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.

*Photo by Justin Knight*

Professor Bjorn Poonen, Claude Shannon Professor of Mathematics at MIT will give the 2019 Arnold Ross Lecture at the 45th American Regions Mathematics League (ARML) at

Pennsylvania State University, May 31, 2019.

Can one use geometry to understand the rational number solutions to multivariable polynomial equations? Yes, at least sometimes! As a warm-up, I will show how the geometry of the unit circle explains the parametrization of all Pythagorean triples. Next I will introduce the more complicated case of elliptic curves, for which some of the most basic problems are still unsolved.

Bjorn Poonen is a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society.

He has received the Chauvenet Prize for mathematical exposition, and the MIT School of Science Prize in Undergraduate Teaching. Nineteen mathematicians have completed a Ph.D. thesis under his guidance. Poonen has co-authored/edited three books, including "The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary".

Earlier, he was a four-time Putnam Competition winner, an International Mathematical Olympiad medalist, and the unique perfect scorer out of 385,000 participants in the 1985 AHSME (now called AMC 12). **He competed in ARML during the first three years it was held at Penn State: 1983, 1984, and 1985.**

Professor Tadashi Tokieda, Professor of Mathematics at Stanford University gave the 2018 Arnold Ross Lecture, *A World from a Sheet of Paper, *at the Saint Louis Science Center, St. Louis, Missouri. He started with a sheet of paper which he folded, stacked, crumpled, and sometimes tore. At one point, he demonstrated to the audience how to trisect any angle using paper-folding. To read more and see photos from his talk click here there is also a video of the winner of the Who Wants to Be a Mathematician game that followed.

Professor Ken Ono, Asa Griggs Candler Professor of Mathematics, Emory University was the 2017 Arnold Ross Lecturer at the Orlando Science Center in Florida. Learn more about his talk *"Why does Ramanujan, 'The Man Who Knew Infinity', matter?"*.

*Photo © 2000 Boston University. All rights reserved*

Professor Nancy Kopell, Professor of Mathematics at Boston University gave the 2016 Arnold Ross Lecture at the Fort Worth Museum of Science and History in Fort Worth, Texas. She spoke about *Brain Rhythms in Health and Disease*. Read more about her talk and the other events.

*Photo courtesy of Bryce Vickmark*

Henry Cohn, principal researcher and one of the founding members of Microsoft Research New England, gave the 2014 Arnold Ross Lecture at The Leonardo in Salt Lake City. He asked the question *What’s the densest sphere packing in a million dimensions?*. More about his Lecture and the Who Wants to Be a Mathematician game is available online.

**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. Read more about her lecture and the Who Wants to Be a Mathematician game here.

**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. Read more about his lecture and the Who Wants to Be a Mathematician game here.

*Photo courtesy of Macalester College*

**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 Copyright ©, Pittsburgh Post-Gazette, 2010, all rights reserved. Reprinted with permission.*

**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. Learn more here.

**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. Read more of the days events at Fort Discovery.

**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. Read more here.

*Photo courtesy*

**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. Read more here.

**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. Read more here.

**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. Read more here.

**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. Read more here.

**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.

**Curtis McMullen**, Harvard mathematics professor and 1998 Fields Medalist, spoke on "From Triangles to Infinity." McMullen motivated the talk by asking the audience what path a lion should take to capture a human, if both are in an enclosed ring. A little later in the talk, he asked students in the audience to assemble polyhedra using interlocking triangles, given the constraint that a fixed number of triangles have to meet at each vertex. As the title of the talk suggests, there were many different areas of mathematics touched on by McMullen, including: Fermat's Last Theorem, Zeno's Paradoxes, hyperbolic and spherical geometry, the harmonic series, and tiling. Near the end of his talk, McMullen showed a path that a human could take to elude the lion and used results about infinite series to demonstrate the path's effectiveness. The teachers and students who filled the Boston Museum of Science auditorium thoroughly enjoyed the subject of the talk and the manner in which it was delivered. Many students sought out McMullen after his talk to ask questions, and some even asked for his autograph.

**Mary Ellen Rudin (University of Wisconsin) and John H. Conway (Princeton University)**, The AMS partnered with the St. Louis Science Center on April 3 to present the twelfth in this series of lectures for talented high school mathematics students. Over 125 students and teachers came to hear this year's invited speakers, Mary Ellen Rudin (University of Wisconsin) and John H. Conway (Princeton University).

Professors Rudin and Conway circulated freely among the students and teachers as they arrived, introducing themselves and chatting. One busload came all the way from Breese, Illinois, two hours away! Conway, in his inimitable style, entertained all and challenged some with his sleight of hand using ropes and metal braids.

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.

**For additional information contact Robin at the American Mathematical Society.**

**Robert A. Fefferman,**University of Chicago**Steven Joel Miller,**Chair, Williams College**Ken Ono,**Emory University**Zvezdelina E Stankova**, University of California at Berkeley