Over the top

I was having fun browsing the 3D Printing marketplace Shapeways, and then I stumbled across this 17 \times 17 \times 17 Rubik’s Cube by Oskar van Deventer and my brain exploded a little bit.


Van Deventer has designed an impressive collection of cube-like puzzles which can only be made by 3D printing.

I have an older puzzle by him called Topsy Turvy mounted on the wall in my office. This one isn’t 3D printed, but it requires lasers to carefully etch the paths so that the numbered coins can stack perfectly until the very end, and then cascade to make a particular permutation. To me it is not interesting as a puzzle at all (and frankly neither is the 17^3 cube), but I like Topsy Turvy as mathematical art, and especially as a “faithful embedding” of the Mathieu group M12 in physical space.

Increasing public access to federally funded research

65,000 people signed a petition to increase public access to the results of federally funded research, and the White House agreed with them.

A memorandum has been issued telling alL the major federal agencies to make plans for making publicly funded research freely available on the internet within 12 months of publication.

This seems like a big step in the right direction. It will be interesting to see what form the NSF’s plan takes, and how the big publishers respond.

Glimpses of Benoît B. Mandelbrot

The AMS Notices has an article this month with personal recollections about Mandelbrot; mathematical recollections will be saved for another article. He comes across as deeply curious and knowledgeable about almost every subject imaginable.

He was sometimes known for being “strangely vain”, but it is hard to not have the impression that this was the defense mechanism of someone who worked in solitude and obscurity for so many years before his ideas were finally recognized as important.

Mandelbrot gave the closing address of the 2006 International Congress of Mathematicians. He congratulated Werner on his Fields Medal, and suggested that this was the third time a mathematician had won a Fields Medal for proving one of his conjectures.

Yoccoz won a Fields Medal, I believe in part for proving a big piece of the conjecture that the Mandelbrot set is locally connected. Apparently the full conjecture is still open. I don’t know enough about the subject to know if this was something that Mandelbrot originally conjectured though.

Also I wonder who he had in mind as the third Fields Medalist? Does anyone know?

A poetic quote from the article, by Michael Frame:

Years ago, when asked if he was a mathematician, a physicist, or an economist, Benoît replied that he was a storyteller. After Benoît died, I saw another interpretation of his answer. By emphasizing how an object grows, a fractal description of the object is a story. Twists and turns of a snowflake in a cloud, rough waves sculpting a jagged coastline, my lungs growing before I was born, the spread of galaxies throughout the deep dark of space. These share something? Benoît told us they have similar stories. Benoît told us science should tell more stories.

Abel prize for Szemerédi

Hungarian mathematician Endre Szemerédi has been awarded the Abel Prize.

Here is a nice interview with him, translated to English by Zsuzsanna Dancso. (Original in Hungarian here.)

I think Szemerédi’s sense of humor comes across well in the interview.

Interviewer: In 2008, when you were awarded the Rolf Shock prize, you commented that in your opinion the Fields medal, the Wolf Prize, and the Abel Prize were the three most prestigious prizes in mathematics. Did you expect to get one of these back then?

Szemerédi: I would like to modify my opinion — now I only regard the Fields medal and the Wolf prize as the most prestigious.

Is Benford’s law really less true now than ever?

Jialan Wang, an assistant professor of finance at Washington University, has posted a fascinating note about the observable departure from Benford’s law over time. I am trying to imagine any other explanation of this other than widespread fraud (or as she puts it more tactfully, “decreased reliability of accounting data).

Please chime in with your own alternate explanations in the comments.