MATH NEWS ARCHIVE

Islamic architects had mastered a sophisticated tile template that allowed them to create a dizzying array of star and polygon decorations more than half a millennium before the concept caught on in the West, according to a new study.
The geometrical know-how of these early Islamic designers, the authors conclude in the journal Science, "led the medieval world" and should force a reappraisal of where important mathematical concepts really originated -- a sentiment echoed by an independent expert who has identified fractal geometry in traditional African culture and who called the new research "absolutely stunning."
Scientists previously believed these medieval Islamic artisans had constructed their complicated motifs with a compass and straightedge. But Harvard University graduate student Peter Lu said that technique is unlikely to explain how designs requiring the piecing together of thousands of tiles with up to ten sides could have been so accurately fit together.
Lu, lead author of the new study, was traveling through central Asia with a cousin volunteering for the Peace Corps when he spotted a familiar pattern on a medieval Islamic building in Uzbekistan: tile work with ten-pointed stars.
As an undergraduate student in the lab of Princeton University physicist Peter Steinhardt, Lu had studied quasi-crystals, or structures based on a type of irregular symmetry that would give professional floor tilers nightmares. Such crystals possess "forbidden symmetry," meaning that five- or ten-sided shapes might look the same when rotated by 36 or 72 degrees but can't be fit snugly together in a repeating pattern without leaving gaps.
In 1974, British mathematical physicist Roger Penrose came up with a two-tile system based on thin and fat rhombus shapes that could finally incorporate the five-fold symmetry into a snug-fitting tile pattern. But Lu's work suggests Islamic architects beat him to the punch by well over 500 years.
With Harvard's extensive library of Islamic architectural examples to guide him, he scrutinized medieval tile work and even Quran adornments featuring five- and ten-pointed stars. Again and again, he found a set of five precisely shaped and decorated tiles could account for the overall designs.
"The big, big picture is that we've discovered -- and I think we've proven rigorously -- that the Islamic architects had a process that would have allowed them to create infinite quasi-crystals," Lu said. "And that's something that we in the West didn't know how to do until the last 30 years."
The advanced knowledge of math and science led to a set of five polygons known as girih tiles. This set, including a rhombus, pentagon, decagon, hexagon, and bow tie-shaped hexagon tile, were all designed to have edges with the same exact length so they could be fit together. Each of the five tiles also featured specific line markings to create embedded geometrical shapes. Furthermore, the angles of the tiles and their intersecting lines were limited to multiples of 36 degrees.
When pieced together, the tile shapes form one geometrical pattern, while their interior lines continue across the tile boundaries to form a separate, zigzagging design.
More than just a theoretical construct, Lu believes sets of girih tiles were being used to trace decorative motifs by 1200 AD, with their adoption spreading across the medieval Islamic world. As proof, he points to a 15th-Century scroll now housed in a museum in Istanbul, Turkey, that contains detailed ink outlines of the five tiles and their lines, and to an "all-star lineup of buildings" in multiple countries whose decorations can be explained by applying the same tile templates.
Prominent adornments on the 13th-Century Abbasid Al-Mustansiriyya Madrasa in Baghdad, 13th-Century Seljuk Mama Hatun Mausoleum in Tercan, Turkey and 15th-Century Seljuk Great Mosque in Narriz, Iran all can be explained by lining up various girih tile combinations into larger patterns.
"The take-home message is that there's a lot more to be learned by looking in this part of the world," Lu said. And if his study motivates other researchers to do just that, "that would be really fantastic."
Ron Eglash, an associate professor of science and technology studies at Rensselaer Polytechnic Institute in Troy, N.Y., agreed, calling the new research "absolutely stunning."
In an e-mail, Eglash hailed Lu's ability to not only analyze the complicated pattern but also demonstrate how Islamic knowledge allowed it to be widely applied.
"That's very important for some of these Islamic societies because they are often looked down on as merely being the 'storehouse' of Western knowledge during the Dark Ages," Eglash said. "Here you have a portrait of them as not only independent innovators, but actually several centuries ahead of the West."
Eglash himself discovered that fractal geometry was widely adopted in traditional African culture long before researchers had assumed such mathematical knowledge arrived from the West. He first identified the use of fractal geometry's similar shapes repeated on ever-shrinking scales in aerial photographs of Tanzanian thatched-roof huts arranged as circular clusters within larger circular clusters. Since then, Eglash has identified the use of fractal geometry in everything from Saharan wind screens to traditional hair braiding and Senegalese fortune telling.
Copyright 2007 Newsday Inc.
Study may change view of mathematical origins

Mathematicians have finally laid to rest the legendary mystery surrounding an elusive group of numerical expressions known as the "mock theta functions."
Number theorists have struggled to understand the functions ever since the great Indian mathematician Srinivasa Ramanujan first alluded to them in a letter written on his deathbed, in 1920.
Now, using mathematical techniques that emerged well after Ramanujan's death, two number theorists at the University of Wisconsin-Madison have pieced together an explanatory framework that for the first time illustrates what mock theta functions are, and exactly how to derive them.
Their new theory is proving invaluable in the resolution of long-standing open questions in number theory. In addition, the UW-Madison advance will for the first time enable researchers to apply mock theta functions to problems in a variety of fields, including physics, chemistry and several branches of mathematics. The findings appear in a series of three papers, the third appearing today in the Proceedings of the National Academy of Sciences.
"It's extremely gratifying to be able to say we solved the 'final problem' of Ramanujan," says co-author Ken Ono, UW-Madison Manasse Professor of Letters and Science, who is widely noted for contributions to number theory. "We simply got really lucky."
Ono worked in collaboration with German mathematician Kathrin Bringmann, a postdoctoral researcher at UW-Madison.
"This is something I really didn't expect anybody to do," says George Andrews, a leading number theorist at Pennsylvania State University who in 2000 called mock theta functions one of the most difficult math puzzles of the new millennium. "It is an outstanding piece of work, a breathtakingly wonderful achievement."
Working from Ramanujan's letter, number theorists believed that mock theta functions are related to a well-understood class of mathematical expressions-the 'theta' functions-that have been in use for centuries. Theta functions constitute a certain sequence of numbers that has proved useful in various problems of mathematical analysis.
Mock theta functions similarly constitute an infinite series of numbers. But what has been completely baffling is what it is about mock theta series that make them so rich and powerful. Over the decades-much to the amazement of mathematicians everywhere-mock theta functions have cropped up amidst calculations in a number of fields, including mathematics, physics, chemistry, and even cancer research.
What made mock theta functions all the more inscrutable was the fact that the first few pages of Ramanujan's letter were lost. Those pages may have contained more clues, but in their absence, the letter merely presented 17 examples of the functions. What's missing is any definition of what the functions are, any hints on how to derive them, and any indication of why they are even important. All those secrets died with Ramanujan just two months after he wrote the letter, when he succumbed to tuberculosis at the age of 32.
"Imagine stringing together a thousand random words and then saying you've come up with the most beautiful poetry," says Ono. "That's essentially what Ramanujan did to us."
Bringmann and Ono made sense of it all by finding a way to represent the power of mock theta functions through another relatively new family of mathematical expressions known as the Harmonic Maass Forms.
A Dutch mathematician named Sander Zwegers had already made that important connection in 2002, but he had focused only on Ramanujan's examples.
It was during a flight to New Hampshire that Ono realized the full depth and meaning of Zwegers' work. Skimming a journal to pass the time, Ono happened upon an old article by George Andrews on mock theta functions. Suddenly, he noticed that some of the mathematics in the paper seemed to resonate with parts of the Harmonic Maass theory, which he and Bringmann just happened to be developing at the time, for other reasons.
The mathematicians found the connection held up beautifully. "We knew we were onto something right away," says Ono. "It was an uncanny set of coincidences that lead us to this solution. It was as if it all just fell into our lap and now we are serendipitously applying our theory to longstanding open problems."
UW scientists unlock major number theory puzzle

