The Creative Side of Math


The Creative Side of Math

An artist and his math prodigy son have teamed up in an unusual use of math: origami. They've used complex math formulas to create sculptures that are on display at the Museum of Modern Art in New York City.
In the computer science lab where they work at MIT, Erik and Martin Demaine have a three-foot-tall metal and plastic sculpture that resembles a sleek, modernist version of a child's Tinkertoy creation.
Erik, a math prodigy who was honored in Popular Science's second annual Brilliant 10, and his father Martin, an artist who was drawn into math through his son, built the piece by starting with a three-dimensional hexagon they folded from paper. They then inputted the shape into a computer and virtually erased all of the paper, so that only the creases remained. Next, they turned back to the tangible and created a dynamic piece of art, using aluminum rods, locked together at the joints with plastic spheres, to represent each crease.
"We took something real and virtualized it, and then made it real again," explains Martin, 66, an MIT instructor and artist in residence.
They also took art, turned it into math and then back into art again. This belief that math and art are complementary endeavors is the key to the Demaines' work. The men use complex mathematics to create beautiful art, some of which is on display at the Museum of Modern Art in New York City. And they construct sculptures to help solve seemingly intractable math problems. Along the way, the lively and often goofy duo have inspired students to think more creatively about their discipline, and have shown the public that math doesn't have to feel inaccessible.
"We view them as very similar things," says Erik, a 28-year-old assistant professor, referring to math and art. "They're both creative processes. They're both about having the right idea."
The Demaines have worked in metal and glass, but are focusing mostly on paper these days, creating swirling, fluid sculptures by folding along curved creases in corkscrewed pieces of paper that are attached at the ends. They don't yet understand why the paper responds the way it does, so they alternate between the blackboard where they scribble out equations, the computer where they work with models, and reams of stiff brown paper that they score with a laser cutter and then fold by hand.
"Mathematically, it's not even clear what the right questions to ask are," Erik says of the curved creases, which are at the cutting edge of folding research.
They turn to sculptures when they're stuck on a formula, and by making incremental changes in the size and shape of the creases, patterns start to emerge. Several of their paper sculptures, including the series of three at MOMA, started as studies in the lab. They've begun making progress on the mathematics to prove that the shapes they're folding can actually be made with the crease patterns they're using.
This may seem like a strange goal -- proving you can make something you just made -- but the Demaines have proven just the opposite before. After 10 years of research, they proved earlier this year that a curved shape called a hyperbolic paraboloid, which they and others had been folding for years, doesn't actually exist.
"The paper is cheating somehow," Erik explains. Extra creases they can't see must be sneaking into the paper while it's folded, because the math now shows that it's impossible to make a 3-D shape using only the creases the Demaines thought they were using.
"It's very cool to make something that doesn't exist," Martin jokes.
While both men are mathematicians and artists, they have clear specialties. Erik is the math genius, having joined MIT at 20, making him the school's youngest professor ever. His interest in folding and origami led to a MacArthur "genius" grant, dozens of papers, and a book. His research on folding goes beyond paper, such as trying to figure out why proteins fold the way they do and studying the best way to collapse robotic arms.
Martin started as a professional artist and home-schooled Erik as they traveled around their native Canada and the United States until Erik started college at 12. Martin figured Erik was a little young to leave him on his own, so he audited Erik's classes. This helped hone Martin's own understanding of folding, which had been a hobby of his for years.
Knowing that the men were inseparable, MIT sweetened its job offer to Erik by giving Martin a two-year position as a researcher in the computer science department. If he could prove that he was a valuable resource to the school, he could stay on. He did, and in addition to collaborating with Erik on mathematical research, he's now the department's first artist in residence.
The men are known as exuberant teachers, and are favorites among computer science and math students, as well as architecture, engineering and biology majors who often take their classes.
"The students are just overjoyed," says MIT architecture associate professor John Ochsendorf. The Demaines are infinitely creative and love to have fun. Erik is known to crack corny jokes mid-lecture. (There are three kinds of mathematicians: those who can count and those who can't.) And Martin has the curiosity of a child, constantly wondering aloud whether he can create new, interesting sculptures, such as an entire, usable bedroom set he made out of old books.
"If I could sum them up in only one word I would say 'playful,'" Ochsendorf says.
He describes a challenge that Erik and Martin proposed: to design a brick building façade that looks like a face, but as the sun crosses the sky throughout the day the face transforms from a baby into an elderly person.
That idea, just like the Demaines' sculptures, comes from a desire to make something beautiful that is based in hard-core mathematical exploration, Ochsendorf says. "It's all about having fun," he says of Erik and Martin's work. Yet, "what comes off as playful is backed up by tremendous understanding and tremendous rigor."

