Still from the 1967 film Bonnie and Clyde, considered a landmark film of the New Hollywood era. A new analysis suggests that this period coincided with a burst of novel elements in cinema.

Tell your film buff friends they’re right: the most creative period in cinema history was probably the 1960s. At least that’s the takeaway from a detailed data analysis of novel and unique elements in movies throughout much of the 20th century.

How do you objectively measure creativity in movies? Though there’s probably no perfect way, the recent research mined keywords generated by users of the website the Internet Movie Database (IMDb), which contains descriptions of more than 2 million films. When summarizing plots, people on the site are prompted to use keywords that have been used to describe previous movies, yielding tags that characterize particular genres (cult-film), locations (manhattan-new-york), or story elements (tied-to-a-chair).

Reported by CNRS (Délégation Paris Michel-Ange) (2012, April 25) in ScienceDaily, May 1 2012.

When stacking apples on a market stall, fruit sellers “naturally” adopt a particular arrangement: a regular pyramid with a triangular base. A French-German team, which includes in particular the Laboratoire de Physique des Solides (Université Paris-Sud / CNRS), has demonstrated that this arrangement is favored for reasons of mechanical stability. This work, which is published on the Physical Review Letters (PRL) website, could contribute to the design of organized porous materials.

Take apples or marbles. The best way to stack them consists in erecting a pyramid layer by layer, which ensures the maximum number of spheres is fitted into the minimum amount of space. There are several arrangements for stacking such identical spheres (of the same volume) with the same, optimal density. Two, in particular, are well known: a structure known as face centered cubic (FCC), whose base is necessarily a triangle for the smallest possible pyramid, and a hexagonally close-packed (HCP) structure with a hexagonal base, also when constructing the smallest possible pyramid. The first arrangement consists of a periodic repetition of three different positions of layers: ABCABC…. In the second, two different positions of layers are periodically repeated: ABABAB…. As early as 1611, while studying the stacking of canon balls, the scientist Johannes Kepler proposed the FCC arrangement as being the most efficient. It is moreover the arrangement used by stall holders to stack their fruit and vegetables.

Who wouldn’t pay a penny for a sports car? That’s the mentality some popular online auctions take advantage of — the opportunity to get an expensive item for very little money.

In a study of hundreds of lowest unique bid auctions, Northwestern University researchers asked a different question: Who wins these auctions, the strategic gambler or the lucky one? The answer is the lucky. But, ironically, it’s a lucky person using a winning strategy.

The researchers found that all players intuitively use the right strategy, and that turns the auction into a game of pure chance. The findings, published by the journal PLoS One, provide insight into playing the stock market, real estate market and other gambles.

An Irish mathematician has used a complex algorithm and millions of hours of supercomputing time to solve an important open problem in the mathematics of Sudoku, the game popularized in Japan that involves filling out a 9X9 grid of squares with the numbers 1-9 according to certain rules.

Gary McGuire of University College Dublin shows in a proof posted online 1 January that the minimum number of clues – or starting digits – needed to complete a puzzle is 17 (see sample puzzle, pictured, from McGuire’s paper), as puzzles with 16 clues or less do not have an unique solution. In comparison most newspaper puzzles have around 25 clues, with the difficulty of the puzzle decreasing as more clues are given.

Reported by Kim Krieger, Science Now, 14 Nov. 2011.

Numerical trees. The image on the left shows the variables Eloy's numerical model used to calculate trees to test his wind-force hypothesis. The image on the right shows a skeleton of a tree before the simulation calculates diameters of the branches. Credit: C. Eloy et al., Phys. Rev. Letters (2011)

The graceful taper of a tree trunk into branches, boughs, and twigs is so familiar that few people notice what Leonardo da Vinci observed: A tree almost always grows so that the total thickness of the branches at a particular height is equal to the thickness of the trunk. Until now, no one has been able to explain why trees obey this rule. But a new study may have the answer.

Leonardo’s rule holds true for almost all species of trees, and graphic artists routinely use it to create realistic computer-generated trees. The rule says that when a tree’s trunk splits into two branches, the total cross section of those secondary branches will equal the cross section of the trunk. If those two branches in turn each split into two branches, the area of the cross sections of the four additional branches together will equal the area of the cross section of the trunk. And so on.

Video: Zooming in on the Mandelbrot set, a famous fractal that illustrates repeating patterns in an infinite series./YouTube, gooozz.

Researchers have found a fractal pattern underlying everyday math. In the process, they’ve discovered a way to calculate partition numbers, a challenge that’s stymied mathematicians for centuries.