Dimitris Achiloptas

Alexander Gamburd

Yi Zuo

The Alfred P. Sloan Foundation has selected three UCSC faculty members to receive 2007 Sloan Research Fellowships: Yi Zuo, assistant professor of molecular, cell, and developmental biology; Dimitris Achlioptas, assistant professor of computer science; and Alexander Gamburd, assistant professor of mathematics.
The Sloan awards are intended to enhance the careers of the very best young faculty members in specified fields of science. This year, a total of 116 fellowships were awarded in seven fields--chemistry, computational and evolutionary molecular biology, computer science, economics, mathematics, neuroscience, and physics. Each award includes a $45,000 grant that provides unrestricted support for research.
Zuo's research revolves around the communication between two classes of cells in the nervous system: neurons and glia. Despite the fact that glia constitute the majority of cells in the nervous system, their roles in neural circuitry have only begun to be understood. Zuo plans to use modern imaging techniques and molecular manipulation to study glia-neuron communication and understand how glia are involved in learning and memory. This research could suggest ways to manipulate brain function through modulating glial signals and lead to potential treatments for various neurodegenerative diseases.
Achlioptas's research in computer science addresses what are known as constraint satisfaction problems (CSPs). The popular number game Sudoku is a classic example of a CSP, where the variables are the contents of the empty squares, and the constraints arise from the rules of the game and contents of the filled-in squares. CSPs conceptually similar to Sudoku are found in many areas ranging from biology and biochemistry to software verification and airplane design, Achlioptas said. But while Sudoku problems can be solved in milliseconds by a computer using exhaustive search techniques, most real-life CSPs could not be solved that way. Achlioptas's work is aimed at designing algorithms for solving real-life CSPs using ideas inspired by statistical physics.
Gamburd's research in mathematics concerns spectral problems in number theory, probability, and combinatorics. He is particularly interested in problems related to random matrices and expander graphs.
One of the oldest fellowship programs in the country, the Sloan Research Fellowship Program began in 1955 as a means of encouraging research by young scholars at a critical time in their careers. The Alfred P. Sloan Foundation, a philanthropic nonprofit institution, was established in 1934 by Alfred P. Sloan Jr., the president and chief executive officer of the General Motors Corporation.

February 26, 2007
Contact: Tim Stephens (831) 459-2495; stephens@ucsc.edu
Sloan Research Fellowships awarded to three UC Santa Cruz faculty

The development of a new breed of "targeted" anti-cancer drugs is being boosted by mathematicians at the University of Dundee.
Dr Fordyce Davidson and Professor Mark Chaplain, both of the Division of Mathematics at the University of Dundee, have been awarded £160,000 to work with biotechnology company Cyclacel Pharmaceuticals, Inc. to develop the effective use of new anti-cancer drugs.
The grant from the Engineering and Physical Sciences Research Council will see the maths experts working alongside Cyclacel's Chief Scientific Officer, Dr Robert Jackson, and scientists at Cyclacel's Dundee, Scotland, laboratories on the company's new drug candidate, CYC116, one of a new breed of "targeted" anti-cancer drugs which are specifically designed to selectively kill cancer cells, leaving most other cells in the body unharmed.
One of the big challenges faced by doctors when treating cancer is to find out quickly whether a given treatment is effective or not for a particular patient. For certain cancers it can be very difficult to measure how quickly the tumour is shrinking in response to treatment - or indeed if it is shrinking at all. It can take several weeks before any change becomes apparent on a scan, for example. For particularly aggressive cancers, this delay can be lethal for the patient.
One possible way around this is to find other methods of measuring whether cancer cells are dying as a result of the treatment. The Maths Department at the University of Dundee has in recent years developed pioneering techniques in mathematical biology, using modelling to map the development of cancer tumours.
When cells are killed by anti-cancer drugs, tell-tale biochemical markers are released into the blood stream by the cell and it is possible that these 'biomarkers' could be used as a quick and accurate measure of the effectiveness of a drug. The test could be as simple as taking a blood sample.
However, as Dr Davidson explains, "The relationship between the amount of anti-cancer drug given to the patient, the effect that drug has on tumour cells and the subsequent concentration of biomarkers in the blood stream is very complex."
"Unfortunately it is not simply the case that higher quantities of a drug kill more cancer cells, it can be unpredictable. Moreover, all drugs can be harmful in large doses, so treatment has to be a clever balancing act."
"It is here that as mathematicians we will help by using powerful tools of mathematical modelling and analysis to understand the processes that take place once the drug is administered and how it can be most effectively applied."
The Dundee mathematicians, including new recruit Hitesh Mistry, will work closely with Cyclacel's scientists, to produce models of how the dose of Cyclacel's drug candidate, CYC116, an orally-available Aurora kinase and VEGFR2 inhibitor, impacts on tumour cell death and how this is reflected in the concentrations of biomarkers in the blood stream.
Dr Davidson said the advances being made in applying mathematical models to cancer diagnosis and treatment could help usher in a new era of personalised medicine.
"Ultimately this could lead to mathematical models in the form of computer packages being used by clinicians who would be able to key in information about a particular patient," he said.
"The model would then tell the clinician the most appropriate treatment regime and would also be able to help identify whether the chosen drug treatment was working. It is very exciting for us to be working with Cyclacel, developing this new technology alongside the new drug candidate".
Dr Robert Jackson, Cyclacel's Chief Scientific Officer commented, "The drug development process is becoming increasingly computer-intensive. The mathematical approaches being developed by Dundee University and those which we are using at Cyclacel together with our own biomarker analysis will help drug developers to interpret their biomarker data, and in the long term may increase drug development success rates and match patient treatments to their individual circumstances."
The project is being funded by the EPSRC via the `Mathematics for Business' scheme.
Dundee mathematicians aid anti-cancer drug development

