[3] These events explore ideas and developments in recreational mathematics, magic, illusion, puzzles, philosophy, and rationality, and foster creative work in all of these areas by enthusiasts of all ages.

[4] Martin Gardner's prolific output as a columnist and writer—he authored over 100 books between 1951 and 2010—put him in contact with a large number of people on a wide range of subjects from magic, mathematics, puzzles, physics, philosophy, logic and rationality, to G. K. Chesterton, Alice in Wonderland, and the Wizard of Oz.

[8] In 2007 board members Rodgers, Berlekamp, Setteducati, Thane Plambeck, and Scott Hudson de Tarnowsky decided that G4G should broaden its reach and expand the scope of its educational programs.

The 14th Gathering took place in April 2022 (delayed for 2 years because of the COVID-19 pandemic) and was a hybrid event, with some participants joining remotely as speakers and audience members.

Another tradition held at these off-site events was the directed community building of original mathematical sculptures under the leadership of George Hart, Chaim Goodman-Strauss and others.

[15] These CoMs vary in size from three people meeting to perform rubber-band magic for each other, to crowds of hundreds of students in highly organized exploratory paper folding activities.

[16] Resources to assist with hosting events are provided through the organization's website, or participants can also just perform a magic trick, or share a puzzle or recreational mathematics problem with friends.