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Newsletter 2003


WHY IS MATHEMATICS IMPORTANT?

In this note we excerpt some of the highlights of Professor Arnold's May 2003 commencement address, titled "Doing the Math and Making an Impact", and given by him for the mathematics and statistics graduation at the University of Illinois in Urbana-Champaign. Professor Arnold is the Director of the Institute for Mathematics and its Applications which is associated with our department. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03

Asking "What makes the math sciences so central?", he answers by quoting Galileo: "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.", adding "Math is the way to understand all sorts of things in the world around us." To elaborate on this point he gives some well-chosen examples, beginning with some insightful comments on the Swiss victory in the 2003 America's Cup. "...you know that Switzerland is a small, mountainous, land-locked country. So how did the Swiss pull this upset off?" While acknowledging that a number of diverse factors had to come together, he makes his point: " Well Switzerland may not have a great sailing tradition (at least until now!) but it does have a very strong tradition in mathematics--Euler's picture appeared on a Swiss 10 franc note--and the Swiss team wisely brought this strength in math to bear on the America's Cup challenge. They enlisted a group of mathematicians specializing in mathematical modeling and numerical computation led by Professor Alfio Quarteroni at the national polytechnical university in Lausanne. The mathematicians used partial differential equations to model the flow of the sea around the hull, the dynamics of the air and the sails, and the turbulent interaction of the ocean, wind, and boat. They then applied advanced numerical algorithms to solve these equations on high performance computers. This allowed them to optimize such things as hull and keel design, sail geometry and placement, and so forth. Their work was essential to the design of the Alinghi, and so to the Swiss victory. They did the math and made a big impact." ("Alinghi" was the name of the Swiss boat.)

On the increasing role of mathematics in biological sciences he comments as follows: "Increasingly math is making an impact in the life sciences as well, prompting biologist Rita Colwell, director of the National Science Foundation, to observe that "mathematics is biology's next microscope--only better." In their recent bio textbook Keener and Sneyd wrote that "teaching physiology without a mathematical description of the underlying dynamical processes is like teaching planetary motion to physicists without mentioning...Kepler's laws;" He then mentions still other areas of applications: "And math increasingly reaches outside the sciences, to economics, sociology, and business for example. ...Illinois's new Applied Mathematics Program ...involves no less than 22 departments from bioengineering to linguistics. ...Problems which need mathematics for their solution also arise throughout industry."

To underline how seriously this is taken worldwide, he cites a strategic plan published by the British government in 2003, seeking to exploit mathematical research to improve the competitiveness of industry in the UK: ""Mathematics is the most versatile of all the sciences. It is uniquely well placed to respond to the demands of a rapidly changing economic landscape...Mathematics now has the opportunity more than ever before to under-pin quantitative understanding of industrial strategy and processes across all sectors of business. Companies that take best advantage of this opportunity will gain a significant competitive advantage: mathematics truly gives industry the edge." He also notes that British government policy in dealing with the hoof-and-mouth disease outbreak a few years ago relied heavily on studies based on mathematical epidemiology.

He states that a major current challenge we face is how to get the most out of all the data that has been accumulated thanks to the modern technology: "For example, how can we exploit the world-wide network of seismic sensors to predict earthquakes? How can we mine the vast genomic databanks to advance biology and medicine? How can we sift through the massive amounts of text, video, web, and satellite data to detect terrorist events before they happen? Well, data means big collections of numbers--remember that text and images are digitized and stored as numbers--and data mining means discovering the patterns and structures hidden in those collections. That's practically a definition of mathematics: the study of structures and patterns in large numerical sets. So you can be sure that in the 21st century--the century of data--math will again have a huge impact."

In conclusion he exhorts the graduates to cultivate and apply logical, mathematical and quantitative thinking even if they do not become research mathematicians. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03

 

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