It's easy to miss the mirror forge at the University of Arizona. While sizable, the Richard F. Caris Mirror Laboratory sits in the shadow of the university's much larger 56,000-seat football stadium. Even its most distinctive feature—an octagonal concrete prominence emblazoned with the school's logo—looks like an architectural feature for the arena next door. But it's that tower that houses some of the facility's most critical equipment.

Inside the lab, a narrow, fluorescent-green staircase spirals up five floors to the tower's entrance. I'm a few steps from the top when lab manager Stuart Weinberger asks, for the third time, whether I have removed everything from my pockets.

"Glasses, keys, pens. Anything that could fall and damage the mirror," he says. Weinberger has agreed to escort me to the top of the tower and onto a catwalk some 80 feet above a mirror 27.5 feet in diameter. A mirror that has already taken nearly six years—and $20 million—to make. "Most people in the lab aren't even allowed up here," he says. That explains Weinberger's nervousness about the contents of my pockets (which are really, truly empty), and why he has tethered my camera to my wrist with a short line of paracord.

The view of GMT's second mirror segment from the top of the Mirror Lab's test tower. Robbie Gonzalez

The disc of glass below me is one of seven mirrors that will eventually comprise the Giant Magellan Telescope. When it turns on in full force in 2025, at Las Campanas Observatory in Chile's Atacama Desert, the GMT will be the largest optical observatory in the world. Its mirrors, each of which weighs roughly 17 tons, will be arranged in a flower-petal configuration, with six asymmetrical mirrors surrounding a central, symmetrical segment. Together, they will span some 80 feet (twice the diameter of existing optical telescopes) and possess a total area of 4,000 square feet (about the area of two singles tennis courts). With a resolving power 10 times that of the Hubble Space Telescope, the GMT is designed to capture and focus photons emanating from galaxies and black holes at the fringes of the universe, study the formation of stars and the worlds that orbit them, and search for traces of life in the atmospheres of habitable-zone planets.

But before GMT can do any of that, the scientists and engineers at the Mirror Lab need to manufacture these colossal slabs of glass. And doing so, as you might expect, is a truly monumental task.