The Math Circle
This is the home page of The Math Circle, a program of courses founded in 1994, designed for students who enjoy math and want the added challenge of exciting topics that are normally outside the school curriculum. Its teachers are experienced, committed, and enthusiastic. Our classes encourage a free discussion of ideas; while the courses are mathematically rigorous, the atmosphere is friendly and relaxed.
Fall 2014Spring 2015 Schedule Information is available!
The Math Circle is delighted to announce that it has received $50,000 from the Flom Family Foundation. This very generous grant will be used to establish a pilot Math Studio in South Bend, Indiana.
The intention is to spread The Math Circle's approach more broadly in a community by establishing a place where people of all ages and backgrounds can experience the exhilaration of mathematical exploration. Although some students may first come to get homework help, the Studio will provide participants with pathways to deeper engagement in mathematics. Sympathetic mentors will help them overcome obstacles and foster their love of mathematics, as they gain confidence with their growing competence in a noncompetitive, collegial, conversational atmosphere.
This pilot program, run by Amanda Serenevy, will allow us to test our techniques, iron out problems, and see how to develop Math Circle Studios and DropIn Centers across the country.
Math Circle Summer Teacher Training Institute
We will hold our eighth Math Circle Summer Teacher Training Institute on the Campus of Notre Dame, in South Bend Indiana, from June 27th to July 1st, 2016.
We will have demonstrations of our approach, practice sessions in running Math Circles, discussions of theory and practice, and conversations about selected math topics. Participants will work with children in 1st through 12th grades each afternoon to try out their own Math Circle ideas.
Tuition is $850 for the week, room and board included.
Inquiries can be made by email to kaplan@math.harvard.edu.
Our
Philosophy

"What you have been obliged to discover
by yourself leaves a path in your mind
which you can use again when the need
arises." G. C. Lichtenberg
[learn more...]
Recent Courses

Sunday
 Elliptic Curves (Notes: 12 3 4)
 Set Theory (Notes: 12 3 4 57)
 The Four Numbers Game (Notes: 1 2 3 4 5)
 Constructing the Real Numbers (Notes: 1 2 3 4)
 Group Theory, Topology, and Physics
 Quantum Mechanics
 Computational Complexity Theory
 NonEuclidean Geometry
Weekday
 Are There Numbers Between Numbers?
 Probability
 The Pythagorean Theorem
 Continued Fractions
 Random Walks
 Graph Theory
Our classes begin with a free discussion of ideas and play of invention around a developing problem; then  once insight blossoms  we link this insight formally to axioms, aiming for elegance and clarity. While the courses are mathematically rigorous, the atmosphere is friendly and relaxed. We want our students to feel free to express their ideas, to suggest their own approaches, and to make mistakes. We work in a spirit of friendship, cooperation, and enjoyment of one another.
Where are our courses located?
schedule
Problems of the Week
 Is there a last prime?
 Are there more decimals than fractions?
 What proportion of the powers of two begin with a "7"?
 What is i^{i}?
 Is n × (n1)+ 41 a prime for every whole number n?
 Can you trisect any angle with straightedge and compass?
 What's a geometry like with no parallel lines?
 Can a polyhedron have an odd number of faces with an odd number of sides?
 A soccer ball is made of pentagons and hexagons, with three edges meeting at each vertex. Why MUST the number of pentagons used be twelve?
 Can you tile a square with squares all of different sizes?
 Which numbers are the sum of two squares?
 Which numbers whose digits are all equal are prime?
 more problems...