Mathematics
THE PARADOX OF PROOF
by Carolyn ChenOn August 31, 2012, Japanese mathematician Shinichi Mochizuki posted four papers on the Internet.
The titles were inscrutable. The volume was daunting: 512 pages in total. The claim was audacious: he said he had proved the ABC Conjecture, a famed, beguilingly simple number theory problem that had stumped mathematicians for decades.
Then Mochizuki walked away. He did not send his work to the Annals of Mathematics. Nor did he leave a message on any of the online forums frequented by mathematicians around the world. He just posted the papers, and waited.
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Below are the title and abstract for my presentation at the STEAM Factory Saturday, April 27, in Columbus Ohio (400 Rich Street).
Title: Processing Art
Abstract: We present an interactive art installation and offer a description of how it is constructed. A rapidly changing sequence of images is generated by via a computer program using mathematical principles — scaling, randomness, superposition of periodic waves, dynamics on a torus. These buzzwords and principles aside, the spectator-participant can interact with the program by tuning the color scheme and changing the letters and shapes generated. (If you like an image, we can save it and email it to you.) Code at github.
Acronym decode: STEAM = Science, Technology, Engineering, Art, and Mathematics
Below is a letter (not published) that I submitted to the Wall Street Journal in response to EO Wilson’s op ed piece in the April 5, 2013 edition.
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April 9, 2013
Dear Editors:
I read with interest the article by E.O. Wilson, a distinguished
scientist whose work I greatly admire. Wilson addresses a problem that
concerns us all: the declining interest of young people in science.
I agree with much in Wilson’s article, e.g., that ideas play a key role,
that disciplined fantasies are the fountainhead of creativity. This
said, I take issue with the implication that mathematical semiliteracy
is an adequate preparation for a young person interested in science. What
is sufficient in one generation may not be in the next. Consider two
fundamental advances in physics: Faraday’s law of induction, which made
possible the electric generator, and Maxwell’s discovery that
electromagnetic waves propagate in a vacuum at the speed of light,
which made possible radio communication. Just thirty years apart, one
discovery was made without mathematics, while the other used the most
sophisticated mathematics of the day — and it did come from “staring at
the equations.”
One sees the same progression in biology. In the days of Linnaeus and
Darwin, mathematics played no role. But now whole fields of biology have
been created using mathematics. It is one thing to cut chromosomes into
pieces with enzymes. It is another to assemble the pieces into a map, a
dictionary of life. That was done with a sophisticated piece of
mathematics, the Smith-Waterman algorithm. Mathematics also plays a key
role in reconstructing the tree of life: when and how did species branch
off from their ancestors? Darwin would be pleased!
Back to Wilson’s concern — no student should be deterred from a
career in science by mathematics — but that same student should know
enough mathematics to collaborate fruitfully and to be conversant with
ideas his colleagues will use: statistical argument, model, simulation,
algorithm, etc. Better to enter the game with a full deck.
Sincerely,
James Carlson
Professor Emeritus
University of Utah
Circle and Rectangle
Image made by Dylan Carlson using Python’s turtle graphics. This image is made up entirely of copies of a large rectangle rotated around one corner. Click on image to see higher resolution version.
zipTimer: an iPod/iPhone app for pacing piano practice, cooking, workouts, you name it.
A Math Problem
The house deals from a huge, essentially infinite, deck of cards composed of spades, hearts, diamonds, and clubs in equal proportions. Each person plays separately against the house. On each round, cards are dealt until a heart appears. The cards are counted. If there are an odd number, the house wins, and the player pays one dollar to the house for each card. If there are an even number, the player wins, and the house pays him $1.04 for each card. Is this a fair game?
Explain.
zipTimer: an iPod/iPhone app for pacing piano practice, cooking, workouts, you name it.
G.H. Hardy
“Hardy made certain to show no reaction as he listened to his own history, the awards and honorary degrees that authorized his renown. It was a litany he had become used to, and which sparked in him neither pride nor vanity, only weariness: to hear listed all he had achieved meant nothing to him, because these achievements belonged to the past, and therefore, in some sense, no longer belonged to him. All that had ever belonged to him was what he was doing. And now he was doing very little.”
The Indian Clerk, by David Leavitt
Part One, Chapter 1
Fractal Cross
Pythnon code at github. Used python3 star.py 4 3 cross to produce image, which will be both displayed and stored in cross3.eps. The image shown here was subsequently altered with Pixelmator (blue overlay added)
My ideas usually come not at my desk writing but in the midst of living.
– Anais Nin
zipTimer: an iPod/iPhone app for pacing piano practice, cooking, workouts, you name it.
Circle and Square 
