(Originally posted at on July 1, 2010 8:46 AM)

Proof is a beautiful play by David Auburn.  It won the Pulitzer Prize in Drama and the Tony Award for Best Play in 2001, among other awards.  (I got a copy of the play from BOOKSALE.)

The main character, Catherine, claims to have written a proof of a very important mathematical theorem. Hal, a mathematician, initially does not believe her, thinking that the proof was actually written by Catherine’s recently deceased father, a famous mathematician.  Eventually, Hal comes to believe Catherine’s claim, and goes to her to apologize.  The following conversation brilliantly shows how the concept of proof in mathematics differs from that in the “real world.”

HAL:  Come on, Catherine.  I’m trying to correct things.
CATHERINE:  You can’t.  Do you hear me?
You think you’ve figured something out?  You run over here so pleased with yourself because you changed your mind.  Now you’re certain.  You’re so . . . sloppy.  You don’t know anything.  The book, the math, the dates, the writing, all that stuff you decided with your buddies, it’s just evidence.  It doesn’t finish the job.  It doesn’t prove anything.
HAL:  Okay, what would?
CATHERINE:  Nothing.


Education and Training

(Originally posted at on June 16, 2010 1:56 AM)

James P. Carse is the author of Finite and Infinite Games (New York:  Ballantine Books, 1986) which is, in my opinion, a very important book.  In it is a section on the difference between education and training:

To be prepared against surprise is to be trained.  To be prepared for surprise is to be educated.

Education discovers an increasing richness in the past, because it sees what is unfinished there.  Training regards the past as finished and the future as to be finished.  Education leads toward a continuing self-discovery; training leads toward a final self-definition.

Training repeats a completed past in the future.  Education continues an unfinished past into the future.

The book requires careful reading.  (It is unfortunate that my copy has a typographical error on the cover.  The cover states “If a finite game is to be won by someone, it must come to a definite end,” whereas the actual text in the book states “If a finite game is to be won by someone, it must come to a definitive end.”)

Top Philippine Universities

(Originally posted at on May 14, 2010 10:24 PM)

According to, four Philippine universities are in the list of the top 200 Asian universities.  (Also see this.)  For 2010, Ateneo de Manila University is at 58 (from 84 in 2009), University of the Philippines is at 78 (from 63), University of Santo Tomas is at 101 (from 144) and De La Salle University is at 106 (from 76).

Dr. Seuss’s 1977 Commencement Address

(Originally posted at on April 4, 2010 8:43 AM)

On June 1977, Theodor Seuss Geisel was invited to give the commencement address of Lake Forest College (outside Chicago). Here is his 75-second address entitled “My Uncle Terwilliger on the Art of Eating Popovers” (from Judith & Neil Morgan, Dr. Seuss & Mr. Geisel: A Biography. New York: Random House, 1995, pp. 234-235):

My uncle ordered popovers
from the restaurant’s bill of fare.
And when they were served,
he regarded them
with a penetrating stare …
Then he spoke great Words of Wisdom
as he sat there on that chair:
“To eat these things,”
said my uncle,
“you must exercise great care.
You may swallow down what’s solid …
you must spit out the air!”

And …
as you partake of the world’s bill of fare,
that’s darned good advice to follow.
Do a lot of spitting out the hot air.
And be careful what you swallow.

Judith and Neil Morgan add: “As Ted sat down, there was bedlam.  Students shouted, cheered and flung their caps into the air.  He was startled, for it was his first experience with the fervor with which many young Americans had begun to canonize Dr. Seuss.  These graduates were of the generation most critical of the Vietnam war, and from their earliest memories of Dr. Seuss books they had assumed that he too must be skeptical of the establishment.  Now they’d heard evidence from the master’s lips.”

On a related note, if ever you are asked to give a commencement address, try not to copy from others.  (See this, this, and this.)

Alice in Wonderland and Mathematics

(Originally posted at on March 25, 2010 9:18 AM)

Many people have tried to more fully explain details in Alice in Wonderland (and Through the Looking Glass), most notably Martin Gardner. There are many hidden references to what was happening during the time the books were written: spoofs of popular songs, how languages and dances were taught, comments on society and politics, Charles Lutwidge Dodgson’s feelings for Alice Pleasance Liddell, and so on.

It now seems that Lewis Carroll has also hidden some references to how he felt about the mathematical advances being made during that time. Helena Pycior (in 1984) and Melanie Bayley (in 2009) have found in Alice what they think are references to Victorian mathematics. Read more about it here.

Perelman Awarded First CMI Millenium Prize

(Originally posted at on March 23, 2010 10:13 AM)

In 2002 and 2003, Grigoriy Perelman posted three preprints on, which are now commonly agreed to provide a proof of the Poincaré Conjecture (pronounced “pwan ka RAY”). (He actually proved a more general conjecture of which the Poincaré Conjecture is a special case.)

In 2006, Perelman was awarded a Fields Medal, which he declined.

Last March 18, 2010, the Clay Mathematics Institute announced that it had awarded its first Millenium Prize to Perelman. (Read more about it here and here.) The prize includes an award of $1 million. Will he also decline this award?