Bill Thurston has died
terrytao.wordpress.com
terrytao.wordpress.com
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."
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:
"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.
http://mathoverflow.net/questions/43690/whats-a-mathematicia...
What a sad thing, to have such a person leave us.
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.
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.
Shouldn't the distance between the quotient and d be less than ɛ?
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/ )