The godmother of digital images
The conundrum Daubechies solved was how to take a recent breakthrough in wavelets – a thing of beauty, by French mathematicians Yves Meyer and Stéphane Mallat, but technically impractical – and make it susceptible to application. To “put it on the head,” Daubechies would say, but without making it ugly. As she put it in Guggenheim’s statement: “This is something mathematicians often take for granted, that a mathematical framework can be really elegant and beautiful, but that to use it in a real application you have to maim it: Well they shrug, that’s life – applied math is always a little dirty. I did not agree with this point of view.
In February 1987, she laid the groundwork for what has become 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, which made it easy for her to program her equations and graph the results. That summer, Daubechies wrote an article and, bypassing a hiring freeze, got a job at AT&T Bell Labs. She started in July and moved into a recently purchased house with Calderbank, whom she married after asking the question the previous fall. (Calderbank had made it known there was a standing offer, but he resisted the proposal out of respect for Daubechies’ stated opposition to the institution of marriage.)
The ceremony took place in May in Brussels. Daubechies prepared the whole wedding dinner (with the help of her fiance), a Belgian-British feast of chicken with endive and Lancashire hotpot stew, a chocolate cake and a trifle (among others) for 90 guests. She had thought that 10 days of cooking and baking would be manageable, only later to realize that she didn’t have enough pots and pans for prep or fridge space for storage, let alone ‘other logistical challenges. His algorithmic solution was as follows: ask friends to lend him the necessary containers; fill the said containers and return them to be kept in a safe place in their refrigerators and for transport to the wedding. She encouraged more foodie guests to bring appetizers instead of gifts. His mother, setting foot on land, bought an army of salt and pepper shakers.
Daubechies pursued her wavelet research at AT&T Bell Labs, stopping in 1988 to have a baby. It was a troubling and disorienting time, as she lost her ability to do research-level math for several months after giving birth. “The mathematical ideas would not come,” she said. It frightened him. She didn’t tell anyone about it, not even her husband, until her creative motivation gradually returned. On occasion, she has since warned young mathematicians about the baby-brain effect, and they’ve been grateful for the advice. “I couldn’t imagine that I would have a hard time thinking,” said Lillian Pierce, a colleague of Duke. But when it happened, Pierce remembered, “OK, that’s what Ingrid was talking about. It will pass. ”The Daubechies students also mention their gratitude for her willingness to lobby for childcare at conferences, and sometimes even take on childcare duties herself.” My advisor s ‘volunteered to entertain my little one while I gave a lecture, “said former Ph.D. student, Yale mathematician Anna Gilbert, recalls.” She seamlessly integrated all aspects of the job and life.”
In 1993, Daubechies was appointed to the Faculty of Princeton, the first woman to become a full professor in the Department of Mathematics. She was drawn to the prospect of mingling with historians and sociologists and their ilk, not just electrical engineers and mathematicians. She has designed a course called “Math Alive” for non-mathematics and non-scientists and has lectured for the general public on “Surfing With Wavelets: A New Approach to Analyzing Sound and Images”. Wavelets were taking flight in the real world, deployed by the FBI in scanning its fingerprint database. An algorithm inspired by wavelets has been used in the animation of films such as “A Bug’s Life”.
“Daubechies wavelets are smooth, well balanced, not too spread out and easy to process on a computer,” says Terence Tao, mathematician at the University of California, Los Angeles. He was a Princeton graduate student in the 1990s and took classes at 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 mathematics (out of curiosity), applied mathematics (for practical purposes), and physical experience as a unified whole. “I remember, for example, a time when she described learning how the inner ear works and realizing that it was more or less the same as a wavelet transformation, which I think led her to propose the use of wavelets in speech recognition. ” The Daubechies wavelet propelled the field into the digital age. In part, wavelets have proven to be revolutionary because they are mathematically so deep. But above all, as Calderbank notes, it is because Daubechies, a tireless community builder, has made it her mission to build a network of bridges to other areas.
In due course, the rewards began to pile up: the MacArthur in 1992 was followed by the American Mathematical Society’s Steele Exhibition Award in 1994 for his book “Ten Lectures on Wavelets.” In 2000, Daubechies became the first woman to receive the National Academy of Sciences Prize in Mathematics. At that time, 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 the South Side of Chicago.) And by all appearances, she was juggling it all.