examination on
"The Garden of Forking Paths"

"What is the meaning of the idea expressed by Yu Tsun that 'everything happens to a man precisely, precisely now.
Centuries of centuries and only in the present do things happen'? What
is the significance of the emphasis on the present moment, the here and
now? Is this related to the carpe diem ('seize the day')
idea? How? How is the present effectively connected to the past and the
future? How is the present associated simultaneously to choices,
actions, and consequences? How is the present moment relevant to the
idea of the 'forking paths'? What is the symbolic meaning of forking
paths when understood as a crossroads? What is a person confronted with
when standing at a crossroads? What are the implications of a choice of
road? May this be connected to the myth of Oedipus and its concerns
with human choices and supposed predestination? What is suggested by
the idea that 'in all fictional works, each time a man is confronted
with several alternatives, he chooses one and eliminates the others; in
the fiction of Ts'ui Pen, he chooses-- simultaneously-- all of them. He
creates, in this way, diverse futures, diverse times which themselves
also proliferate and fork'? What does it mean to make all choices at
once? What view of life do such beliefs embody?"