The puzzle that Daubechies solved was how to take a recent wavelet advance — a thing of beauty, by the French mathematicians Yves Meyer and Stéphane Mallat, but technically impractical — and make it amenable to application. To “put it on its head,” Daubechies would say, but without making it ugly. As she said in the Guggenheim statement: “It is something that mathematicians often take for granted, that a mathematical framework can be really elegant and beautiful, but that in order to use it in a true application, you have to mutilate it: Well, they shrug, That’s life — applied mathematics is always a bit dirty. I didn’t agree with this point of view.”
By February 1987, she constructed the foundation for what grew into a “family” of Daubechies wavelets, each suited to a slightly different task. One key factor made her breakthrough possible: For the first time in her career, she had a computer terminal at her desk, so she could easily program her equations and graph the results. By that summer, Daubechies wrote up a paper and, sidestepping a hiring freeze, secured a job at AT&T Bell Labs. She started in July and moved into a house recently bought with Calderbank, whom she married after popping the question the previous fall. (Calderbank had made it known there was a standing offer, but he resisted proposing out of respect for Daubechies’ declared opposition to the institution of marriage.)
The ceremony was in May in Brussels. Daubechies cooked the entire wedding dinner (with some help from her fiancé), a Belgian-British feast of chicken with endive and Lancashire hotpot stew, chocolate cake and trifle (among other offerings) for 90 guests. She had figured that 10 days of cooking and baking would be manageable, only later to realize that she had neither enough pots and pans for the preparation nor refrigerator space for storage, not to mention other logistical challenges. Her algorithmic solution went as follows: Have friends lend her the necessary vessels; fill said vessels and pass them back for safekeeping in their fridges and for transport to the wedding. She encouraged the more gourmand guests to bring hors d’oeuvres instead of presents. Her mother, putting her foot down, bought an army of salt-and-pepper shakers.
Daubechies continued her wavelets research at AT&T Bell Labs, pausing in 1988 to have a baby. It was an unsettling and disorienting period, because she lost her ability to do research-level mathematics for several months postpartum. “Mathematical ideas wouldn’t come,” she says. That frightened her. She told no one, not even her husband, until gradually her creative motivation returned. On occasion, she has since warned younger female mathematicians about the baby-brain effect, and they have been grateful for the tip. “I could not imagine that I would ever have trouble thinking,” Lillian Pierce, a colleague at Duke, says. But when it happened, Pierce reminded herself: “OK, this is what Ingrid was talking about. It will pass.” Daubechies’ female students also mention their gratitude for her willingness to push for child care at conferences, and sometimes even to take on babysitting duties herself. “My adviser volunteered to entertain my toddler while I gave a talk,” a former Ph.D. student, the Yale mathematician Anna Gilbert, recalls. “She seamlessly included all aspects of work and life.”
In 1993, Daubechies was appointed to the faculty at Princeton, the first woman to become full professor in the mathematics department. She was lured by the prospect of mingling with historians and sociologists and their ilk, not only electrical engineers and mathematicians. She designed a course called “Math Alive” aimed at nonmath and nonscience majors and gave talks for the general public on “Surfing With Wavelets: A New Approach to Analyzing Sound and Images.” Wavelets were taking off in the real world, deployed by the F.B.I. in digitizing its fingerprint database. A wavelet-inspired algorithm was used in the animation of films like “A Bug’s Life.”
“The Daubechies wavelets are smooth, well balanced, not too spread out and easy to implement on a computer,” Terence Tao, a mathematician at the University of California, Los Angeles, says. He was a Princeton grad student in the 1990s and took courses from Daubechies. (He won the Fields Medal in 2006.) Daubechies wavelets, he says, can be used “out of the box” for a wide variety of signal-processing problems. In the classroom, Tao recalls, Daubechies had a knack for viewing pure math (for curiosity’s sake), applied math (for practical purpose) and physical experience as a unified whole. “I remember, for instance, once when she described learning about how the inner ear worked and realizing that it was more or less the same thing as a wavelet transform, which I think led to her proposing the use of wavelets in speech recognition.” The Daubechies wavelet propelled the field into the digital age. In part, wavelets proved revolutionary because they are so mathematically deep. But mostly, as Calderbank notes, it was because Daubechies, a tireless community-builder, made it her mission to construct a network of bridges to other fields.
In due course, the awards began piling up: The MacArthur in 1992 was followed by the American Mathematical Society Steele Prize for Exposition in 1994 for her book “Ten Lectures on Wavelets.” In 2000 Daubechies became the first woman to receive the National Academy of Sciences award in mathematics. By then she was mothering two young children. (Her daughter, Carolyn, 30, is a data scientist; her son, Michael, 33, is a high school math teacher on Chicago’s South Side.) And by all appearances she was handily juggling it all.