US Students Win Second Consecutive Math Olympiad

As Americans get hyped for the 2016 Rio Summer Olympics, most people will be completely aloof to the incredible math prowess of American high school students at the premiere math competition in the world. In late July, the United States math team took first place at the 2016 International Math Olympiad in Hong Kong. This was the second consecutive win for the American team, besting competitors from academic math powerhouses like China (Shanghai), South Korea, Singapore, and Japan. The IMO is the pinnacle of math competition for high school mathletes who begin their competitive drive with math contests like the AMC8/10/12, the AIME (American Invitational Math Exam), and the IMO.

Participants were selected through a series of competitions organized by the Mathematical Association of America (MAA), culminating with the USA Mathematical Olympiad. The six team members joined 48 of their peers at Carnegie Mellon University (CMU) in June for three weeks of immersion in problem solving at MAA’s Mathematical Olympiad Summer Program (MOSP). Established in 1974 to train the first U.S. team to the IMO, MOSP has expanded over the years and broadened its goals. 

Perhaps, someday our politicians, billionaire philanthropists, edu-reformers, and the media will seek to promote academic competition as a way of elevating the stature of education in this country. For a country obsessed with media coverage exposing weaknesses of American schools, there is almost no media coverage of the incredible successes our students achieve. Imagine if young students were offered and encouraged to pursue scholarship opportunities in competitive math or science or speech/debate. Wouldn't it be incredible progress to promote media coverage of academic college signings as much as athletic. Nearly all the mathletes will use their skills professionally - almost no athletes will. 

Just one more example of how in America we are ignoring our best and brightest.

This year’s IMO featured an unusually large number of non-standard problems which combined multiple areas of mathematics into the same investigation. The most challenging problem turned out to be #3, which was a fusion of algebra, geometry, and number theory. On that question, the USA achieved the highest total score among all countries, ultimately contributing to its overall victory — a historic repeat #1 finish (2015 + 2016), definitively breaking the 21-year drought since the last #1 finish in 1994, and the first consecutive #1 finish in the USA’s record.

Let’s give it a try. Here’s IMO 2016 Problem 3:

Let P = A₁ A_{2 …} A_k be a convex polygon on the plane. The vertices A_1, A_{2, …,} A_k have integral coordinates and lie on a circle. Let S be the area of P. An odd positive integer nis given such that the squares of the side lengths of P are integers divisible by n. Prove that 2S is an integer divisible by n.