This month, the Abel Prize was awarded to Karen Uhlenbeck, who is the first woman to receive the award. Uhlenbeck pioneered the field of geometric analysis, and developed techniques now commonly used by many mathematicians. “She did things nobody thought about doing,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee, “and after she did, she laid the foundations of a branch of mathematics.” Learn more about Uhlenbeck and her work at nytimes.com.