For many students, calculus is both a brave new world of mathematical challenge and also the very last math class they will ever take. And yet, calculus itself is almost 200 years old. How can it be that most people, even some of the most educated, are missing over 200 years of discoveries in mathematics? Diane Hoffoss, PhD, professor of mathematics at University of San Diego (USD) and lead creator of the art piece *Unfolding Humanity*, wants to change the way we think about math.

“I don’t think many people have a sense that mathematics is always growing and there are a million things we don’t know. There is a lot of activity and growth and discovery all the time.”

Hoffoss researches topology at USD, which is the study of the shapes of objects disregarding distortion. “Imagine looking at a shape made of rubber, that can be squeezed and deformed, and then trying to understand fundamental aspects of that object.” Her interest in topology helped inspire *Unfolding Humanity*, an art sculpture meant to bring mathematics to life.

The sculpture is 12 ft tall and built from twelve pentagonal faces, forming a dodecahedron. These faces are meant to unfold, at least partially, to allow a viewer to enter the inside of the shape. While the outside is illuminated in “raining matrix characters” and LED lighting, the inside is composed entirely of mirrors that create an infinity effect with even more LEDs that act like stars. The sculpture was built jointly at San Diego CoLab and on USD campus with the help of almost 50 volunteers, including many USD undergraduates. *Unfolding Humanity* is meant to engage viewers with three modern questions in mathematics.

The first point originated almost 500 years ago with the artist Albrecht Dürer, who asked: can every convex polyhedron, or object composed of flat polygons, be cut along some of its edges so that it unfolds flat without overlap? So far, every polyhedron investigated has led to a positive answer. “Just because every shape you’ve *tried* works, doesn’t mean *everything* will work,” says Hoffoss, noting that modern geometers still consider the problem unsolved.

The dodecahedral shape of *Unfolding Humanity* is meant to unfold completely into a single, flat surface per Dürer’s conjecture. Viewers are thus asked to consider how a seemingly simple question of geometry can still elude modern mathematicians even 500 years later.

The second inspiration for *Unfolding Humanity* comes from cosmology, which in part studies the expansion of the universe to determine its shape. Is it finite or infinite? Flat or curved? This is a question of active research in the world of mathematics and astrophysics. It has implications not only for the Big Bang, but also for the eventual end of the universe as we know it. If the universe is curved and finite, it could form a sphere that would eventually collapse in on itself in a “big crunch”. If it is flat and infinite, it would expand forever until slowing to a complete stop in a “big freeze.” Most calculations suggest the latter.

However, new data from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP), which measures background radiation in the universe, could be interpreted otherwise. In fact, a paper published in *Nature* in 2003 proposed that all current data could be explained if the universe is actually shaped like a dodecahedron. That would mean that the universe is finite and curved, a paradigm very different from the current model.

While inside *Unfolding Humanity*, viewers can have the experience of entering into the seemingly infinite, repeating space of a dodecahedron shaped mirror room and ponder the question of the shape of the universe for themselves.

Finally, *Unfolding Humanity* asks the viewer to consider the role that technology plays in or interactions with both mathematics and each other. What does it mean that a mathematical shape illuminated with “raining matrix characters” can isolate us entirely from the surrounding world? Is there a way to use mathematics and modern discovery to bring us all together instead of driving us apart? Hoffoss hopes that the piece will allow each viewer to answer that for themselves.

*Unfolding Humanity *debuted at Burning Man 2018 outside of Gerlach, NV in August. The event drew close to 90,000 participants, all of whom were free to explore the art in any capacity they chose. Hoffoss was overwhelmed by how well the project was received. “It was always busy with people and it inspired such play!” She describes viewers pretending that it was a rocket ship about to blast off, doing magic tricks inside, and trying to figure out how to open and close the dodecahedron.

“One guy said he spent six hours inside one night, just talking to people as they came by. When he was alone, he felt introspective because of all the mirrors. Then he would have very deep and soul-opening conversations with people who stopped in to join him.”

*Unfolding Humanity* will be available for view at Maker Faire San Diego on the plaza of the Old Globe Theatre October 6^{th} and 7^{th}, 2018. While Maker Faire technically ends at 6pm, be sure to come by after dark to see the structure fully illuminated.