NEW YORK, Feb. 20 /PRNewswire/ -- ACM, the Association for Computing Machinery, has named Frances E. Allen the recipient of the 2006 A.M. Turing Award for contributions that fundamentally improved the performance of computer programs in solving problems, and accelerated the use of high performance computing. This award marks the first time that a woman has received this honor. The Turing Award, first presented in 1966, and named for British mathematician Alan M. Turing, is widely considered the "Nobel Prize in Computing." It carries a $100,000 prize, with financial support provided by Intel Corporation.
Allen, an IBM Fellow Emerita at the T.J. Watson Research Center, made fundamental contributions to the theory and practice of program optimization, which translates the users' problem-solving language statements into more efficient sequences of computer instructions. Her contributions also greatly extended earlier work in automatic program parallelization, which enables programs to use multiple processors simultaneously in order to obtain faster results. These techniques have made it possible to achieve high performance from computers while programming them in languages suitable to applications. They have contributed to advances in the use of high performance computers for solving problems such as weather forecasting, DNA matching, and national security functions.
"Fran Allen's work has led to remarkable advances in compiler design and machine architecture that are at the foundation of modern high-performance computing," said Ruzena Bajcsy, Chair of ACM's Turing Award Committee, and professor of Electrical and Engineering and Computer Science at the University of California, Berkeley. "Her contributions have spanned most of the history of computer science, and have made possible computing techniques that we rely on today in business and technology. It is interesting to note Allen's role in highly secret intelligence work on security codes for the organization now known as the National Security Agency, since it was Alan Turing, the namesake of this prestigious award, who devised techniques to help break the German codes during World War II," said Bajcsy, who is Emeritus Director of the Center for Information Technology Research in the Interest of Society (CITRIS) at Berkeley.
"Fran Allen's work on the Parallel TRANslation (PTRAN) project built on her earlier work on program optimization," said Andrew A. Chien, Intel's Vice President of Research. "Over the years, this foundation has enabled the advance of programming-productivity based on the co-evolution of higher level programming language and optimization technologies. It is particularly timely that this award comes as parallel computing is becoming an element of the most pervasive of computing platforms - laptop and desktop personal computers - and the opportunities for new and important contributions to parallel programming and efficient implementation abound," he said.
In 1989, Allen was the first woman to be named an IBM Fellow. In 2000, IBM created the Frances E. Allen Women in Technology Mentoring Award, naming her as its first recipient. As her Turing Award citation notes, she has been an inspirational mentor to younger researchers and a leader within the computing community. She is an Advisory Council Member of the Anita Borg Institute for Women and Technology, whose goal is to increase the participation of women in all aspects of technology. She also received the first Anita Borg Award for Technical Leadership, which was presented at Grace Hopper Celebration of Women in Computing in 2004.

Background

Allen joined IBM's T. J. Watson Research Center in 1957, to teach FORTRAN, a revolutionary high-level programming language, to the scientists at IBM. FORTRAN allowed scientists and engineers to write programs that closely resembled the mathematical formulas they normally relied on. Allen recognized the opportunity to address a grand challenge of high performance computers -- delivering the performance potential of computers to solve problems without exposing the underlying computer infrastructure.
Allen's 1966 paper, Program Optimization, laid the conceptual basis for systematic analysis and transformation of computer programs. Her 1970 papers, Control Flow Analysis and A Basis for Program Optimization established "intervals" as the context for efficient and effective data flow analysis and optimization. Much of her early work was done in collaboration with John Cocke, an IBM computer scientist who died in 2002. Her 1971 paper with John Cocke, A Catalog of Optimizing Transformations, provided the first description and systematization of optimizing transformations. She developed and implemented her methods as part of building compilers for the IBM STRETCH- HARVEST and the experimental Advanced Computing System. This work established the feasibility of modern machine- and language-independent optimizers.
In 1984, she formed and led IBM's PTRAN project to address the emerging challenge of parallel computers, which simultaneously executes related tasks for faster results. This project led to many advances including the concept of the program dependence graph, the primary structuring method used by most parallelizing compilers today.
In 1995, Allen was president of the IBM Academy of Technology, a global organization of IBM technical leaders charged with providing technical advice to the company. Before she retired in 2002, she was a Senior Technical Advisor to the Research Vice President for Solutions, Applications and Services. She is a member of the National Academy of Engineering, the American Academy of Arts and Sciences, and the American Philosophical Society. She was named a Fellow of ACM in 1994.
Allen has been a member of the Computer Science and Telecommunications Board (CSTB), the Computing Research Association (CRA) Board, and the National Science Foundation's Computer and Information Science and Engineering (CISE) Advisory Board. Her recent professional activities for ACM include membership on ACM's Job Migration Task Force, which produced the widely reported "Globalization and Offshoring of Software" study www.acm.org/globalizationreport/pdf/fullfinal.pdf. In addition, she was active in the ACM Special Interest Group on Programming Languages (SIGPLAN), and has served on the editorial boards of several ACM journals.
Among Allen's teaching and lecturing roles were visiting professor at New York University from 1970-73; consulting professor at Stanford University; the Chancellor's Distinguished Lecturer and Mackay Lecturer at the University of California, Berkeley in 1988-89; and Regents Lecturer at the University of California, San Diego in 1997. She was awarded Honorary Doctor of Science degrees from the University of Alberta in 1991; from Pace University in 1999; and from the University of Illinois, Urbana-Champaign in 2004. She graduated from Albany State Teachers College -- now the State University of New York at Albany -- with a degree in mathematics. She received a master's degree in mathematics at the University of Michigan.
ACM will present the Turing Award at the annual ACM Awards Banquet on June 9, 2007, in San Diego, CA.

About the ACM A.M. Turing Award
The ACM A.M. Turing Award was named for Alan M. Turing, the British mathematician who articulated the mathematical foundation and limits of computing, and who was a key contributor to the Allied cryptanalysis of the German Enigma cipher during World War II. Since its inception, the Turing Award has honored the computer scientists and engineers who created the systems and underlying theoretical foundations that have propelled the information technology industry. For additional information, click on http://www.acm.org/awards/taward.html.

