Since its founding in 2003 by Margaret Wertheim and Christine Wertheim the IFF has staged public lectures in Los Angeles and New York on subjects such as tiling patterns, hyperbolic space, early computational devices, and tensegrity structures. The Welsh writer Merrily Harpur has written that "the duty of artists everywhere is to enchant the conceptual landscape." The IFF was founded on the principle that science, mathematics and other techno-logical pursuits may also achieve this goal.
In spring 2006 a lecture series at Telic Arts Exchange in Los Angeles, entitled The Insect Trilogy, presented leading zoologists talking about how flies fly, how spiders see, and the ecology of a termite's gut. In New York, the Institute co-hosts events with Cabinet magazine, an international arts and culture quarterly. The IFF organizes and participates in exhitions at museums and art galleries. Exhibitions have included Crocheting the Hyperbolic Plane at Machine Project in Los Angeles and Philosophical Toys at apexart in New York, (co-curated by Sina Najafi of Cabinet.) The latter show included the drawings and models of Shea Zellweger an outsider logician who has spent the past 50 years exploring the geometric relationships underlying in modern logic. Dr. Zellweger's work is the subject of an exhibition curated by the Institute at the Museum of Jurassic Technology opening March 2007.
In August 2006 the IFF curated an exhibition on the Business Card Menger Sponge, a giant origami fractal made by engineer Jeannine Mosely. Assembled from 66,048 business cards, Dr. Mosely's sponge is a material manifestation of a Level 3 fractal called the Menger sponge - the first three dimensional fractal mathematicians became aware of, discovered in 1926 by Karl Menger
A recent highlight of the IFF's work was the exhibition "Inventing Kindergarten" at the Williamson Gallery, Art Center College of Design. Based on the radical educational system invented by the nineteenth century German crystallographer Friedrich Froebel, the exhibition presented works from the collection of writer/collector Norman Brosterman.
For the past two years much of the IFF's energy has been going into the creation of a vast crocheted coral reef, based on the techniques of hyperbolic crochet discovered by mathematician Daina Taimina of Cornell University. In spring 2007, the first sub-reefs of the IFF's overall Hyperbolic Crochet Coral Reef were exhibited at the Andy Warhol Museum in Pittsburg as part of the exhibition Six Billion Perps Held Hostage: Artists Reflect on Global Warming. In Fall 2007, the full Crochet Reef was exhibited at the Chicago Cultural Center, in association with the Chicago Humanities Festival, and in Spring 2008 it was the subject of two exhibitions in New York, one in the Broadway Windows at NYU, the other at the Winter Garden at the World Financial Center. During Summer 2008 the Reef will be shown at the Hayward Gallery in London. The crochet reef project is an interdisciplinary marriage of non-euclidean geometry, marine ecology, environmental activism, feminine handicraft and collective feminist practice. Just as living reefs propagate by sending out spawn, so too the crochet reef reproduces through an almost organic process - inspired by the efforts of the IFF, citizens of Chicago and New York have created their own Sister City Reefs, another of which is currently under construction in London.
The IFF has an active publication program, including an ongoing relationship with Cabinet. Each issue of the magazine carries articles and interviews related to IFF lectures and other topics of interest. The Institute publishes books related to its lecture and exhibition subjects - including its "field guide" series such as The Field Guide to Hyperbolic Space and the Field Guide to the Business Card Menger Sponge. The organization's acronym – IFF – is the symbol for the logical operation "if and only if" and expresses in three symbols the Institute's guiding ethos.