Stephen Colbert cited a Cambridge study that said it isn’t possible, but...
But engineers at Stanford University were unconvinced by the findings. In a new video using technology created in 2014, a member of the school's Biomimetics and Dextrous Manipulation Lab demonstrated that by distributing a person's weight across a number of synthetic adhesive pads, scaling a vertical glass wall is indeed possible.
In the Cambridge study, the school's department of zoology compared the weight and footpad size of more than 200 animals that use adhesive pads to climb surfaces. They found that, because the size of an animal is typically proportional to the size of the sticky pads needed to climb vertical surfaces, a human would need to have 40 percent of its body surface covered in adhesive pads to climb the way that animals like geckos do.
While this may be true, Stanford's adhesive pads are not like the ones found in nature. Each "gecko-inspired climbing device" is made up of 24 adhesive pads, each coated in microscopic saw-tooth shaped polymer structures optimized primarily for flat surfaces. When pulled upon, the pads apply an evenly distributed force to each adhesive tile, causing the saw-tooth polymer structure to flatten and stick with greater strength than a gecko's—but only on "relatively flat, smooth and clean vertical glass" according a paper lead researcher Elliot Hawkes and his co-authors wrote.
Hawkes and co-author Eric Eason stated in 2014 that they believe the technology could be used to help robots lift things like glass panels, or gently latch on to space debris. It's not quite as fun as helping humans scale walls like Spider-Man, but probably more practical.