
Bill Thurston has died - gruseom
http://terrytao.wordpress.com/2012/08/22/bill-thurston/
======
kevinalexbrown
Like most individuals, and probably, most mathematicians outside his field, I
do not deeply understand much of Thurston's work. But he did have a rather
large impact on my life insofar as a paragraph of his has stayed with me
several years (not many do, I'm afraid), and has been my reminder to slow down
whenever I find myself saying "psh, that was easy, all I had to do was browse
through the documentation":

 _I prided myself in reading quickly. I was really amazed by my first
encounters with serious mathematics textbooks. I was very interested and
impressed by the quality of the reasoning, but it was quite hard to stay alert
and focused. After a few experiences of reading a few pages only to discover
that I really had no idea what I'd just read, I learned to drink lots of
coffee, slow way down, and accept that I needed to read these books at 1/10th
or 1/50th standard reading speed, pay attention to every single word and
backtrack to look up all the obscure numbers of equations and theorems in
order to follow the arguments._

If a Fields medalist needed to slow down to read some maths, I can slow down
to really understand whatever it is that I'm doing. And when I tell myself
"I've learned that already!" I stop and ask whether I learned it at a "1/50th
pace."

<http://matrixeditions.com/Thurstonforeword.html>

~~~
gruseom
Wow. That entire foreword is just beautiful. Thank you.

~~~
oscilloscope
I wish the book itself was available as HTML or PDF. Amazing forward.

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tokenadult
Fields medalist Terence Tao writes about earlier Fields medalist William
Thurston, "In addition to his direct mathematical research contributions,
Thurston was also an amazing mathematical expositor, having the rare knack of
being able to describe the process of mathematical thinking in addition to the
results of that process and the intuition underlying it. His wonderful essay
“On proof and progress in mathematics“, which I highly recommend, is the
quintessential instance of this; more recent examples include his many
insightful questions and answers on MathOverflow."

Besides "On proof and progress in mathematics,"

<http://arxiv.org/abs/math.HO/9404236>

which I also highly recommend, I especially like Thurston's article
"Mathematical Education,"

<http://arxiv.org/abs/math/0503081>

which is full of good advice about thorough development of budding
mathematicians.

From Tao's blog, another link to a remembrance of Thurston:

<http://www.math.columbia.edu/~woit/wordpress/?p=5059>

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impendia
From his "about" page on his MathOverflow profile:

"Mathematics is a process of staring hard enough with enough perseverence at
at the fog of muddle and confusion to eventually break through to improved
clarity. I'm happy when I can admit, at least to myself, that my thinking is
muddled, and I try to overcome the embarassment that I might reveal ignorance
or confusion. Over the years, this has helped me develop clarity in some
things, but I remain muddled in many others. I enjoy questions that seem
honest, even when they admit or reveal confusion, in preference to questions
that appear designed to project sophistication."

Such beautiful modesty from a brilliant mathematician who inspired many.

[1] <http://mathoverflow.net/users/9062/bill-thurston>

~~~
Radim
I like the embarrassing arguments from MathOverflow moderators re. not closing
Mr. Thurston's (vague, subjective, "not a question") question on MathOverflow.

Nicely put by Georges Elencwajg in one of the comments:

 _...posed by somebody else, this question would have been closed within a
picosecond. The rationale, ironically, being that professional mathematicians
of quality would flee this site in droves because the question is
"discussiony", "vague", "has no right answer", etc. This is the Matthew effect
in all its glory: "For to all those who have, more will be given, and they
will have an abundance; but from those who have nothing, even what they have
will be taken away" (Matthew 25:29) Needless to say, I'm euphoric at the
thought of Bill's participation in MathOverflow._

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gruseom
I agree with everyone who recommends the stellar "On Proof and Progress in
Mathematics". It a gem that could only have been written by a lovely man.

<http://arxiv.org/pdf/math/9404236v1.pdf>

The parts about how communication works inside mathematical specialties and
about the difference between math and computer programming are worth their
weight in gold.

Really, everyone, just do yourself a favor and read it – all the way to its
astonishing final section and beautiful ending. It doesn't require you to
remember any math.

------
noblethrasher
It's been a while since I've done serious mathematics so I'm almost certainly
wrong about this, but the "logical" definition for a derivative looks
incorrect under the section "How do People Understand Mathematics?" (pg 3).

Shouldn't the distance between the quotient and _d_ be less than ɛ?

<http://arxiv.org/pdf/math/9404236v1.pdf>

~~~
mturmon
You're right. I've read that several times over several years and never
noticed.

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alister
If you've wondered what topology was about and wanted to get a better feel for
it than just a dictionary definition, then see the 20-minute video in the
article.

A blurb about the video:

 _The computer animation "Outside In" explains the amazing discovery, made by
Steve Smale in 1957, that a sphere can be turned inside out by means of smooth
motions and self-intersections. Through a combination of dialogue and
exposition accessible to anyone who has some interest in mathematics, "Outside
In" builds up to the grand finale: Bill Thurston's ``corrugations'' method of
turning the sphere inside out. Along the way, the narrators discuss the
related case of closed curves and why they generally cannot be turned inside
out. Everyday analogies such as train tracks, belts, smiles and frowns are
used throughout, all richly animated and complete with sound effects._ (quoted
from <http://www.geom.uiuc.edu/docs/outreach/oi/> )

~~~
creamyhorror
I just watched this on Youtube and was not disappointed. There was just a
great clarity to the question-and-answer format of the dialogue; the
animations and sound effects fit the exposition to a tee. I hope they're still
making brilliant educational videos like this, somewhere.

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zacharyz
Outside In, the movie referenced in the article, can be found on youtube:
<http://www.youtube.com/watch?v=HeYo7MHuj0g>

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ta12121
Perhaps you mean, he _left_?
(<http://c2.com/cgi/wiki?MathematiciansWhoHaveLeft>)

~~~
gruseom
I read that Japanese uses the charming phrase "he changed worlds".

~~~
pjscott
I suppose you could say that he changed over to the world of "not existing
anymore." Or you could just state the tragedy outright, and say that he's
dead. Please excuse my bluntness; a person's obliteration is something I'd
prefer not to swathe in soft euphemisms.

