Tag Archives: International Mathematical Union

Mathematicians get illustrative

Frank A. Farris, an associate Professor of Mathematics at Santa Clara University (US), writes about the latest in mathematicians and data visualization in an April 4, 2017 essay on The Conversation (Note: Links have been removed),

Today, digital tools like 3-D printing, animation and virtual reality are more affordable than ever, allowing mathematicians to investigate and illustrate their work at the same time. Instead of drawing a complicated surface on a chalkboard, we can now hand students a physical model to feel or invite them to fly over it in virtual reality.

Last year, a workshop called “Illustrating Mathematics” at the Institute for Computational and Experimental Research in Mathematics (ICERM) brought together an eclectic group of mathematicians and digital art practitioners to celebrate what seems to be a golden age of mathematical visualization. Of course, visualization has been central to mathematics since Pythagoras, but this seems to be the first time it had a workshop of its own.

Visualization plays a growing role in mathematical research. According to John Sullivan at the Technical University of Berlin, mathematical thinking styles can be roughly categorized into three groups: “the philosopher,” who thinks purely in abstract concepts; “the analyst,” who thinks in formulas; and “the geometer,” who thinks in pictures.

Mathematical research is stimulated by collaboration between all three types of thinkers. Many practitioners believe teaching should be calibrated to connect with different thinking styles.

Borromean Rings, the logo of the International Mathematical Union. John Sullivan

Sullivan’s own work has benefited from images. He studies geometric knot theory, which involves finding “best” configurations. For example, consider his Borromean rings, which won the logo contest of the International Mathematical Union several years ago. The rings are linked together, but if one of them is cut, the others fall apart, which makes it a nice symbol of unity.

Apparently this new ability to think mathematics visually has influenced mathematicians in some unexpected ways,

Take mathematician Fabienne Serrière, who raised US$124,306 through Kickstarter in 2015 to buy an industrial knitting machine. Her dream was to make custom-knit scarves that demonstrate cellular automata, mathematical models of cells on a grid. To realize her algorithmic design instructions, Serrière hacked the code that controls the machine. She now works full-time on custom textiles from a Seattle studio.

In this sculpture by Edmund Harriss, the drill traces are programmed to go perpendicular to the growth rings of the tree. This makes the finished sculpture a depiction of a concept mathematicians know as ‘paths of steepest descent.’ Edmund Harriss, Author provided

Edmund Harriss of the University of Arkansas hacked an architectural drilling machine, which he now uses to make mathematical sculptures from wood. The control process involves some deep ideas from differential geometry. Since his ideas are basically about controlling a robot arm, they have wide application beyond art. According to his website, Harriss is “driven by a passion to communicate the beauty and utility of mathematical thinking.”

Mathematical algorithms power the products made by Nervous System, a studio in Massachusetts that was founded in 2007 by Jessica Rosenkrantz, a biologist and architect, and Jess Louis-Rosenberg, a mathematician. Many of their designs, for things like custom jewelry and lampshades, look like naturally occurring structures from biology or geology.

Farris’ essay is a fascinating look at mathematics and data visualization.

Mathematics of Planet Earth lives on past 2013

A Université de Montréal (Québec, Canada) Dec. 11, 2013 news release (also on EurekAlert) proclaims a new life for a worldwide mathematics initiative (Note: I have added paragraph breaks for this formerly single paragraph excerpt),

Although you might not know it, mathematics is able to shed light on many of the issues facing Planet Earth – from the structure of the core of our planet to the understanding of biodiversity, from finding ways to advance cutting edge solar technology to better understanding the Earth’s climate system, and from earthquakes and tsunamis to the spread of infectious diseases – and so mathematicians around the world have decided to launch an international project, Mathematics of Planet Earth (MPE), to demonstrate how their field of expertise contributes directly to our well being.

Mathematics of Planet Earth is growing out of a year-long initiative that was the brainchild of Christiane Rousseau, professor of mathematics at Université de Montréal and vice-president of the International Mathematics Union.

Beginning in 2014, the program will continue under the same name with the same objectives: identify fundamental research questions about Planet Earth and reach out to the general public. As Prof Rousseau observed, “Mathematics of Planet Earth has been a great start. But identifying the research problems is not enough. Mathematics moves slowly, the planetary problems are very challenging, and we cannot expect great results in just one year.” “The International Mathematical Union enthusiastically supports the continuation of Mathematics of Planet Earth. The success of this initiative attests to the foundational role of the mathematical sciences and interdisciplinary partnerships in research into global challenges, increasingly valued by society,” says Ingrid Daubechies, President of the International Mathematical Union.

