The purpose of this series of lectures for talented high school mathematics students is to stimulate their interest in mathematics beyond the traditional classroom and to show them the tremendous opportunities for careers in mathematics--as mathematics teachers and as researchers in government, industry, and university programs. The lectures are intended to illustrate some recent development in mathematical research. Read the background behind the Arnold Ross Lectures.

**Henry Cohn**, principal researcher and one of the founding members of Microsoft Research New England, will give the 2014 Arnold Ross Lecture and at The Leonardo in Salt Lake City on Wednesday, November 5, 2014.

(Photo courtesy of Bryce Vickmark)

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What’s the densest sphere packing in a million dimensions?

I’m not going to answer the title question in this talk, because I don’t know the answer. In fact, nobody knows. Instead, we’ll use the packing problem as an excuse to think about high dimensions. The packing problem deals with how efficiently you can cram things into the space you have available. It’s a familiar concept in the three-dimensional world we live in, but it’s not so obvious why anyone would care about four-dimensional packing (let alone a million dimensions). The answer is data: although the physical world is three-dimensional, the world of information can naturally be modeled using much higher dimensions. In this talk, we’ll take a look at why that is, without assuming any prior knowledge of more than three dimensions, and we’ll explore ways of thinking about very high dimensions. Is there any hope of visualizing a million dimensions? Perhaps not, but we’ll try our best in this talk.

**Biography:** Henry Cohn is a principal researcher at Microsoft Research New England, where he was one of three founding members in 2008, and an adjunct professor of mathematics at MIT. He received his Ph.D. from Harvard in 2000 under the supervision of Noam Elkies, after which he joined the theory group at Microsoft Research in Redmond, WA for a year as a postdoc. From 2001 to 2007 he was a researcher at Microsoft Research and affiliate faculty member at the University of Washington. Cohn's research is in discrete mathematics, with interests including discrete geometry, coding theory, cryptography, combinatorics, computational number theory, and theoretical computer science.

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Past Arnold Ross Lectures

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2013 Fall Lecture

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**Bryna Kra** of Northwestern University gave the Fall 2013 Arnold Ross Lecture*, Patterns and Disorder: How Random Can Random Be*? The lecture was held at the Museum of Science and Industry in Chicago, Illinois.* *To read more about her lecture and the Who Wants to Be a Mathematician game click here.

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2013 Spring Lecture

**Erik D. Demaine **of the Massachusetts Institute of Technology gave the Spring Arnold Ross Lecture,* Algorithms Meet Art, Puzzles, and Magic. *The lecture was held at the new** ****Museum of Mathematics** in New York City. To read more about his lecture and the Who Wants to Be a Mathematician game click here.

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2011 Lecture

**Joan P. Hutchinson,** Professor Emerita, Macalester College, gave the Arnold Ross Lecture, *From crayons to color graphics: How mathematicians use color*. The 2011 Lecture was held at the Science Museum of Minnesota in St. Paul.

**Photo courtesy of Macalester College**

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2010 Lecture

**Thomas C. Hales**, Mellon Professor of Mathematics, University of Pittsburgh, gave the 2010 Arnold Ross Lecture, *Can Computers Do Math? * The Lecture was held at the __Carnegie Science Center __in Pittsburgh, Pennsylvania, on Thursday, October 14, 2010. To find out more click here.

**Photo Copyright ©, Pittsburgh Post-Gazette,**

2010, all rights reserved. Reprinted with permission.

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2009 Lecture

**Dana Randall** of the Georgia Institute of Technology, gave the Arnold Ross Lecture, *Domino Tilings of the Chessboard: An Introduction to Sampling and Counting *at the National Science Center/Fort Discovery in Augusta, Georgia, on Thursday, October 29, 2009. Click here to read more of the days events at Fort Discovery.

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2008 Lecture

**David C. Kelly**, Hampshire College, gave the 2008 Arnold Ross Lecture, *From Pascal's Triangle to Sierpinski's Triangle in Base 2* at the Oregon Museum of Science and Industry on Thursday, October 23. To read more click here.

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2007 Lecture

**Barry Mazur**, Harvard University, gave the 2007 Arnold Ross Lecture on *How many prime numbers are there?* at the Museum of Science in Boston, MA on Thursday, November 1. To read more click here.

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2006 Lecture

**Manjul Bhargava**, Princeton University, gave the 2006 Arnold Ross Lecture on* The Mathematics of Rhythm* at the Museum of Science and Industry, Chicago on Tuesday, October 24. To read more click here.

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2005 Lecture

**Kenneth A. Ribet, **University of California, Berkeley, gave the 2005 Arnold Ross Lecture on* **Fermat's Last Theorem and Beyond* at the New York Hall of Science on Thursday, November 3. To read more click here.

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2004 Lecture

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**Elwyn Berlekamp, ** University of California at Berkeley, gave the 2004 Arnold Ross Lecture on *The Dots and Boxes Game: Sophisticated Child's Play* at the St. Louis Science Center on April 21. Following the lecture AMS Public Awareness Officer Mike Breen emceed the "Who Wants To Be A Mathematician" game, during which five talented high school students won a total of $7,000 from the AMS. As a grand finale to the day's events, Berlekamp played many of the high school students in the audience in a simultaneous game of Dots and Boxes. To read more click here.

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2003 Lecture

** ****Paul J. Sally Jr., **University of Chicago, gave the 2003 Arnold Ross Lecture on *Problems in Mathematics from Zero to Infinity* to an enthusiastic crowd of approxomately 250 high school students and teachers. This lecture was further enhanced by a game show that was held after refreshments.

The successful mathematics game show, *Who Wants to be a Mathematician*, was run in conjunction with the lecture by the AMS Public Awareness Office. The exuberant student audience contributed to the atmosphere of excitement and enjoyment as they cheered on the contestants.

Comments from students who attended a recent Arnold Ross Lecture:

"We are three students who attended the recent Arnold Ross Lecture at the Museum of Science and Industry in Chicago and wanted to thank you for bringing the lecture here. It was a great experience and we had a lot of fun.We hope the lecture returns soon."

To read more click here.

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Background

In the late 1980s, with the encouragement of Professor Paul J. Sally, Jr., (1933-2013) of the University of Chicago, the American Mathematical Society instituted a series of lectures aimed at talented high school mathematics students. In 1993, the series was dedicated to Professor Arnold E. Ross of Ohio State University for his many contributions to the development of mathematical and scientific talent.

As chairman of the mathematics department at the University of Notre Dame,** **Dr. Arnold Ross started a mathematics enrichment program for high school teachers in 1947. He started his multi-level summer program for gifted high school students in 1957 and ran it every summer until 2000, giving the number theory lecture each morning.

In keeping with this prestigious tradition, the American Mathematical Society is proud to present the annual Arnold Ross Lecture for talented high school mathematics students. These lectures are sustained, in part, by an endowment established in 1996, by Professor Sally.

This is a time of exciting progress in the mathematical sciences. Mathematical research has stimulated new ideas in many subject areas--computer science, physics, engineering, biology, the behavioral sciences, and other disciplines.

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Committee for Arnold Ross Lectures

**Allan P. Donsig**, *University of Nebraska, Lincoln*

Donald A. Outing, *West Point*

**Glenn Stevens, ***Boston **University*

Peter E. Trapa, **Chair**, *University of Utah *

**For additional information email us by clicking here.**Robin

updated by rha 3-10-14