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Advance in snowflake growth simulation

Scientific American are reporting that “a team of mathematicians has for the first time succeeded in simulating a panoply of snowflake shapes using basic conservation laws, such as preserving the number of water molecules in the air”.

This explains that previous simulations often simulate the crystal surface using interlocking triangles, but that:

the triangles often deform and collapse in simulations, leading to singularities that bring the simulation to an abrupt halt… Garcke’s team got around this difficulty by devising a method to describe the curvature and other geometric information about the snowflake surface so that it could be appropriately encoded into a computer.

Emmy Noether biography in NY Times

A biography of Emmy Noether has been published in the New York Times.

Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation. Some consider Noether’s theorem, as it is now called, as important as Einstein’s theory of relativity; it undergirds much of today’s vanguard research in physics, including the hunt for the almighty Higgs boson. Yet Noether herself remains utterly unknown, not only to the general public, but to many members of the scientific community as well.

Source: The Mighty Mathematician You’ve Never Heard Of.

Math/Maths 90: Maths is to Mathematics as Math is to…?

A new episode of the Math/Maths Podcast has been released.

A conversation about mathematics between the UK and USA from This week Samuel and Peter spoke about: Endre Szemerédi wins the Abel Prize 2012; Automatically tagging the World Service archive; Intel Science Fair; 72nd Putnam; The Spanish link in cracking the Enigma code; Greater Manchester sunflowers to test Alan Turing theory; e-petition: Put Alan Turing on the next £10 note; Five Math Things to do Before You Die; Music helps children learn maths; Alcohol boosts ability to solve problems creatively; Spiked Math IQ Test; Mondrian of Life; Journalism lecturer to take maths GSCE to test ‘dumbing down’; The Proof is Trivial; Angry Birds Space Mirrors Real Rocket Science; Rosenthal Prize; The New MAA Store; new NCETM contract; Reviving the Carnival of Mathematics; Google interviews: would you get a job with the search giant?; and more.

Get this episode: Math/Maths 90: Maths is to Mathematics as Math is to…?

Investigative journalist attempts to test whether GCSE maths is ‘dumbed down’

Barnie Choudhury, principal lecturer at the University of Lincoln’s school of journalism with a background in investigative journalist, is taking the GCSE examinations in an attempt to “test whether or not the allegations made in recent years that exams had been ‘dumbed down’ were true”. An article in the Lincolnshire Echo says:

He sat his O-level in maths in 1981 and came out with a B grade.
If he does not match this when the GCSE grades are revealed in August, Mr Choudhury believes this will prove that exams today are harder.

Flaws in the experimental methodology left as an exercise for the reader, although Mr Choudhury hints at some when he is quoted saying:

A part of me is hoping that journalists are right – that exams are easier. But I see my daughter’s mathematics work now and I don’t know any of it. So I thought if she was going through the pain, then so would I and I’d see for myself how tough the exams are.
But now I’m wishing I hadn’t started. It has not been dumbed down at all – if anything, I’m finding it more difficult the second time around, even though I’m older and I’ve sat lots of exams in my life. Maybe my brain has slowed down but it really is difficult.

Source: University of Lincoln lecturer inspired to take maths GSCE by his children.

Spanish link in cracking the Enigma code

The BBC has reported that a pair of Enigma machines used in the Spanish Civil War have been given to the head of GCHQ, Britain’s communications intelligence agency. Apparently these machines are two of “around two dozen” discovered “a few years ago, in a secret room at the Spanish Ministry of Defence in Madrid.” The article explains how these “fill in a missing chapter in the history of British code-breaking”. Apparently the use of commercial Enigma machines between Spain and Germany during the Spanish Civil War gave British codebreakers access to live traffic, since military signals used within Germany were too weak to hear in Britain. Within six or seven months, in April 1937, Dilly Knox produced his first decryption of an Enigma message.

As to how this relates to the better known Enigma story, the article explains that:

The machines used in Spain were modified versions of the commercial Enigma machine. The military machine that would be used by Germany during World War II was an order of magnitude more secure because a plugboard was attached to the front.

These more complex signals are where the better known Polish/Bletchley Park story of Enigma fits into the story.

The BBC explains the trade made for the two Enigma machines:

In return the UK handed over a number of items including a German four rotor Naval Enigma machine recovered from Flensburg in May 1945, an Enigma rotor box and related documents. The idea is that this could serve as the foundation of a display on code-making and code-breaking at the Spanish Army Museum

One machine will be held at GCHQ and the other will be placed on public display at Bletchley Park. The full article gives some interesting insight from the GCHQ historian and the director of Spain’s intelligence service.

Source: BBC News – The Spanish link in cracking the Enigma code.

Music and alcohol may improve maths and problem solving skills

The Telegraph is reporting that “Listening to music in maths lessons can dramatically improve children’s ability in the subject”, although the text of the article explains that the technique in question “uses music notation, clapping, drumming and chanting to introduce third-grade students to fractions”.

A paper which the Telegraph says is “due to be published” in Educational Studies in Mathematics apparently reports on a study involving 67 students at a California school, “half” of which used this technique and “scored significantly higher on math tests than their peers who received regular instruction”.

Susan Courey, assistant professor of special education at San Francisco State University and author of the proposed paper, is quoted saying:

If students don’t understand fractions early on, they often struggle with algebra and mathematical reasoning later in their schooling. We have designed a method that uses gestures and symbols to help children understand parts of a whole and learn the academic language of math.

Meanwhile, New Scientist highlights an article in Consciousness and Cognition in which 40 men were given either a vodka-based cranberry drink or a non-alcoholic one after which they took, according to the paper abstract, “a common creative problem solving task, the Remote Associates Test (RAT)”. The abstract for the paper says that the:

Intoxicated individuals solved more RAT items, in less time, and were more likely to perceive their solutions as the result of a sudden insight.


Telegraph: Music helps children learn maths.

New Scientist: Alcohol boosts ability to solve problems creatively.

Uncorking the muse: Alcohol intoxication facilitates creative problem solving.