# Mathematics

Sports pundits across the country have been comparing the so-far unbeaten 2007 New England Patriots to the perfect 1972 Dolphins all year. A New York cardiologist has used the scientific statistics used in large-scale medical trials to determine which of the two teams is superior.

Using a format and approach typically reserved for the cardiovascular therapy studies he writes and reviews, Dr.

Three-dimensional snowflakes can now be grown in a computer using a program developed by mathematicians at UC Davis and the University of Wisconsin-Madison.

No two snowflakes are truly alike, but they can be very similar to each other, said Janko Gravner, a mathematics professor at UC Davis. Why they are not more different from each other is a mystery, Gravner said.

Who needs a computer? Two theoretical physicists at Rensselaer Polytechnic Institute grabbed a piece of paper and described the motion of interstellar shock waves — violent events associated with the birth of stars and planets.

The mathematical solution developed by Wayne Roberge, lead author and professor of physics, applied physics, and astronomy at Rensselaer and his colleague, adjunct professor Glenn Ciolek, reveals the force and movement of shock waves in plasma, the neutral and charged matter that makes up the dilute “air” of space. Unlike many previous studies of its kind, the researchers focused specifically on shock waves in plasma, which move matter in very different ways than the uncharged air on Earth.

For centuries, human beings have been entranced by the captivating glimmer of the diamond. What accounts for the stunning beauty of this most precious gem?

As mathematician Toshikazu Sunada explains in an article in the Notices of the American Mathematical Society, some secrets of the diamond's beauty can be uncovered by a mathematical analysis of its microscopic crystal structure. It turns out that this structure has some very special, and especially symmetric, properties. In fact, as Sunada discovered, out of an infinite universe of mathematical crystals, only one other shares these properties with the diamond, a crystal that he calls the "K_4 crystal".

Adult humans possess some mathematical abilities that are unmatched by any other member of the animal kingdom but there is increasing evidence that the ability to count sets of objects nonverbally is a capacity that humans share with other animal species.

In PLoS Biology, Elizabeth Brannon and Jessica Cantlon discuss how humans and nonhuman animals share a capacity for nonverbal arithmetic. The researchers tested monkeys and college students on a nonverbal arithmetic task in which they had to add the numerical values of two sets of dots together and choose a stimulus from two options that reflected the arithmetic sum of the two sets.

*Monkeys perform addition like humans.*

The journal *Experimental Mathematics*, started in 1992, publishes “formal results inspired by experimentation, conjectures suggested by experiments, descriptions of algorithms and software for mathematical exploration, [and] surveys of areas of mathematics from the experimental point of view.” The founder wanted to make clearer and give more credit to an important way that mathematicians come up with new ideas. As the journal’s statement of philosophy puts it, “Experiment has always been, and increasingly is, an important method of mathematical discovery.

One of the foundations of Einstein's Special Relativity is that no particular frame of reference is better than any other - whether you're sitting on the couch or barreling through space on a rocket, physics doesn't change. On the other hand, as many physics undergrads learn, choosing the right reference frame can simplify your homework problems a lot.

Thanks to Einstein, physicists know that the world looks different depending on how fast you're moving.

As the weather cools and Halloween approaches, creaks in the stairs and scary stories become more believable -- but not to physics professor Costas Efthimiou.

The laws of physics and math debunk popular myths about ghosts and vampires, according to a paper published by Efthimiou and Sohang Gandhi last year.

Using Isaac Newton's Laws of Motion, Efthimiou demonstrates that ghosts would not be able to walk and pass through walls. Basic math disproves the legend of humans turning into vampires after they are bitten, Efthimiou explains, because the entire human population in 1600 would have been wiped out in less than three years.

*Doomed by mathematics*

Scientists at the U.S. Department of Energy's Brookhaven National Laboratory have developed a method for correlating the results of microscopic imaging techniques in a way that could lead to improved understanding, diagnosis, and possibly treatment of a variety of disease conditions, including Alzheimer's disease. The Laboratory has filed a U.S. provisional patent application for the invention.

The invention is essentially a micron-scale metallic marking grid upon which scientists place their samples - biological tissues or inorganic samples such as minerals - prior to imaging with different methods.

A group of scientists, led by mathematicians, has taken on the challenge of building a common model of immune responses. Their work will radically improve our understanding of the human immune system by allowing all the scientific disciplines working on it to have a common reference point and language.

The mathematicians will investigate how the different cellular components of the immune system work together and devise a theoretical and computational model that can be used by immunologists, mathematicians, computer scientists, physicists and engineers.

The model promises to help a multi-disciplinary research community work together to bring about medical advances for patients.