The puzzle the Daubechies solved was how to take a recent wavelet advance – a thing of beauty, but technically impractical – by French mathematicians Yves Meyer and Stephan Mallat and make it amenable to application. To “turn it on its head”, the Daubechies would say, but without making it ugly. As he said in Guggenheim’s statement: “It is something that mathematicians often take for granted, that a mathematical framework may indeed be elegant and beautiful, but that to use it in a true application, you must distort it.” Gotta do: Well, they shrink, that’s life – applied math is always a little dirty. I didn’t agree with that point of view.”
By February 1987, they had built up the foundation for what had evolved into a “family” of Daubechies waves, each suited to a slightly different function. A major factor made his success possible: for the first time in his career, he had a computer terminal on his desk, so he could easily program his equations and graph the results. By that summer, Daubechies had written a paper and, bypassing a hiring freeze, secured a job at AT&T Bell Labs. She started in July and recently moved into a house she bought with Calderbanks, who she married last fall after the question popped up. (Calderbank had pointed out that there was a permanent proposal, but he opposed the proposal of Dubucci’s declared opposition to the institution of marriage.)
The ceremony was in Brussels in May. The Daubechies cooked the entire wedding dinner (with the help of their fiancée), a Belgian-British feast of chicken with endive and Lancashire hotpot stew, chocolate cake and trifle (among other offerings) for 90 guests. She thought 10 days of cooking and baking would be manageable, only to realize later that she had neither enough pots and pans for preparation nor refrigerator space for storage, not to mention other logistical challenges. Not there. His algorithmic solution was as follows: Have friends lend him the utensils he needs; Fill the said utensils and send them back for safe keeping in their fridge and transport to the wedding. She encouraged more gourmet guests to bring hors d’oeuvres instead of gifts. His mother bought an army of salt-pepper shakers with her foot down.
Daubechies continued her Wavelet research at AT&T Bell Labs stopped in 1988 to produce a baby. It was a disturbing and disorienting period, as she lost her ability to do research-level math for several months after delivery. “Mathematical ideas won’t come through,” she says. This scared her. She didn’t tell anyone, not even her husband, until her creative inspiration slowly returned. On occasion, she has since warned young female mathematicians about the baby-brain effect, and is grateful for the tip. “I couldn’t imagine I’d ever have trouble thinking about it,” says Lillian Pierce, an aide to Duke. But when it did, Pierce reminded himself: “Well, that’s what Ingrid was talking about. This will end.” Daubechies’ female students also mention their gratitude for their willingness to emphasize child care at conventions, and sometimes for taking care of the children themselves. A former Ph.D. student, Yale mathematician Anna Gilbert, recalls. “It covers all aspects of work and life seamlessly.”
In 1993, Dubechis was appointed to the Faculty of Princeton, becoming the first woman to become a full professor in the Department of Mathematics. She was attracted not only by the prospect of mingling with electrical engineers and mathematicians, historians and sociologists, and people like her. He designed a course called “Math Alive” aimed at nonmath and nonscience majors and talks “Surfing with Wavelets: A New Approach to Analyzing Sounds and Images” for the general public. Wavelets were just starting out in the real world being deployed by the FBI to digitize its fingerprint database. A wave-inspired algorithm was used in the animation of films such as “A Bug’s Life”.
“Doubachy wavelets are smooth, well-balanced, not too stretched and are easy to implement on a computer,” Terence Tao, mathematician at the University of California, Los Angeles. He was a graduate student at Princeton in the 1990s and took courses from Dubechies. (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, the Daubechies had a knack for seeing pure mathematics (for the curiosity), applied mathematics (for practical purposes) and physical experience as a unified whole. “I remember, for example, once he described learning about how the inner ear works and realizing that it was more or less akin to a wavelet change, which led me to think he had a speech. proposed the use of waves in detection.” The Daubechies wavelet propelled the field into the digital age. In part, wavelets proved to be revolutionary because they are mathematically very deep. But mostly, as Calderbank notes, it was because Dubachez, a tireless community-builder, made it his mission to build a network of bridges in other areas.
Over time, prizes began to accumulate: in 1992 MacArthur was awarded the American Mathematical Society Steel Prize for Exposition in 1994 for his 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 had become the mother of two young children. (His 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 doing it all with ease.