Bryna Kra Gives the Fall 2013 Arnold Ross Lecture in Chicago, Followed by Who Wants to Be a Mathematician
"Thanks again for a terrific event. The contest was great, and the kids are still talking about the lecture. I think Dr. Ross would have been happy to know that such a terrific lecture series encourages kids to do mathematics."
"My students who attended had a great time, and appreciated having Dr. Kra there to speak."
"This is a great opportunity for math students, it certainly was for me and my class. We enjoyed the lecture. It gave me a chance to talk with my students about how math is a living subject (theorems that are not proven yet, or even discovered) and creative and imaginative (most people don't put creativity and math together...) I enjoyed the lectureaccessible to the students, perhaps inspiring for many. And the game was great. Thanks again."
"It was a great time and the kids very much enjoyed it!"
About 150 Chicagoarea high school students and their teachers got the chance to hear about some exciting mathematics during Bryna Kra's Fall 2013 Arnold Ross Lecture, "Patterns and Disorder: How Random Can Random Be?" The lecture took place at Chicago's Museum of Science and Industry on November 7. Following the lecture, eight of the students played Who Wants to Be a Mathematician. Here's a slideshow from the day.
The Arnold Ross Lecture: Patterns and Disorder: How Random Can Random Be?, Bryna Kra, Northwestern University
Arnold Ross Committee Chair Jack Lee (University of Washington), pictured at left, gave an overview of the lecture series and introduced Professor Kra, telling the audience that "the world of mathematics is more deep and mysterious than you ever imagined." In the video below he acknowledges the support of the lecture series by Paul Sally, Jr. (University of Chicago) and introduces Bryna Kra.

Kra began her lecture by giving dictionary definitions of "pattern" and showing examples of periodic and nonperiodic patterns, some of which involved numbers, while others were geometrical.
She then gave definitions of "disorder" and "random" and showed how collectionssuch as the one pictured above rightcould appear to be without order but upon closer inspection they reveal that they do have patterns. After discussing several examples, Kra closed with a theorem and two conjectures. She first cited the MorseHedlund Theorem, which states when a sequence over a finite alphabet (such as {0,1}) is periodic, and noted that no one knows if the theorem extends to twodimensional arrangements of finite alphabets. Kra said that she expects that one of the students in the audience would resolve the conjecture. Then she put up a slide showing a conjecture of Erdős, which says that if A is a sequence of positive integers such that the series formed by taking reciprocals of each term diverges, then the original sequence must contain arbitrarily long arithmetic progressions. The GreenTao Theorem shows that the set of prime numbers satisfies the statement.
During the questionananswer period that followed, a student asked Kra how she got interested in patterns. She responded that her interest stems from a series of lectures on patterns that she heard at Stanford University that were "the most beautiful lectures she'd ever heard."
Who Wants to Be a Mathematician
Following a break in which audience members had the opportunity to consume special AMS 125th anniversary cookies, eight of the students (who were chosen a few weeks earlier) played Who Wants to Be a Mathematician.
Left to right: Bryna Kra, Rileigh Luczak and Lev Kendrick (both from Walter Payton College Prep), Caroline Coughlan (St. Ignatius College Prep), Anton Karpovich and Joanne Lee (Illinois Mathematics and Science Academy), Sam Korsky and Samantha Crowe (Glenbrook North Nigh School), and Andrew Harris (St. Ignatius)
Here are videos of the games:
Lev and Anton (back) answered all the questions correctly in the first game. Caroline (front left) edged ahead of Samantha (front right) on question five, but Samantha regained third place on the next question and finished there at the end. In the tiebreaker, Anton was the first to answer correctly, and thus won $500 from the AMS and a TINspire CX from Texas Instruments.

Game two started like game one, with Andrew and Sam (front) answering all of the first four questions correctly. Sam answered question five correctly, which put him alone in first place at that point. Rileigh (back right) moved into first by answering question seven correctly and held on to win by being the only one to correctly answer question eight. That earned her the same prizes as Anton had earned in game one, and put her in the SquareOff Round against Anton, competing for another $500 and a chance at the $2000 Bonus Question. 
Rileigh and Anton both missed on their first attempt at the question, but Anton was first to be correct on the second try and advanced to the Bonus Round, which was a question about integerlengthed sides of right triangles. Anton had three minutes but didn't need nearly that much time, finishing figuring and thinking in about half the allotted time. The audience was split on the correct answer but Anton was sure and gave a nice explanation of the question and why only one choice could be correct. It was sound reasoning and the choice was indeed correct, bringing Anton's total winnings to $3000.
Here are all the prizes and money won that day.
 TINspire CX from Texas Instruments and $3000 from the AMS: Anton Karpovich
 TINspire CX from Texas Instruments and $500 from the AMS: Rileigh Luczak
 Maple 17 from Maplesoft: Lev Kendrick and Andrew Harris
 Calculus by Anton, Bivens and Davis from John Wiley and Sons: Samantha Crowe and Sam Korsky
 What's Happening in the Mathematical Sciences from the AMS: Caroline Coughlan and Joanne Lee
The AMS thanks sponsors Texas Instruments, Maplesoft, and John Wiley and Sons for their continued generous support of Who Wants to Be a Mathematician. Thanks also to the Chicago Museum of Science and Industry for hosting the event and to Sebrina Williams of the museum who helped arrange everything.
Photographs and videos by Robin Aguiar, AMS Meetings and Professional Services. Text and other photos by AMS Public Awareneness Officer and Who Wants to Be a Mathematician emcee Mike Breen.
Find out more about the Arnold Ross Lecture series and Who Wants to Be a Mathematician.