About ACM
ACM, the Association for Computing Machinery http://www.acm.org, is an educational and scientific society uniting the world's computing educators, researchers and professionals to inspire dialogue, share resources and address the field's challenges. ACM strengthens the profession's collective voice through strong leadership, promotion of the highest standards, and recognition of technical excellence. ACM supports the professional growth of its members by providing opportunities for life-long learning, career development, and professional networking.
First Woman to Receive ACM Turing Award

EU regulations currently set maximum limits on how much of a packaging additive can end up in foods, with the general principle that none should be in the product in the first place.
A European Commission proposal made last year would impose even tougher regulation on packaging chemicals migration. Companies can be forced to pay for costly recalls if their food products are found to be over the limits.
The new modelling system was developed by researchers at the Fraunhofer Institute for Process Engineering and Packaging IVV as a means of helping companies stay on the right side of the law.
They are working with nine packaging companies as part of a collaborative EU-funded project called FoodMigrosure. So far the results suggest that current means of calculating additive migration may be two low.
The scientists claim their method is cheaper and more accurate than existing methods of calculation. They estimate companies can save on testing costs by a factor of between a hundred and a thousand times compared to sending samples to a laboratory.
"The cost of computer-assisted testing is much lower than for a laboratory test, and the results are far more accurate," the scientists claimed.
To develop the model the Fraunhofer scientists took random food samples and subjected them to chemical tests in a laboratory.
The researchers based their mathematical model on investigations of genuine foods rather than food simulants. The analyses were performed by all ten of the companies involved in the project – resulting in what the scientists are saying is the world's only systematic collection of such data.
Normally, for such experiments testers replace the foodstuffs with legally prescribed food simulants such as olive oil and mixtures of water with acetic acid or alcohol.
"However, we have found that it is not usually possible to draw conclusions about solid foods on the basis of results obtained with liquid food simulants," said project coordinator Roland Franz. "In many cases the contamination of the foodstuffs is higher than hitherto assumed, and that necessitates costly product recalls."
Using their alternative method to test genuine foods, the scientists next developed various models on the basis of these data.
One model shows how the additives move about in the plastic. Another shows how many of the substances migrate from the plastic packaging material into a particular food.
A third model describes how the migrants disperse in the food itself, Franz said. The researchers devised a formula to summarise the models.
The formula takes into account such characteristics as structure, fat content and consistency and weds the data to the type of plastic packaging material used. The model also takes into account the various additives and the average quantity of the foodstuff actually eaten by consumers.
The same formula can thus be used on one occasion to calculate how many packaging additives are present in cheese, and on another occasion to do the same for meat or orange juice.
Last year the European Commission proposed legislation that would define the manufacturing practices the bloc's processors would have to take in ensuring that packaging materials do not migrate into foods.
All companies would be required to follow what the law defines as "good manufacturing practice" (GMP) in ensuring that packaging chemicals do not transfer to the foods.
GMP would require food companies to change their production methods to prevent the possibility of packaging substances transferring to foods. The proposed requirements would apply to chemicals that might not give rise to particular health concerns but which should not be in foods. They also apply to active and intelligent materials used in packaging to extend shelf life or indicate when food is off.
The proposals are partially an outcome of food safety crisis in November 2005 in which Italy's regulators discovered that a printing chemical from a Tetra Pak package was found to have migrated into a Nestlé milk product for babies.
The EU last year opened a commmunity reference lab in Italy designed aas joint research centre into the safety of specific packaging chemicals, such as those used in inks or for making the material.
EU legislation requires that all materials that come into contact with food comply with health standards so that safe food remains safe.
The new EU reference laboratory will set standards for testing practices for food contact materials across the EU.
It will also serve as a point of reference for issues relating to the enforcement of legislation on food contact materials.
This will be achieved through a network of national reference laboratories set up by each member country.
It will develop methods, reference substances, and training procedures to ensure consistent testing practices are done nationally to ensure the best possible implementation of EU legislation, said the science and research commissioner, Janez Potoènik.
New mathematical model developed for plastic packaging

John Forbes Nash is a reluctant celebrity. The arclights are on him and he looks old and weary in the glare. Just this month, at least three Nobel laureates have visited India. Two of the three — all equally accomplished and distinguished in global academic circles — have landed and left without much ado or fanfare. But Nash is the chosen darling of the media.
The ensuing circus, however, has little to do with his pioneering work in mathematics and game theory. The point of interest is the award-winning film A Beautiful Mind, starring Russell Crowe. It was the film that shot Nash out of academic circles and into dinner table conversations, making him a household name.
But Nash sits slouched in a plush armchair in the Maurya Sheraton in south Delhi, visibly exhausted and besieged by reporters. "This has been like a business trip," he says quietly, burrowing deeper into the armchair.
Nash is in India for a week on the invitation of the ministry of external affairs to flag off its new Nobel Laureate Lecture series. Within three days of being in Delhi, he has delivered a public lecture and met the Prime Minister and the President. He was in Bangalore on Friday to meet Infosys chief mentor Narayana Murthy, and then in Mumbai for a lecture on "Ideal Money and Asymptotically Ideal Money."
Worn out after a day trip to Delhi's landmarks and a constant salvo of questions and meetings, 79-year-old Nash just sits silently, surrounded by his wife, Alicia and his son, John Martin. It's a surreal picture — Nash carries a humungous calculator, and John, a book called Windows for Dummies.
But surreal, really, is better used to describe Nash's roller-coaster ride of a life. A PhD holder at 22, he went on to solve many of the seemingly impenetrable mathematical challenges of the time. His interest in mathematics was kindled when he was a young boy and read the book Men of Mathematics by E.T. Bell. But it was his slender 27-page doctoral thesis, "Non-cooperative Games", as a Princeton student on game theory that won him the Nobel Prize for economic sciences in 1994.
"Nash's work on game theory is the central nerve of the field. I use the Nash Equilibrium in half of my work," says US-based Pradeep Dubey, game theorist and a personal friend of Nash. Nash established the mathematical principles of game theory, which offers to explain the complicated process through which governments, corporations and individuals reach strategic options. Game theory can be applied to almost anything, from a conflict situation to international negotiations to marriages. A lesser known fact about Nash is that he co-invented two famous games, Hex and So Long Sucker, which are still played across campuses.
But as young Nash stood at the edge of what was expected to be an extraordinary career dotted with achievements, fate had other designs. The debilitating illness of paranoid schizophrenia and irrational voices in his head gradually drove Nash out of academic elite circles and frequently banished him into involuntary confinements in hospitals. But even during the so-called irrational period of his life, Nash published numerous papers which have inspired subsequent work as well.
But the brief periods of remission were like coming up for air, as he kept slipping back every time. It took him nearly 25 years to finally shake off the illness. During these years, Nash came to be known as the "Phantom of the Fine Hall" in Princeton, where he wandered about silently, doodling arcane equations on blackboards. Nash was slowly able to defeat the disease without hospitals or medication.
Apart from his innate genius, Nash's stalwart has been Alicia, his wife, friend and loyal companion. Married in 1957, Alicia was pregnant with their first child when Nash started to decline into a delusional abyss. By 1963, Alicia and Nash were divorced, though she did take him back as a lodger in 1970. Alicia's faith and patience were instrumental in Nash's re-emergence as a normal mathematician.
He was back to normal life in Princeton by the time the Nobel was announced. "He asked me to stay at home and listen to the phone. Finally I think I answered it and we were both…," said Alicia throwing up her hands.
Alicia re-married Nash in 2001, after 38 years. Her life has been dedicated to Nash, through illness and recovery, and to their son. Unfortunately, Martin has also been diagnosed with schizophrenia and has suffered nervous breakdowns. "It is like déjà vu. But an illness is an illness. Knowing about it or living it twice doesn't cure it," says Alicia.
Nash is a deeply private person. He refused to dole out personal details either for the highly acclaimed biography A Beautiful Mind by Sylvia Nasar, or the motion picture. "He once told me that he was relieved to see the movie because he didn't feel that his privacy was invaded. It's a take-off on his life. The film showed Nash breaking a lot of codes for the US government but I don't think he did that," says Dubey.
And to answer the oft-asked question, Nash does not look anything like the pumped-up Crowe in the film. But Martin uncannily resembles Crowe, towering over everyone in a baseball cap.
Nash's life is scripted almost along cinematic lines, as if it were always meant to be one. From early childhood, through the prolific years of his youth, tortured delusions and then back to a normal life, mathematics has always stood by him. Ironically, his greatest award in 1994 was not for his work in pure mathematics but for economics. And that too for his work in the 1950s. "Nash should have received the Nobel years back. To give it so late makes the Nobel prize slightly less noble," says Dubey.
For all his personal and academic milestones, people close to Nash say he is grounded and considerate — an individual without airs. "He is very real. He is like a little boy," says actress Lushin Dubey, a friend to both Alicia and Nash. And just as the three of them walk away to another busy evening, Nash turns back slowly to add, "I would have liked to see more of the Indian countryside. Maybe another time." Just like he said in 1950, for a perfect solution, you win some, you lose some.
IT'S ALL IN THE MIND