Partition numbers track the different ways an integer can be divvied up. The number 3, for example, has three unique partitions: 3, 2 + 1, and 1 + 1 + 1. Partition numbers grow so fast that mathematicians have a hard time predicting them.

“The number 10 has 42 partitions, but with 100 you have 190,569,292 partitions. They get impossibly huge to add up,” said mathematician Ken Ono of Emory University.

Since the 18th century, generations of mathematicians have tried to find a way of predicting large partition numbers. Srinivasa Ramanujan, a self-taught prodigy from a remote Indian village, found a way to approximate partition numbers in 1919. Yet before he could expand on the work, and convert it to a clean equation, he died in 1920 at the age of 32. Mathematicians ever since have puzzled over Ramanujan’s manuscripts, which tie the primes 5, 7 and 11 to partition numbers.

Ken Ono and Zachary Kent./Emory University.

Inspired by Ramanujan’s work and that of the late mathematician A.O.L. Atkin, Emory mathematicians Amanda Folsom and Zachary Kent joined Ono to discover an infinite, fractal-like pattern to the series. It is described in a paper hosted by the American Institute of Mathematics.

“It was like living in a darkened home for years, and then finally someone turned on the lights. When Zach and I realized the structure, we knew we were right,” Ono wrote in an e-mail to Wired.com. “We see the same mathematical structures over and over and over again, similar to how you see repeating elements in the Mandelbrot set as you fly through it. That’s why we say they’re fractal,” he said.

In a separate paper, Ono and Jan Hendrik Bruinier of Germany’s Darmstadt Technical University describe a function, deemed “P,” that can churn out any integer’s partition number.

The combined research doesn’t quite reveal a mathematical representation of the universe’s structure, Ono said, but it does kill partition numbers as a way to encrypt computer data.

“Nobody’s ever going to do that now, since we now know partition numbers aren’t random,” Ono said. “They’re completely predictable and we should no longer pretend they’re mysterious.”

The discoveries should help solve similar problems in number theory, but Ono said he’s most excited about closing an exceptionally “frustrating but romantic” chapter in mathematical history.

A draft solution to the so-called “P versus NP” problem generated excitement in 2010 – will 2011 bring a correct proof?

Vinay Deolalikar made waves in August when his draft solution to a mathematical problem that haunts computer science hit the internet.

It’s known as “P versus NP”, and a correct solution is worth $1 million. Sadly for Deolalikar, of Hewlett-Packard Labs in Palo Alto, California, his work didn’t check out. But the flurry of online activity surrounding the paper demonstrated a new way of doing mathematics – via blogs and wikis – and generated fresh excitement around the problem.

Formulated in 1971, P versus NP deals with the relationship between two classes of problems that are encountered by computers. P problems are relatively easy for computers to solve. But it can take an impracticably long time to solve NP problems, such as finding the shortest route between several cities – though it is easy to show whether a possible solution is correct.

If P = NP, computers may eventually be able to solve a host of complex problems, from protein folding to factorising very large numbers. The ability to solve the latter would spell trouble for algorithms that we rely on for internet security. Most people assume the opposite is true, that P ≠ NP; had Deolalikar’s paper been correct, it would have proved this.

The Clay Mathematics Institute in Cambridge, Massachusetts, has promised $1 million to the first person who can prove it one way or the other. To find out how likely this is to happen in 2011, see “Prediction: Its time has not come”.

Prediction: Its time has not come

Unlike many problems in science, highly theoretical enigmas like P versus NP are rarely solved piecemeal. Instead, they tend to remain unsolved for years and then, apparently out of nowhere, a proof that works pops up.

Predicting these breakthroughs might seem impossible, but we devised a way to estimate the likelihood of P versus NP being solved next year. We compared its “age”, or the time since the problem was formulated, to other long-standing mathematical problems.

First we compared P versus NP with 18 mathematical problems, from Fermat’s last theorem to the Poincaré conjecture, that were not solved until more than a decade after their “births” (see graph). This made arriving at a solution to P versus NP in 2011, when it will turn a sprightly 40, look premature: just 22 per cent of these other problems were solved before they turned 40. By the same logic, in 2024, we should be on the lookout for a solution to P versus NP. That’s when it turns 53, the age by which 50 per cent of the problems we examined were solved.

Here’s hoping that solving P versus NP turns out to be faster than proving the Honeycomb conjecture, which states that if you need to divide a surface into tiled shapes of equal size, a hexagon is the shape that requires the smallest length of dividing lines. Proving that took more than 1500 years.

We also compared P versus NP to 26 other problems that still haven’t been solved. In 2011, it will be younger than 81 per cent of those. Samuel Arbesman and Rachel Courtland