Math Performing Heart Surgery


Math Performing

Heart Surgery

People are as different on the inside as they are on the outside, so deciding which surgery to perform is sometimes a life-or-death guessing game. 
However, a professor at Stanford University has created a computer program that models each patient's unique cardiovascular system, taking the guesswork out of major heart surgery. 

Predicting Successful Surgeries

Bioengineers Combine Mathematical Equations, Data to Simulate Surgeries


December 1, 2005 — A new hi-tech method takes the guesswork out of cardiovascular surgery. Using mathematical equations, bioengineers build a personalized computer model of each heart patient, then perform the surgery on the computer model before it is ever done on a patient. The aim of this approach is to perform more successful surgeries and eliminate unnecessary operations.

STANFORD, Calif.--People are as different on the inside as they are on the outside, making it difficult to predict which heart surgery will help which patient. Now, a new, high-tech approach may predict which patients will and will not have successful surgeries.
Heart attack survivor, David Lesesky says, "When I started having problems, I just didn't want to take the chance." He didn't take a chance. Lesesky made it through the heart attack and survived surgery and is doing just fine. The outcome, however, is not always the same: Each patient and each surgery brings its own risks.
"There's no way to guess as to how much blood flow is going to be restored," says Charles Taylor, a bioengineer at Stanford University in Calif. But now Taylor may have found a high-tech way of taking the guess work out of cardiovascular surgery. "We build a computer model to predict what will happen to a patient in a given surgical procedure."
The computer model is a personalized layout of each heart patient. Taylor says, "We actually do the surgery on the computer model before it is ever done on a patient." The program shows a 3D model of a patient with cardiovascular disease and incorporates imaging data and mathematical equations.
"The question we have for this patient is that would she benefit from a procedure -- bypass procedure -- to improve blood flow down to the legs?" Taylor says after examining a patient's 3D model on the computer. The yellow on the model shows the potential bypass path. When blood flow is simulated, it's revealed that two of the vessels going into the legs were clotted off -- the surgery would not have been successful.
"What it will mean for the patient is fewer operations -- conceivably more successful operations," Taylor says. And it will help keep hearts beating -- longer.
The computer model is being tested right now, retrospectively, on patients who are already planning to have surgery. So far results show it will be successful in predicting the outcome of cardiovascular surgeries.
BACKGROUND: A professor at Stanford University is applying his engineering expertise to take some of the guesswork out of predicting surgical outcomes by making a new computer model of the cardiovascular system. Charles Taylor spent 10 years taking detailed information gleaned from diagnostic imaging tools like CT scans and MRI to build his computing modeling program.
THE PROBLEM: People are unique on the inside as well as on the outside, and this can make it difficult for surgeons to predict how any given person will respond to surgery. Currently the only tools available are statistics and educated guesses.
HOW THE MODEL WORKS: The new model incorporates imaging data into a Web-based tool that includes 3D views and surgical sketchpads. Millions of complex equations involving how blood flows through the body and individual physiology are used to demonstrate what might happen under various "what if" scenarios. Taylor has also taken into account the flexibility of veins and arteries. The model is currently being tested by taking data before and after surgery and determining how well the model predicted what actually occurred. Taylor recently reported that in large-animal studies, the model can predict blood flow after an aortic graft within 10 percent.

Food Poisoning? Not If Math Can Help It



Food Poisoning? 

Not If Math Can Help It…

Smoked salmon is a gourmet favorite, but unfortunately it’s also a big hit with microbial bacteria.
Scientists with the U.S. Department of Agriculture have been busy cooking up a mathematical model to make sure that when people eat salmon, that’s all they’re eating.
Scientists with the U.S. Department of Agriculture (USDA) are helping ensure that the smoked salmon that's always a hit at festive gatherings also is always safe to eat, including among their achievements the development of a first-of-its-kind mathematical model that food processors and others can use to select the optimal combination of temperature and concentrations of salt and smoke compounds to reduce or eliminate microbial contamination of the product.

Invincible Formula


A new kind of computer can crunch through our frequently used data encryption algorithms, creating a data security crisis.  
But it turns out that an obscure thirty-year-old code is resistant to all known decryption methods.  See what makes this formula different.