American mathematician and economist John Nash will be arriving in Mumbai on Monday to deliver a lecture on the economics of money and, in his words, "to explore the new, emerging India for himself." Nash, famously portrayed in the Oscar-winning movie A Beautiful Mind by Russell Crowe, won the Nobel Prize for economics in 1994. Josy Joseph spoke to the 79-year-old mathematician ahead of his Mumbai sojourn.

Having been a mathematical prodigy very early in life, what advice would you give children on learning to love numbers?
When I was young, I was sort of generally scientifically interested rather than specifically mathematics. I like to accumulate scientific knowledge. I could work with mathematics to do calculations — I had that interest. What is possible to do is simply to develop the ability to work with larger numbers.
How important is mathematics to an aspiring economist? Do the two go hand in hand?
It helps to have a good foundation in mathematics, to study mathematical economics. I can't say exactly how much one should study; there are a lot of variations. Counting and measuring is something age old. The Babylonians learnt how to keep accounts. That is sort of right at the beginning on a world basis, except for western hemisphere.
They also developed independently.
A genius is a difficult state of mind and being. You are being asked to comment on everything from globalisation to Hollywood. How do you handle all that?
I don't accept the genius concept, this is a word many people use. I don't say they shouldn't use it either. I haven't ever tried an IQ test. It is something meant for children, they need to develop. People generally ask questions. I am effectively fame-less. There are many people out there who have more fame than me in many ways, than I do. They may not be so broad but they have distinguished reputation.
How has been life after the movie, A Beautiful Mind? Has the movie made much impact on your life?
The movie has been out for a while now. It was made in 2002, so that is now five years ago. There has been a quite a change in the reaction I got — a lot more fan mail for one.
Do other factors, gadgets like mobile phone contribute to distractions?
The mobile phone is a very interesting example. A great technological advancement. I think time would come when we all ought to have it. I am avoiding it, I say I don't want to be distracted. It saves money. For an older person it might be a life-saver.
I think there will come a time when you really ought to have one, fitted into your car. So if you have a breakdown in your car, or such situations, it would be a life-saver. I don?t know if it is affordable. I don't use a portable computer also. But I have a computer (PC) at home, also one at office, which are pretty old. Notebooks are pretty recent.
How are the principles of game theory being applied in today's political scenario?
In the US there was a considerable effort to apply game theory during the Cold War period. A more recently case for analysis is the situation in Iraq, when it was reported that the US lost five helicopters and its crew in a short period of time because people were using smaller missiles to shoot them down. The American side said the shock- and-awe tactics would do the work. But then the US army began using helicopters like buses to transport soldiers from one point to another.
As a mathematician and economist how do you look at the future of globalisation?
There is a general lesson in economics and finance that it is always learnt and then forgotten — you have to expect surprises, things will not just continue smoothly.
There will be surprises.

John Nash unplugged
John Forbes Nash, Jr. was born on June 13, 1928 in Bluefield, West Virginia. He studied engineering and chemistry at the Carnegie Mellon University before switching to mathematics.
In 1978, Nash was awarded the John Von Neumann Theory Prize for his invention of non-cooperative equilibria, now called Nash equilibria. He won the Leroy P Steele Prize in 1999.
He shared the 1994 Nobel Prize in Economics with two other game theorists, Reinhard Selten and John Harsanyi.
Nash is known in popular culture as the subject of the Hollywood movie, A Beautiful Mind, about his mathematical genius and his struggles with schizophrenia.
There are many people out there who have more fame than me: Nash

