Does the Fields medal mean more to you than any other award you have won?
Any award is a milestone, which encourages one to go further. I don’t know that I think of any award as meaning more to me personally than any other. The mathematics that led to the medal was far more exciting to me than the medal itself.

The award citation says that you were inspired to extend Gauss’s law of composition in an unusual way. Can you explain what that is, and what you did?
Gauss’s law says that you can compose two quadratic forms, which you can think of as a square of numbers, to get a third square. I was in California in the summer of 1998, and I had a 2 x 2 x 2 mini Rubik’s cube. I was just visualising putting numbers on each of the corners, and I saw these binary quadratic forms coming out, three of them. I just sat down and wrote out the relations between them. It was a great day!

Have any of your other discoveries had unusual origins?
I do tend to think about things very visually, and the Rubik’s cube is a concrete example of that visual approach. But that one is probably the most unusual and unexpected origin of all.

You have proved several theorems. Do you have a favourite?
Mathematicians often say that choosing a favourite theorem is like choosing one’s favourite child. Although I don’t yet have any children, I understand the sentiment. I enjoyed working on all the theorems I have proved.

Are there any mathematicians, living or dead, that you have particularly looked up to?
My mother [Mira Bhargava, a mathematician at Hofstra University in Hempstead, New York] has been a source of inspiration to me from the very beginning. She was always there to answer my questions, to encourage and support me, and she taught me how much the human mind is capable of.

This year a woman, Maryam Mirzakhani at Stanford University, has finally won one of the Fields medals, after 52 consecutive male winners. How do you view this achievement?
This is long overdue! Hopefully in a few years we will not even need to discuss this, as more and more females receive the award. I am honoured to be a recipient in the same year as Maryam. It has been a pleasure to know her – we overlapped for a year early in our careers at Harvard, and later at Princeton. Her work is absolutely fantastic. I hope the media will not speak of her only as a top-rate female mathematician, but also as a top-rate mathematician who is doing truly groundbreaking work.

Read more: “Iranian woman wins maths’ top prize, the Fields medal“

This article appeared in print under the headline “Insight from a Rubik’s cube”

A woman has won the maths world’s “Nobel prize” for the first time. Maryam Mirzakhani of Stanford University, California, will receive the Fields medal tomorrow at the International Congress of Mathematicians in Seoul, South Korea.

The medal is awarded once every four years to at most four recipients, who must be aged under 40 at the start of that year. All the previous 52 Fields medallists, dating back to 1936, have been male.

Mirzakhani, who is Iranian, studies the geometry of moduli space, a complex geometric and algebraic entity that might be described as a universe in which every point is itself a universe. Mirzakhani described the number of ways a beam of light can travel a closed loop in a two-dimensional universe. To answer the question, it turns out, you cannot just stay in your “home” universe – you have to understand how to navigate the entire multiverse. Mirzakhani has shown mathematicians new ways to navigate these spaces.

Mirzakhani first attracted international attention as a high-school student in 1995, when she was the first Iranian student to achieve a perfect score in the International Mathematics Olympiad.

“She is very, very well known in Iran, where she is held out as an example for younger students,” says Ingrid Daubechies, the president of the International Mathematical Union, which selects the Fields medallists.

“Speaking as a woman myself, it is a wonderful thing to see her win,” Daubechies adds. “It will lay to rest the often-quoted fact that a woman has never won.” In future, she says, the idea of a woman winning the top maths award will no longer seem exceptional.

The three other winners are Brazilian-born Artur Avila of Denis Diderot University in Paris, France, who studies how chaotic systems evolve when constrained by certain rules; Manjul Bhargava, a number theorist at Princeton University; and Martin Hairer, an expert in partial differential equations at the University of Warwick, UK.

Two new satellites are now in orbit around the moon, and they could reveal whether our moon ate a sibling many moons ago.

The , which launched together in September, separately went into orbit on 31 December and 1 January.

They are designed to produce the most detailed map ever made of the lunar gravitational field, which is lumpy thanks to mountains, craters, lava flows, and larger irregularities – the moon’s far side is much more mountainous than its near side, for example.

“We don’t actually know why the near side and far side are different,” says mission principal scientist of the Massachusetts Institute of Technology in Cambridge.

One theory is that Earth once had two moons, and the second one wrapped itself around the lunar far side in a low-velocity collision that created the highlands. GRAIL will look for signs of such a crash.

Surviving eclipse

Orbiting at a height of 55 kilometres, the twin satellites will use microwave signals to measure the distance between them, which varies according to the pull of the underlying terrain, to within the width of a human hair.

