What is a Math Circle?

### Math circles are enrichment programs for participants to investigate math non-competitively. For pre-college students this generally means studying mathematics not in the standard school curriculum, for example:

#### Graph theory, a college math subject with many problems that are accessible to kids of all ages. “Can you walk and cross all of the bridges once without going over any bridge twice?” While the content is advanced, in practice it’s hands on. Draw a picture and try to figure out the puzzle–that experience becomes the basis for a rich mathematical conversation.

#### Problem solving in Number Theory: 15 cookie jars are labeled 1 to 15, and the number on the outside of the jar gives the number of cookies on the inside. On a ‘turn’ you can take the same number of cookies out of any number of jars that you like–but you have to take exactly that number (you can’t take 5 cookies from a jar that has only 3 cookies!) What’s the fewest number of turns it takes to empty the jars?

#### The Pigeon Hole Principle, an elementary idea that can be applied in many different contexts, but is not an explicit part of what is studied in schools. “Must there exist two people on earth with the same number of hairs on their head?” Math circle students learn that questions that seem impossible to resolve can have simple explanations, and, more importantly, the related thinking can be applied to many other problems!

#### Questions like these engage students and give them entry into the deep ideas of mathematics and push them to begin to actively pursue their own mathematical research.

#### The Math Circles of Chicago focus on grades 5-12. MC^{2} is committed to providing enrichment for children throughout Chicago. Ultimately we seek to provide circles located citywide for any student interested in pursuing mathematics beyond the classroom. We also manage QED, the Chicago Youth Math Symposium.

#### Math Circles: A Brief History

Math circles have been in existence for about a century, originating in Bulgaria and Russia. A significant number of mathematics professors in these countries had formative experiences in math circles. Their history in the US goes back about 35 years, and prominent Math Circles in America include those at Berkeley and UCLA.

In Chicago, the Payton Math Circle was founded in 2011. Teachers from several schools in the city (Payton, Whitney Young, Kelly, Lindblom, Skinner North, etc.) have led sessions there, along with graduate students and faculty from Chicago’s universities. Payton’s circle serves students in 5th to 12th grades in nine separate groups, and meets on Saturdays throughout the year. In 2012, a new circle was founded at Audubon Elementary School, which moved to Lane Tech at the start of the 2014 school year. In 2014 a third circle was opened in Chicago’s Bridgeport neighborhood. These latter two sites host middle school students and were an outgrowth of the efforts of doctoral students in UIC’s Mathematics Department.

In 2015 the Math Circles of Chicago introduced two new sites. In Pilsen we partner with the Gads Hill Center. We’ve partnered with the Young Scholars Program in order to help maintain their Academic Year program at the University of Chicago (the YSP summer program is popular with many motivated math students in the metropolitan area). The UChicago YSP Math Circle serves 5th to 12th graders, and meets on Saturdays.

In 2017 and 2018 MC2 added after school sites for middle schoolers at Infinity High School in Little Village and Morgan Park High School. In the fall of 2019 MC2 added Back of the Yards, with a Saturday site serving 5th-12th graders.

In the spring of 2020, MC2 quickly transition to offering online sessions in the advent of Covid-19. This fall all of our sites are moving online for the time being. Once we are back in person, we will continue to maintain an ‘Online Site’, which will be our 9th ‘Location’ in the future.

MC2 has held free summer camps since 2017. In 2020 our 6 camps were held online, including a high school camp which was led by the prominent mathematician Eugenia Cheng.

In the interest of promoting school aged students to do independent mathematical research, QED, Chicago’s Youth Math Symposium was created in 2013. This annual event is also sponsored by the Math Circles of Chicago, and is held in December. The spirit of QED is much like that of a science fair, with math students producing extended mathematical research, often based on extensions of problems they have studied in the classroom or in a mathematics competition.

In 2019 MC2 piloted ‘Math Circles in a Box’ (MC2iaB) at Little Village Academy and Goudy Elementary School. MC2 sessions were held in the afterschool programs at these two schools. The pilot was extremely successful, and in the 2020-2021 we plan to open 15 such MC2iaB sites, generally in Back of the Yards, Little Village, and Austin.