My 40 minutes with Nobel Laureate John Forbes Nash Jr was a little strange. The 79-year-old mathematician who won the 1994 prize for economics said he was suffering jet lag and a packed schedule, but there was something else.
The external affairs ministry, which organised the interview, had said there should be no questions about paranoid schizophrenia, the illness he was diagnosed with when he was 30, and for which he spent six involuntary hospitalisations. His biography, A Beautiful Mind, made into a film, says he spent the next 30 years coming to terms with it, and that his story was one of "genius, madness, reawakening". And so I thought it was something in the past.
During the chat, Nash appeared a man who was cautious. His answers were uneven, and at time, inexplicable. And on two occasions our eyes met — for the most part he kept diverting his gaze — I saw an unsettling fear and sadness. Yet when a maths-related question was posed, he seemed to change into a different person: lucid and brilliant. I did not give it much thought at the time. But later, I woke up in the middle of the night, with the realisation that perhaps I witnessed a battle between genius and madness within an individual.
Not exactly, practicising psycho-analyst Madhu Sarin says: "High IQs have been linked to greater sensitivity; brilliance and battiness have gone hand-in-hand." Nimesh G. Desai, head of psychiatry at the Institute of Human Behaviour and Allied Sciences, says the rate of disorders is high at the extremes of intelligence. "The hallmark of creativity is original thought," Desai says. "Original thoughts often fall within the realm of abnormal. This abnormal idea may be something that can make a critical difference to humanity, or it may stem from a psychiatric disorder. The boundary between the two may be blurred."
Schizophrenics lose a sense of continuity, says Sarin, so they lose a sense of self. In turn, this means they lose sight of the other person as well. So during the conversation, what was happening was that Nash was responding to however I gestured — but on a moment-to-moment basis. The only constant for him, perhaps, was a literal feeling of coming apart, Sarin says, which projected onto me as an eerie feeling.
"The kind of anxiety schizophrenics feel you can't begin to imagine," Sarin says. And to deal with uncertainty, schizophrenics take refuge in a rational universe — like mathematics — where their feelings are neatly packaged. True enough, Nash spoke about 9/11. Unlike most other Americans, he spoke of it calmly, as an incident perpetrated by insane people, directing his criticism at his government's reaction to the incident. As he could not handle an intensity of emotion, he took his analysis to a logical extreme.
So my earlier notion, that his battle against schizophrenia had been long won, was wrong. "It's never over, you can only improve the quality of life," says Sarin. For 40 minutes, I had a glimpse of his beautiful mind's fight against a dissipating self, and saw that indeed, beauty is fragile.

(With Neha Mehta)
The mind battles on

A classroom in Rhodes Hall was packed on Friday afternoon when mathematicians, physicists, engineers and other fans of the MathWorld website gathered to hear its creator, Eric Weisstein '90, give a talk entitled "MathWorld: Communicating Mathematics on the Internet" as part of the Center for Applied Mathematics Colloquium series.
MathWorld is a free online encyclopedia of mathematical terms, concepts and definitions. To date, it has over 12,600 pages, and is updated continually to reflect new discoveries and information. Many Cornellians, students and faculty alike consider the site an invaluable resource. What most don't realize is that Weisstein wrote nearly every page entirely by himself.
MathWorld's initial form was created in 1987 when Weisstein was an undergraduate physics major at Cornell. Possessed with an admirable work ethic, Weisstein typed up all of his physics and math lecture notes in Microsoft Word.
"The reason [MathWorld] exists is because it didn't exist when I was a student, and I really, really wanted it to," Weisstein said. "This is made for you."
By 1991, he had amassed 82 pages of detailed, neatly typed math notes, saved as a Word document on his computer. When the first version of Netscape came out in 1994, he decided to convert his notes into a web page, titled "Eric's Treasure Trove of Mathematics."
"I wanted to spread the gospel of mathematics," he said. "I had hoped to do so through my research papers, but I realized that the number of people who were seeing my website was about an order of magnitude higher than the number of people who read my papers."
After a legal dispute, the site went back up in 2001, and has been growing steadily ever since. Today, if it were published as a book, MathWorld would be about 4,300 pages long. The site gets hundreds of thousands of page hits every day from all over the world. Google search results rank it as the number one math and science website. According to Weisstein, most people who find their way to MathWorld do so through Google: if you Google an obscure mathematical fact, MathWorld will nearly always come up as one of the top hits.
Weisstein mentioned that there are a number of other ways to navigate the MathWorld site as well, including its own internal search engine and the "Random Entry" link. Weisstein once got an e-mail from a user who relied extensively on the "Random Entry" link as a research tool.
"One time he was trying to remember a concept from linear algebra, and he couldn't remember its name, but he knew someone must have written about it at some point. So he hit 'Random Entry' 800 times to see if it would come up. And he found it!" Weisstein said. "If you make the tools, people will use them."
To Weisstein, the most important function that MathWorld serves is reaching as wide and diverse an audience as possible.
"MathWorld disseminates math knowledge to people worldwide — to teachers, students, farmers in Africa..." Weisstein said. "It shows potential scientists and mathematicians that math is fun and interesting and it's something they can do — it's not something they should be scared of. That's the important thing," he said. While thousands of users have contributed comments and corrections to MathWorld, 99 percent of it was authored exclusively by Weisstein. When asked if he would ever consider hiring people to help him write, Weisstein was reluctant.
"This was a labor of love for me," he said. "I love writing about it, and I think I have a different approach than a lot of textbooks I've read."
Keeping the style and the level of accessibility consistent is more important to him than being able to publish more quickly and efficiently.
Catherine Elder '08, who attended the talk, prefers MathWorld to Wikipedia.
"When I was working on a physics problem set and I couldn't remember something that I learned in high school, I used to Google it," she said. "A lot of the time, MathWorld or Wikipedia would come up. Recently, I noticed that the Wikipedia articles often cite MathWorld. Now, I just go straight to MathWorld."
Throughout his talk, Weisstein was funny, entertaining and personable.
"It was nice to put a personality to the website," Elder said. "It seemed like we could relate to each other a lot."
A number of students and professors approached Weisstein after the talk to thank him, including one of Weisstein's former professors, David Chernoff, astronomy. "I thought his talk was wonderful," Chernoff said. "He has a creative and independent spirit with a strong personal interest in learning and explicating the math and science he covers on his web site. ...His approach makes it possible to gain a broad understanding of mathematical terms and ideas with a minimum of effort. It's been extremely helpful to those of us who aren't experts but want a better sense of the meanings and connections of various terms."

By Lisa Grossman at Feb 19 2007 - 1:43am
Alum Creates Math Encyclopedia on Web

Speaking in a symposium titled "New Vistas in the Mathematics of Ecology and Evolution" at the annual meeting of the American Association for the Advancement of Science in San Francisco, theoretical ecologist Mercedes Pascual will discuss how models that she and coworkers have developed can aid short-term forecasting of infectious diseases, such as cholera, and inform decisions about vaccination and other disease-prevention strategies.
In research done over the past seven years, Pascual and colleagues have found evidence that a phenomenon known as the El Nino-Southern Oscillation (ENSO), a major source of climate variability from year to year, influences cycles of cholera in Bangladesh. They also showed that the coupling between climate variability and cholera cycles has become stronger in recent decades.
Now, Pascual is examining the feasibility of using a model developed during that work as an early warning system.
"The question we asked was whether, using data from 1966 to 2000, we could have predicted cholera outbreaks over the past five years," said Pascual, an associate professor of ecology and evolutionary biology. "We also wanted to know whether incorporating ENSO into the model would improve the accuracy of our predictions." The challenge for the model was particularly interesting because the past five years were atypical, with fewer cholera cases than usual and no strong climate anomalies. However, the model performed well, Pascual said.
"Our results showed that for the past five years, we would have done fairly well predicting cholera cases one year ahead, and that the model that uses ENSO makes prediction even more accurate."
Cholera, a serious health problem in many parts of the world, results from a bacterial infection. The bacterium takes up residence in the intestines, causing vomiting and diarrhea, which can lead to severe dehydration and death if patients are not promptly treated.