Thirty-Year-Old Encryption Formula Can Resist Quantum-Computing Attacks That Defeat All Common Codes



The core advantage of quantum computing -- the ability to compute for many possible outcomes at the same time and therefore crunch data much more quickly than classical computers -- also creates a problem for data security. Once the first high-powered quantum computers are functioning, they'll be able to quickly saw through many of our most common data encryption algorithms. But as it turns out, an obscure encryption code created in 1978 is resistant to all known methods of quantum attack.
Hang Dinh at the University of Connecticut and a few colleagues figured out that CalTech mathematician Robert McEliece's code is structured in such a way that a quantum computer couldn't just pull it apart, at least not by any known process. Rooted in a mathematical puzzle called the hidden subgroup problem, standard quantum fourier analysis simply can't crack the code.
What does all that mean? For a more extensive mathematical explanation, click through to Tech Review's more thorough and astute review of quantum encryption. But in summary, encryption is often conducted using asymmetric codes, meaning there's a public key that anyone can use to encrypt data and a private key for decrypting it. The basis of these encryption schemes is math that flows easily in one direction but not so easily in the other.
Such asymmetric code can be tricky for a classical computer to figure out but quantum computers are well suited to such work. To take a simple example, say a message was encrypted using basic multiplication -- one number is multiplied by a number to get a third number. It's not so easy to look at the third number and quickly determine the two numbers that spawned it.
In math, the process of doing this is called factorizing, and mathematicians factorize through a quality called periodicity -- the idea that a mathematical entity with the right periodicity will divide an object correctly while others will not. In 1994, a mathematician created an algorithm that does this very well, and that shortcut to finding periodicity has a quantum analogue known as quantum fourier sampling. Using fourier sampling, quantum computers can quickly factorise codes, rendering most of our most common encryption schemes useless.
But McEliece's little-used code doesn't rely on factorization, meaning quantum fourier analysis can't break it down. That means it's essentially impervious to all known forms of quantum attack. That's not to say that new modes of quantum hacking won't be developed to decrypt McEliece's system, but it's interesting that while standing at the threshold of a new era of computing power researchers are finding solutions that can keep our data safe more than three decades in the past.

Math That Can See Right Through You


With A Bit of Math, Researchers Find a Way to See Through Opaque Materials


Using some clever math, researchers have figured out how to “see” through opaque materials.
Learn more about the matrix that could make it possible to see through walls.

Seeing Through Opaque Materials By packing the properties of an opaque material into a complex matrix, researchers should in theory be able to see through the sugar cube on the right just as they can see through the clear lens on the left. American Physical Society
Light is essential to vision, at least the kind we perform with our naked eyes. This is why we can see through a glass lens but not through a brick wall (though we're working on that). But what about materials that let some light pass while scattering it in seemingly chaotic ways? Our naked eyes can't reassemble that light into coherent images, but using some clever math, a team of researchers has devised a way to focus light through opaque materials to "see" objects on the other side -- provided they have enough data about the material.
The team developed a numerical transmission matrix based on the way light passes through a layer of opaque zinc oxide, a common ingredient in white paints. The matrix captured the various ways the light changed upon passing through (and by various, we mean various; the matrix included over 65,000 numbers detailing the way the material scattered the light), creating a model for how light should pass through zinc oxide every time.
Using that transmission matrix, they were able to manipulate the beam on the transmission side such that it came out the other side focused. They then flipped the experiment on its head, measuring the light emerging from the opaque material and using the matrix to assemble an image of an object behind it.
Theoretically, such a transmission matrix could be developed for any opaque material, but while seeing through paper and white paint may not seem so terribly tantalizing, the experiment really shows the potential for opaque materials in optical devices. At the nano-scale it become increasingly difficult to construct transparent lenses. With a good enough transmission matrix, researchers could better peer through opaque biological materials like cell walls and other membranes that currently obscure our view of what's happening on the other side.
opaque = "blocking the passage of radiant energy and especially light"
translucent = "transmitting and diffusing light so that objects beyond cannot be seen clearly"
transparent = "having the property of transmitting light without appreciable scattering so that bodies lying beyond are seen clearly"

Doing the Math to Find the Good Jobs

Mathematicians Land Top Spot in New Ranking of Best and Worst Occupations in the U.S.

It's a lot more than just some boring subject that everybody has to take in school.  It's the science of problem-solving.


One of the benefits of studying mathematics is the variety of career paths it provides. A 2009 study showed that the top three best jobs in terms of income and other factors were careers suited for math majors. Another recent survey shows that the top 15 highest-earning college degrees have a common element: mathematics.


