The concept of math circle came into being in the erstwhile USSR and Bulgaria, around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age".
[3] The concept of a math circle, on the other hand, with its emphasis on convening professional mathematicians and secondary school students regularly to solve problems, appeared in the U.S. in 1994 with Robert and Ellen Kaplan at Harvard University.
[3] Many of them successfully climbed the academic ladder to secure positions within universities, and a few pioneers among them decided to initiate math circles within their communities to preserve the tradition which had been so pivotal in their own formation as mathematicians.
'Project-based clubs may spend a few meetings building origami, developing a math trail in their town, or programming a math-like computer game together.
Math-rich projects may be artistic, exploratory, applied to sciences, executable (software-based), business-oriented, or directed at fundamental contributions to local communities.
Museums, cultural and business clubs, tech groups, online networks, artists/musicians/actors active in the community, and other individual professionals can make math projects especially real and meaningful.
Increasingly, math clubs invite remote participation of active people (authors, community leaders, professionals) through webinars and teleconferencing software.
Problems considered "good" are easy to pose, challenging to solve, require connections among several concepts and techniques, and lead to significant math ideas.
Robert & Ellen Kaplan, in their book Out of the Labyrinth: Setting Mathematics Free,[6] make a case for this format describing the non-profit Cambridge/Boston Math Circle they founded in 1994 at the Harvard University.
Students in these circles appreciate and start to attain a very special way of thinking in research mathematics, such as generalizing problems, continue asking deeper questions, seeing similarities across different examples and so on.
Club members write and read essays, pose and solve problems, create and study definitions, build interesting example spaces, and investigate applications of their current topic.
More examples of fruitful applied math pathways include history, storytelling, art, inventing and tinkering, toy and game design, robotics, origami, and natural sciences.
As with all tests requiring limited time, the problems focus more on the empirical accuracy and foundations of mathematics work rather than an extension of basic knowledge.