Note: This story has been adapted from a news release issued by University of Michigan.
Mathematical Model Predicts Cholera Outbreaks

Professor Martin Golubitsky

Posted on 15 Feb 2007 by Tlaventure
Patterns Patterns Everywhere

Related Links:
Rachel Karchin's Lab Page: http://karchinlab.org/
Institute for Computational Medicine at Johns Hopkins: http://www.icm.jhu.edu/
Johns Hopkins Department of Biomedical Engineering: http://www.bme.jhu.edu

MEDIA CONTACT: Phil Sneiderman, JHU Media Relations, 443-287-9960, prs@jhu.edu
Computer Tool Helps Pinpoint Risky Gene Mutations; Mathematical Analysis Could Aid in Predicting Cancer Cases

As a result it will be possible not only to gain a thorough understanding of the processes that occur with microscopic water droplets in the zone of the fire, but also to select optimal, that is the most effective and economical, means to put out a fire. Information support for the project comes from the International Science and Technology Centre, whose specialists found the project to have immense potential.
At the heart of the project, which involves the work of specialists from the All-Russia Research Institute of Experimental Physics (Sarov) and their colleagues from the St. Petersburg State Polytechnic University, lies the use of sprayed water where the individual droplets are about 100 microns in size. While it may seem strange to the layperson that such small droplets could put out a blazing fire, the specialists are in no doubt at all. Its advantages are in the following.
An aero-suspension (aerosols or droplets in air) has an immense specific surface, so the burning zone rapidly cools. The volume of the dispersed water cloud, too, is an order greater than from a jet of water of the same mass. Therefore the efficiency coefficient or, more specifically, the coefficient of water use, is tens of times higher as compared with a usual jet, even if such a jet is both powerful and precisely directed. Furthermore, in the event of a forest fire, for example, when the area of coverage is very large, it is practically impossible to cope with the fire with individual jets or with a localized strike per se; while pouring on water in one place, the fire flares up in another. In addition, the damage caused to a building by putting out a fire is comparable to the damage from the fire itself, while a mist would be very unlikely to even affect electronic equipment.
In theory, there is no doubt that the method has considerable promise. However, in practice things do not always turn out so simply. To ensure the method really is effective, a multitude of factors have to be borne in mind. These factors include the correlation between the specific power of the focal point of the burning and the sizes of the space to be protected, the size, concentration and rate of movement of the droplets, the intensity and duration of the process of extinguishing the fire for different fire fighting systems that use fundamentally different means of obtaining the active material and many others.
Furthermore, serious theoretical studies are needed, relative to the formation and the behaviour of water droplets at high temperature, and to the parameters of gas flows in the area of the fire and in its direct vicinity. The fact is that the high efficiency of this method is conditioned by the fact that dispersed water rapidly cools the zone of the burning, while water vapour forces out the oxygen from it. This is the so-called phlegmatization method, in part resembling how fire is covered with a thick blanket, only here a cloud of mist covers the entire zone of the fire at once, depriving the fire of heat, air and, finally, its very life. However, this is of course if the dispersed water reaches the zone of the fire, and in the sufficient quantity. Therefore, conditions have to be created so that its convection flows were as if drawn into the area of the fire before the minute droplets can evaporate from the heat or before they are carried away by a flow of hot gases.
Mathematical modelling helps the scientists to cope with such complicated and multiple-factor research. They have already achieved serious success in developing the mathematical model of certain processes that occur during the burning and extinguishing of fires with dispersed water. However, virtual experiments alone are not enough for a complete solution of the set tasks; what are needed are genuine, full-scale experiments, as it is these that will enable the more precise definition of the numerical model and the final determination of the optimal means for putting out a fire with dispersed water.
VNIIEF has the required conditions, that is, a testing ground, where such experiments may be conducted. However, unfortunately it is not yet sufficiently equipped with the requisite equipment, such as IR sensors that would enable rapid measurement of temperature in any point, both in the very focal point of the fire and in the space around it. Yet the scientists know for sure what equipment they need and they are confident that, with the required financing, they could develop the technology to help put out a fire rapidly, effectively and as safely as it could possibly be done. The guarantee of success lies in the colossal experience and knowledge that is available.
Small drops to put out large fires

Fellow researchers: Tuy poses with Russian mathematician L.V. Kantorovitch, 1974 Nobel Prize winner in economics. — File Photos

Passing the torch: Professor Tuy still teaches in the capital.