The resulting gravity map is expected to be 100 times more accurate than our existing knowledge of the lunar near side, and 1000 times more accurate on the far side. “When we can improve by a factor of two, we can learn a lot, and improving by a factor of 1000 is transformative,” says Zuber.

Both the probes’ batteries and solar panels are generating more power than expected. Zuber thinks they will have enough power to survive a lunar eclipse in June – when the Earth blocks sunlight from falling on them. That should allow the probes to keep operating for six more months.

If so, the team will lower the spacecraft to an adventurous “treetop-skimming” orbit only 25 km above the surface. This will enable them to study the structure of craters spanning just 15 km – “the most common landform on the surfaces of terrestrial planets”, Zuber says.

The mystery of how the moon got its surface water has just got deeper, following the failure of an attempt to replicate the mechanism that was thought to produce it.

Three separate space missions last year reported detecting a sheen of water only molecules thick over large parts of the moon’s surface. Many planetary scientists assumed the water was created when particles from the solar wind hit lunar soils, but this idea has now been thrown into doubt.

“The solar wind cannot produce water in sufficient quantities to account for the results of the three missions that observed it,” says , a member of the team at University of Virginia, Charlottesville, that tried to reproduce this effect in the lab.

For years, theorists have believed that protons from the solar wind could produce water on the moon by prying oxygen atoms away from minerals in the lunar soil and combining with them to form hydroxyl radicals (OH) or water (H₂O). This hypothesis gained credibility recently with the observations of hydroxyl and water by NASA Deep Impact and Cassini missions, and the Indian probe Chandrayaan-1.

Bone dry

Baragiola and colleagues tested the idea by blasting protons at crystals of ilmenite and anorthite, two of the most common lunar minerals, in a high vacuum. They found no sign that water or hydroxyl radicals were produced. In fact, they found the opposite: the protons destroyed any traces of water that had remained in the minerals after 24 hours of baking prior to the experiment.

of Brown University in Providence, Rhode Island, who was lead author of last year’s report from Chandrayaan-1, admits to being puzzled by the results.

But Jeffrey Gillis-Davis, a planetary geologist at the University of Hawaii, thinks the established hypothesis might yet be correct. “This does not put the final nail in the coffin” of the solar wind hypothesis, he says. True lunar soil could behave differently from the crystals tested, as it consists of about 60 per cent agglutinated glass.

Gillis-Davis says texture is important in promoting chemical reactions that might produce water in lunar soil. “Space weathering” processes like this are more likely to occur in powdery soils than in crystals, he says.

Baragiola is planning to repeat his experiments with real lunar soil.

Journal reference:

The title of the 1909 hit song By the Light of the Silvery Moon was not just poetic, it was also prophetic. A NASA spacecraft that crashed into the moon last year has found what appears to be silver, perhaps buried under a small layer of moon dust.

Last October, NASA crash-landed a rocket near the lunar south pole, lofting water in the resulting debris. Newly published studies of this mission, called LCROSS, reveal that about 5.6 per cent of the ejected material was water, and that similar concentrations of water may exist under the surface in a “permafrost” layer. Lead scientist at NASA’s Ames Research Center in California estimates that there could be a billion gallons of water within 10 kilometres of the probe’s impact site.

Other chemicals were also detected in the impact plume by a spacecraft flying behind the impactor. “We’re seeing a kitchen sink of other stuff that may be useful for human exploration,” says Michael Wargo, NASA’s chief lunar scientist.

One of the big surprises was two strong ultraviolet emission lines of silver. Because they appeared a few seconds after impact, Colaprete and his colleagues suspect that the silver might be in a layer of rock buried below the surface.

Hopping around

To create the observed spectral lines, the silver would have to be much more concentrated than the 100 parts per billion measured in rocks returned by the Apollo astronauts. On Earth, silver is concentrated by geologic processes such as flowing water, but such processes do not operate on the moon.

So what might be concentrating the silver? One theory holds that volatile elements, such as mercury and magnesium, may hop along the moon’s surface one atom at a time until they hit a “cold trap” – such as the permanently shadowed crater LCROSS smashed into – and stick.

Silver is not usually considered a volatile, but of the Pacific Northwest National Laboratory in Richland, Washington, who is not a member of the mission team, says it probably behaves like one in the vacuum and temperature conditions on the moon. Other useful metals, such as tellurium, indium, and selenium, may behave the same way, he says.

of the Lunar and Planetary Institute in Houston, Texas, cautions that the spectral lines are not definitive. “We really need a surface rover mission,” he says. “We can argue about emission spectra from now until doomsday, but I want an on-the-spot measurement before I’ll finally believe it.”

Journal reference: (vol 330, p 468)