In the late 1920s, Ullman began mountain climbing during his vacations from Princeton University. In Switzerland, he climbed the Matterhorn and the Jungfrau. He also climbed Popocatepeti in Mexico and the Grand Teton in Wyoming, the latter of which he considered the most challenging. Later, when he returned to school, he participated in events such as the Ivy Race and the Ice Capades. After graduating from Princeton in 1930, Ullman joined an expedition to Mount Everest led by George Mallory. The team attempted to be the first to reach the top of the world but disappeared without a trace while searching for a way through the Western Cwm. This incident inspired Ullman to begin climbing more seriously. He traveled to Canada's Rockies, where some of the best rock climbing in North America can be found. Here, Ullman met up with other climbers including Earl Bates, Alfred Hayes, and Lawrence Josephson, who would become good friends. They discovered many beautiful spots where they could practice their skills, among them Mount Assiniboine and Mount Rundle. Ullman also visited Alaskan mountains where he became friendly with Harry Karstens who invited him to join an expedition to K2. The pair planned to climb the highest mountain in each of the seven continents, with help from others. However, financial difficulties prevented them from going ahead with the plan. Nevertheless, this experience helped Ullman develop his skills as a leader.