The Aperiodical 

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Laziest torus identified

By Christian Lawson-Perfect. Posted April 13, 2012

Or, in similarly simplified headlinese, “Math finds the best doughnut”. A little bit more precisely, Fernando C. Marques and André Neves claim in a preprint on the arXiv to have proved the Willmore conjecture, that the minimum achievable mean curvature of a torus is $\frac{2}{\pi^2}$.

The article I linked to is some surprisingly non-stupid coverage from the Huffington Post. It seems they have a maths professor writing a column. I will never understand that site. I don’t know if there’s a Serious Business way of framing this, but the result is nice to know.

Richard Elwes has written a very short post on Google+ with some more real-maths information about what’s going on.

A Noether Theorem for Markov Processes

By Christian Lawson-Perfect. Posted March 7, 2012

• Puzzle 1. Suppose I have a box of jewels. The average value of a jewel in the box is \$10. I randomly pull one out of the box. What’s the probability that its value is at least \$100?

• Puzzle 2. Suppose I have a box full of numbers—they can be arbitrary real numbers. Their average is zero, and their standard deviation is 10. I randomly pull one out. What’s the probability that it’s at least 100?

John Baez and Brendan Fong claim to have answered questions like these, but in a general way that is useful for quantum mechanics:

They’ve written a paper and a blog post.

Every odd integer larger than 1 is the sum of at most five primes

By Peter Rowlett. Posted February 13, 2012

Terence Tao has uploaded to the arXiv a paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. He says this result is:

in the spirit of (though significantly weaker than) the even Goldbach conjecture (every even natural number is the sum of at most two primes) and odd Goldbach conjecture (every odd natural number greater than 1 is the sum of at most three primes). It also improves on a result of Ramaré that every even natural number is the sum of at most six primes. This result had previously also been established by Kaniecki under the additional assumption of the Riemann hypothesis, so one can view the main result here as an unconditional version of Kaniecki’s result.