The Best and Worst Jobs
Of 200 Jobs studied, these came out on top -- and at the bottom:
The Best
The Worst
1. Mathematician
200. Lumberjack
2. Actuary
199. Dairy Farmer
3. Statistician
198. Taxi Driver
4. Biologist
197. Seaman
5. Software Engineer
196. EMT
6. Computer Systems Analyst
195. Roofer
7. Historian
194. Garbage Collector
8. Sociologist
193. Welder
9. Industrial Designer
192. Roustabout
10. Accountant
191. Ironworker
11. Economist
190. Construction Worker
12. Philosopher
189. Mail Carrier
13. Physicist
188. Sheet Metal Worker
14. Parole Officer
187. Auto Mechanic
15. Meteorologist
186. Butcher
16. Medical Laboratory Technician
185. Nuclear Decontamination Tech
17. Paralegal Assistant
184. Nurse (LN)
18. Computer Programmer
183. Painter
19. Motion Picture Editor
182. Child Care Worker
20. Astronomer
181. Firefighter


  Math In The Movies

Mathematicians To Thank For Great Graphics

 100 powerful supercomputers perform geometrical, algebraic and calculus-based calculations to animate Pixar's characters. The laws of physics that inform the dynamics of fabric movement are most used in the computations.




If you are wondering what are the applications of mathematics in the movies, ask yourself if you have seen the movies “Finding Nemo”, “Lion King” or “Transformers”. If you have seen at least one animated film or a movie where CGI characters or objects are used, then you must have an idea why math is involved in the movies. Mathematics is behind the graphics or improvement of the graphics in movies.
Just like in the field of robotics, mathematics plays an integral role in making movies. In this day of Computer Generated Imagery (CGI), mathematics is an inevitable tool to make motion pictures (especially cartoons) better to watch.
According to research, 100 powerful supercomputers perform geometrical, algebraic and calculus-based calculations to animate Pixar’s characters. The laws of physics that inform the dynamics of fabric movement are most used in the computations.

Most students in high school dread their math classes and wonder when they will ever use the information in "real life." Now, with so much work being done on computers, the algebra and trigonometry learned in high school is actually being put to good use.
The animation industry is one that can be a math teacher's best friend. It is high school math that can actually help bring animated movies to life. Tony DeRose, a computer scientist at Pixar Animation Studios, realized his love of mathematics could transfer into a real world, real interesting job by bringing the pretend world of animation to life. He told DBIS, "Without mathematics, we wouldn't have these visually rich environments, and visually rich characters."
Advances in math can lead to advances in animation. Earlier math techniques show simple, hard, plastic toys. Now, advances in math help make more human-like characters and special effects. DeRose explains the difference a few years can make, "You didn't see any water in Toy Story, whereas by the time we got to Finding Nemo, we had the computer techniques that were needed to create all the splash effects."
How exactly do the high school math classes help with the animation? Trigonometry helps rotate and move characters, algebra creates the special effects that make images shine and sparkle and calculus helps light up a scene. DeRose encourages people to stick with their math classes. He says, "I remember as a mathematics student thinking, 'Well, where am I ever going to use simultaneous equations?' And I find myself using them every day, all the time now."

BACKGROUND: Pixar Animation Studios is undergoing a digital revolution thanks to advances in areas such as computer technology, computational physics, and approximation theory. Tony Derose provided a behind-the-scenes look at the role that geometry plays in the revolution using examples drawn from Pixar's feature films, such as Toy Story I and II. Upcoming movie characters will be animated using a new advancement in geometry recently developed at Pixar.
ABOUT ANIMATION: The term animation refers generally to graphical displays in which a sequence of images with gradual differences results in the same effect as a photographed movie. Computer generated animations are getting more and more common, replacing hand drawn images and other special techniques. There are several ways to generate dynamic changes in computer graphics. Geometry animation is the most complex, and requires changing the geometric elements of a scene dynamically. This is also what most people generally refer to when using the term "animation," evidenced by motion pictures like "Toy Story" and "A Bug's Life."
HOW PIXAR DOES IT: Perhaps the most difficult aspect of animation is making people and clothing look real. Pixar's software is based on complex studies of how cloth moves when draped on a character, based on the laws of physics. For instance, drape a bedsheet between two points, and the center will hang downward, adjusting itself until it comes to rest in a state of pure tension. The animators begin with drawings of the characters, which they use to build computer puppets, later adding digital "strings" that correspond to various geometric points on the puppet. These strings serve as animation controls, ensuring that as each string is "pulled," the puppet's movements reflect what would occur in real life. Color and lighting effects are added last before the puppet is "animated." Pixar uses 100 powerful supercomputers that run 24 hours a day, seven days a week. It still takes the computers five to six hours to render a single frame lasting 1/24th of a second. For every second of film, it takes the computer six days.
WHAT IS GEOMETRY? Geometry is the field of mathematical knowledge dealing with spatial relationships. The earliest written records -- dating from Egypt and Mesopotamia about 3100 BC -- demonstrate that ancient peoples had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers. Beginning about the 6th century BC, the Greeks gathered and extended this practical knowledge and from it generalized the abstract subject now known as geometry, from the combination of the Greek words geo ("Earth") and metron ("measure") for the measurement of the Earth. 