How did I not hear about this project before now? Well, it’s better to get there late then never get to the party at all. From the news release,

Under the patronage of UNESCO, the MPE initiative brought together over 100 scientific societies, universities, research institutes, and foundations from around the world to research fundamental questions about Planet Earth, nurture a better understanding of global issues, and help inform the public about the essential mathematics of the challenges facing our planet. “The Mathematics of Planet Earth (MPE) initiative resonates strongly with UNESCO’s work to promote the sciences and science education, especially through our International Basic Sciences Programme. Math advances fundamental research and plays an important role in our daily life. More than ever we need to develop relevant learning materials and to spark in every student, especially girls, a sense of joy in the wondrous universe of mathematics and the immense potential unleashed by this discipline. In this spirit, we commend this initiative and fully endorse the proposal to continue this programme beyond 2013,” said Irena Bokova, Director-General of UNESCO.

It’s not about preaching to the converted. “The curriculum material developed for Mathematics of Planet Earth provides schools and educators a free-of-charge wealth of material for and will be used for many years to come. The initiative has presented the public, schools and the media with challenging applications of mathematics, with significant answers to questions like ‘What is mathematics useful for?'” said Mary Lou Zeeman, MPE coordinator for Education. “Mathematics of Planet Earth wonderfully contributed to diffuse an informed culture of environment and helps to get a common mathematical toolkit necessary to deal the dramatic challenges faced today by our planet,” said Ferdinando Arzarello, President of the International Commission of Mathematical Instruction (ICMI).

It’s not only the mathematicians and mathematics pedagogues who’ve gotten excited about this initiative,

MPE2013 has drawn the attention of other disciplines as well. Among its partners are the American Geophysical Union, the International Association for Mathematical Geosciences, and the International Union of Geodesy and Geophysics (IUGG). The research on planetary issues is interdisciplinary, and collaboration and networking are essential for progress. “Great mathematicians understood the importance of research into planet Earth many centuries ago,” said Alik Ismail-Zadeh, a mathematical geophysicist and the Secretary General of the IUGG. “Pierre Fermat studied the weight of the Earth; Carl Friedrich Gauss contributed to the development of geomagnetism and together with Friedrich Wilhelm Bessel made significant contribution to geodesy; Andrei Tikhonov developed regularization techniques intensively used in studies of inverse problems in many areas of geophysics. Mathematics of Planet Earth 2013 highlighted again the importance of international multidisciplinary cooperation and stimulated mathematicians and geoscientists to work together to uncover Earth’s mysteries.”

The news release closes with these interesting bits of information,

About Mathematics of Planet Earth

On January 1, 2014, Mathematics of Planet Earth 2013 (MPE2013) will continue as “Mathematics of Planet Earth” (MPE). The objectives remain unchanged – identify fundamental research questions about Planet Earth and reach out to the general public. With support from the U.S. National Science Foundation, MPE will maintain a website where additional educational and outreach materials will be posted. New modules will be developed and added to the MPE Exhibition. Plans for more MPE activities exist in several countries in the form of workshops, summer schools, and even the creation of new graduate programs in Mathematics of Planet Earth.

About Christiane Rousseau

Christian Rousseau is a professor at Université de Montréal’s Department of Mathematics and Statistics, Vice-President of the International Mathematics Union, and a member of the Centre de recherches mathématiques. Professor Rousseau conceived and coordinated Mathematics of Planet Earth 2013.

About Mathematics of Planet Earth 2013’s Achievements

MPE2013 activities have included more than 15 long-term programs at mathematical research institutes all over the world, 60 workshops, dozens of special sessions at society meetings, two major public lecture series, summer and winter schools for graduate students, research experiences for undergraduates, an international competition, and an Open Source MPE Exhibition. In addition, MPE2013 has supported the development of high-quality curriculum materials for all ages and grades available on the MPE2013 Web site.

Encouraging Research

The scientific activities of MPE2013 were directed both to the mathematical sciences community, whose members are encouraged to identify fundamental research questions about Planet Earth and their potential collaborators in other disciplines. The program provides evidence that many issues related to weather, climate, sustainability, public health, natural hazards, and financial and social systems lead to interesting mathematical problems. Several summer and winter schools have offered training opportunities for junior researchers in these areas.

Reaching Out

The outreach activities of MPE2013 were as important as the scientific activities. More than sixty public lectures have been given with audiences on all five continents. Particularly noteworthy were the MPE Simons Public Lectures, now posted on the MPE2013 Web site, which were supported financially by the Simons Foundation. MPE2013 has maintained a speakers bureau, supported the development of curriculum materials, maintained a collection of posters, and produced special issues of mathematical magazines and other educational materials. Many activities took place at schools in several countries. The permanent MPE Open Source Exhibition is now hosted on the website of IMAGINARY and can be used and adapted by schools and museums.

Daily Blog

The dual mission of MPE2013 – stimulating the mathematics research community and reaching out to the general public – is reflected in the Daily Blogs (one in English, the other in French), each of which has featured more than 250 posts on topics ranging from astronomy to uncertainty quantification. The blog gets several hundred hits a day.

You can find out more about MPE 2013 and its future here. (English language version website) or go here for the French language version. For those who prefer to read the news release about the ‘morphing’ MPE in French, go here.