I came to Hoang Tuy's home on Ha Noi's Doi Can Street on a winter day in late 2006. The professor, now 79-years-old and beholden to a hearing aid, received me with a big smile.
Tuy is considered one of the fathers of optimisation theory, a mathematical technique designed to find the best possible outcome given a series of constraints. The theory is considered a cornerstone of modern economics and credited with clearing the muddy waters of everything from long-distance transport to rice growing. So it should come as little surprise that some of the world's top mathematicians and programmers will celebrate Tuy's 80th birthday when they gather in Rouen, France, a little under a year from now.
Tuy was born on December 12, 1927 to family of Confucian scholars in Xuan Dai Village, located in the province of Quang Nam. The family was well known thanks to the brother of his grandfather, Hoang Dieu (1832-1882), a northern provincial leader who killed himself when the fort of Ha Noi fell to French invaders.
The family was also renowned for its scholarly achievements. One of Hoang Tuy's brothers, Hoang Kiet, became a famous artist while two others, Hoang Phe and Hoang Chung, are accomplished professors.
In his early childhood, Tuy was the top student in his village school, excelling in both math and literature. A young Tuy was eventually sent to the famous Quoc Hoc School in Hue for secondary studies. There, while he still topped his class in both subjects, he began devoting more time to mathematics.
At the age of 15, he was stricken with a severe bout of pneumonia that left him partially paralysed. Thanks to treatments from a local acupuncturist he recovered, but had to leave Quoc Hoc and join a private school. In 1946, despite all the difficulties, he topped national high school examinations and travelled to Ha Noi to attend the College of Sciences.
Unfortunately, war broke out and forced him to return home. But before he left, he criss-crossed Ha Noi in search of mathematical texts. In 1951, he was teaching in a resistance zone when he learned that renowned professor Le Van Thiem was returning to Viet Bac, located in mountainous northern Viet Nam, from Switzerland. He immediately asked the local Department of Education for permission to travel to Tuyen Quang, the capital of the resistance government, to meet the eminent professor. At the time, the route along the Truong Son Range was still very much a small mountain path amidst the jungle unlike the later famous Ho Chi Minh Trail.
After receiving the go-ahead, an enthusiastic Tuy set off, bringing along only rice, water, his mathematical books and anti-malarial drugs. Travellers along the route face constant threats from French ambushes, tiger attacks and disease carrying mosquitoes.
It took Tuy almost six months of walking before he arrived in Tuyen Quang, only to learn that the professor he sought had already left for China. So, he decided to extend his trip. After crossing the border into China, he headed for Naning, where he joined other Vietnamese students.
When Ha Noi was liberated in 1954, he returned and was appointed lecturer at the College of Sciences. In July 1957, he was among the first eight scientists sent to the Soviet Union for post graduate work. He spent just over a year completing his doctorate thesis, a surprisingly short period of time for a man who studied almost by himself.
In 1997, as he approached his 70th birthday, the Swedish LinkoŠping University's Institute of Technology held a three-day seminar under the banner "Optimisation – From Local to Global" in honour of Tuy. A publishing house released the workshop's proceedings, which were gobbled up by international scientists. Tuy's reputation as the father of global optimisation had been born.
Today, most mathematicians in the world acknowledge his contributions, which include Tuy's Cut, Tuy-type algorithms and Tuy's inconsistency condition to name a few.
In September 2002, the Operation-Research Bulletin, the forum of Asia-Pacific operations mathematicians, published a special issue on Tuy that included articles by several eminent scientists. Tuy also co-authored Global Optimisation – Deterministic Approaches. The book was first published in 1990 and then revised in 1993 and 1996. It is considered by many as 'the Bible of optimisation'. Apart from the books, he is also the author of some 140 internationally recognised studies.
Today, Tuy still works tirelessly for the Institute of Mathematics in Ha Noi and continues to assert his great influence in the world of optimisation. He has received many prestigious awards from the Government of Viet Nam for his dedication and contributions to the country's development, including the Ho Chi Minh Award. — VNS
Viet Nam's mathematical superstar

Scott Zeger,
Johns Hopkins University
Bloomberg School of Public Health

Professor Scott Zeger, chair of the department of biostatistics at the Johns Hopkins University Bloomberg School of Public Health, will deliver a talk entitled "When Counting is Not as Easy as 1, 2, 3: Iraq Mortality Since the U.S. Invasion" at Carleton College on Tuesday, Feb. 13 at 3:30 p.m. in Olin Hall, room 149. The lecture is free and open to the public.
In October 2006, The Lancet, a highly-respected British medical journal, published a study estimating that close to 650,000 Iraqi civilians have been killed since the March 2003 U.S.-led invasion of Iraq. Zeger was an advisor to the study, which was conducted by researchers at the Bloomberg School along with Iraqi physicians. The study sparked significant controversy, despite its approval by many other statisticians and public health officials. President Bush, however, suggested that "The methodology is pretty well discredited."
Zeger is the Hurley-Dorrier Professor and Chair of Biostatistics at Johns Hopkins Bloomberg School of Public Health. He received his BA in biology from the University of Pennsylvania and his PhD in statistics from Princeton University. Zeger is a Member of the National Academy of Sciences Institute of Medicine and Fellow of the American Association for the Advancement of Science and the American Statistical Association. He is co-editor of the Oxford Press journal Biostatistics and a member of the Springer-Verlag editorial board for statistics. He was awarded the 1987 Snedecor Award (with co-author Dr. Kung-Yee Liang) for the year's best paper in biometry. The American Public Health Association recognized Zeger in 1991 with the Spiegelman Award for contributions to health statistics. In 1987, 2002 and 2005, the Johns Hopkins Student Assembly awarded him the Golden Apple for excellence in teaching. Science Watch notes Zeger as one of the top 25 most-cited mathematical scientists of the past decade.
Zeger's appearance is sponsored by the Carleton math department and the QuIRK (Quantitative Inquiry, Reasoning, and Knowledge) initiative. QuIRK is an innovative project intended to help Carleton and other institutions of higher education better prepare students to evaluate and use quantitative evidence in their future roles as citizens, consumers, professionals, business people, and government leaders.

For more information, contact the math department at (507) 646-4360.
Influential Statistician to Speak at Carleton College

Santiago Schnell

More information about the Systems Biology Laboratory at the IU School of Informatics is at http://www.informatics.indiana.edu/systemsbiology. To arrange an interview with Santiago Schnell or to receive a copy of the American Scientist article, contact Joe Stuteville at 317-946-9930 or jstutevi@indiana.edu.
Math models add more options for life sciences, cancer researchers

Betty Jespersen -- 778-6991
bjespersen@centralmaine.com
Making math sound easy

A homogeneous, convex body
with just two balance positions (top)
and as it appears in nature
on the shell of an Indian Star Tortoise
(bottom)

Related Links:
Original story (fn.hu, in Hungarian)
Mono-monostatic Bodies: The Answer to Arnold's Question (Paper by P. L. Várkonyi and G. Domokos, in English)

Hungarian scientific discovery makes waves

- - - -

CONTACT: Monte Basgall, Duke University Office of News & Communications, 919-681-8057, monte.basgall@duke.edu
Duke University Geologist's Book Assails Unrealistic Mathematical Models

* The writer is professor of Mathematics at Cairo University.
Mathematics in Ancient Egypt

Dave Gershman can be reached at 734-994-6818 or dgershman@annarbornews.com.
Noted peace researcher Rapoport dies at 95

RELATED LINKS:
The proof by Polster and his colleagues
Martin's proof "Mathsnacks"
a column by Polster and Marty Ross for Vinculum magazine

Strange but True: Turning a Wobbly Table Will Make It Steady

Beau Janzen, Konrad Polthier
MESH
Springer 2007
DVD (PAL) EUR 29.95, £23.00, $29.95, sFr 52.00,
ISBN: 978-3-540-28478-9
DVD (NTSC) EUR 29.95, £23.00, $29.95, sFr 52.00,
ISBN: 978-3-540-28484-0
The visual beauty of discrete geometry, The new mathematical film Mesh is a prizewinner