1995 The Art of Doing Science and Engineering: Learning to Learn aka Hamming on Hamming. Incredible lecture series, in 33(?) parts x 45mins. On thinking, thinking style, computers, maths/science, his life, Can machines think?, What is thinking?, What is reality?, Who to learn from and what to learn from them, What questions to ask, etc etc.
You and Your Research – the final lecture from that course. Maybe it’s good to watch it first. It has been printed and reprinted many times.
The whole course is available in book form. Also I’ve read two of his other books, Methods of Mathematics and Numerical Methods for Scientists and Engineers; they’re both wonderful, full of mathematical tools, presented by someone who worked with and on them for decades. He tries to share his experience and style of thinking in all his writings, aware of the interpersonal and philosophical aspects of his subject, and that what cannot be put into words is the most important.
One day I asked, “if what they were working on was not important, and was not likely to lead to important things, then why were they working on them?” – Richard Hamming, You and Your Research
John Horton Conway
Tangles, Bangles and Knots
FRACTRAN: A Ridiculous Logical Language
Geometric Folding Algorithms: Linkages, Origami, Polyhedra 2012
Advanced Data Structures 2012
Planar Graph Algorithms 2011
featured in the documentary Between the Folds (2008) about origami in art and science.
Bill Thurston (1946-2012)
Landau lectures, Jerusalem Pt 1 (contains a screening of Not Knot) Pt 2 Pt 3 1996
A discussion on geometrization 2001
The Mystery of 3-Manifolds 2010
Interview with Dai Fujiwara and Thurston at the Issey Miyake Fashion Show in Paris
paper On Proof and Progress in Mathematics
1989 paper: Groups, Tilings and Finite State Automata
Once, a niece of mine in kindergarten told me she knew what 3 times 11 was: 33.
I asked “Well then, what’s 7 times 11?”
“Okay, I bet you don’t know what 12 times 11 is.”
“Twelvety-twelve”, she gleefully replied.
We agreed that twelvety-twelve is a perfectly good number, we know what it means, but if we were talking to other people we would tell them one hundred and thirty-two – for us, twelvety-twelve is just fine. – Bill Thurston, Groups, Tilings and Finite State Automata, p27
…most mathematicians are lost most of the time during lectures. (If you do not believe me, ask around.) – TW Körner, In Praise of Lectures, 2004
N is a Number: A Portrait of Paul Erdös (58 mins)
Use the Feynman Method
Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!” – Gian-Carlo Rota, Ten Lessons I Wish I Had Been Taught