First Leelavati Prize Goes to Simon Singh

SIMON SINGH 
WINS FIRST

LEELAVATI 

AWARD


Simon Lehna Singh, physicist-turned British author of Indian origin has been chosen for the first Leelavati Award that has been instituted for outstanding contribution to public outreach in mathematics by an individual. 


This international award had been instituted on the name of the 12th century Sanskrit book “Leelavati” dealing with arithmetic and algebra. 


In medieval India mathematics used to be popularized and taught in verse. The superb example is the treatise “Leelavati”. The book posed problems in verse and also gave hints for solutions. 


Leelavati, a Daughter of India


Leelavati is told to be the daughter of 12th century mathematician Bhaskaracharya who wanted to teach mathematics to his daughter. He did so by composing this treatise


One can imagine how lucid it would have been teaching and learning of mathematics during that time though the education was allowed to the select few. Compare it with how mathematics is taught in a boring fashion today by incompetent teachers in India.


One may ask what Simon Lehna Singh has done to deserve this ten lakh rupees prize? He actually tried using latest media TV and Film to do a little bit exactly the same what Bhaskaracharya had done eight hundred years ago—popularize mathematics by Leelavati. 


Why No Indian Living in India Becomes a Simon
Question however in India will crop up why any Simon Lehna Singh could not grow up here. Obviously the current money-minting culture of media is to blame for this. It does not care to create opportunities of such kind of serious work. 

Simon, whose parents emigrated from Punjab to Britain in 1950, like millions thronging UK now, in 1990 joined BBC’s ‘Science and Features’ department. And it made all the difference. In 1996 he directed a documentary Fermat’s Last Theorem. 

This was after the acclaimed solution, by the British mathematician Andrew Wiles in 1995, of one of the world’s most challenging problems in mathematics – the proof of the famous conjecture made by the French mathematician Pierre de Fermat in 1637. 

The documentary exploration of the celebrated problem also formed the subject for Singh’s first book, Fermat’s Last Theorem (1997). This was perhaps the first-ever popular book on mathematics to become a best-seller. 

The Great Maths Show By Women


Great Maths 

Show by 

Women 



First Time in August this year top women mathematicians from all over the world would assemble in Hyderabad. The occasion is a two day International Conference of Women Mathematicians just before the most prestigious International Congress of Mathematicians. 


Only recently women have started asserting their place in the field of mathematics which has been reflecting in girls achieving notable success in the International Math Olympiad. During last twenty five years many girls have almost reached up to the top, remained behind just by a whisker.


Hyderabad women conference would not only raise the self esteem of women mathematicians, but also bring forth some issues which keep women laggards in this field. It is said no women could get Fields Medal, considered as good as Nobel Prize, because it is given to mathematicians who are under forty years. 


Since women also have to have children and look after them before 40, this award becomes non-existent for them. 

Need to Encourage Girls in Maths

A great need is being felt that girls be encouraged to opt mathematics as a career and research option. If this happens then within a decade perhaps some woman may be able to win Fields medal. Recently the Abel prize has been introduced which is also considered as important as Nobel Prize. Only nine mathematicians have won this so far, but no woman. 


No Indian man also has won any of these two most prestigious awards given for great research in mathematics. This raises a question if ever the situation would change in India. Everybody knows that quality research does not take place in India. Indian Universities even do not care to update their curriculum for decades. Bright students remain far behind because of this callousness of Indian academicians. So much so teachers in Delhi University are unashamedly fighting against even introduction of semester system.

We Had Ramanujan Once

Average Indians feel proud only in telling that we had once Ramanujan whose problems no mathematician in the world has been able to solve so far rather than solve them themselves if this is a great mathematical issue. 


It is great that International Conference of Women Mathematicians is taking place in India. It is the  European Women in Mathematics that had taken initiative in this matter. Prof (Ms) Shobha Madan of IIT-Kanpur is championing the cause in India.


In India we had last year seen a national conference of women mathematicians at the Jawahar Lal Nehru University, Delhi. But it had mixed attendance, almost equal number of men mathematicians. The Hyderabad conference is expected to be truly a women show on a grand scale.

Bhama Srinivasan

The job of activating women mathematicians around the globe started much earlier by forming the Association for Women in Mathematics in 1971. An American Indian Bhama Srinivasan also had been its President during 1981-83. Bhama Srinivasan, born and grew up in Chennai, got the spark from her grandfather who was an amateur practitioner of mathematics.
de>