The year 2010 marks the 50th anniversary of the publication of Eugene Wigner’s famous essay on the “unreasonable effectiveness of mathematics in the natural sciences”. The intervening five decades have witnessed an explosion in the variety and scope of the applications of mathematics, to the extent that one can now speak of an ongoing “mathematization” of many branches of science and indeed of society as a whole. Number theory, traditionally viewed as far removed from the sphere of applications, now plays a central role in questions pertaining to the design of efficient networks as well as in areas like robotics, computer vision, statistics, coding theory, computer security, and cryptography. By extending the reach of calculation and the potential of the experimental method, ever-more powerful and sophisticated software packages like Maple, Magma and SAGE are transforming the way in which number theorists approach their subject.
The 2010 Winter semester (January 1 April 30) will be devoted to recent developments in number theory with a specific focus on significant practical applications, as well as on the many ways in which the field stands to be affected by the emergence of new software and technologies.