She's Got Their Number

There's a calculus to knitting. An untamed batch of wool gets twisted and fed into a spinning wheel, a wooden contraption about as high-tech as an abacus, that binds the fibers into a single strand of yarn. That yarn, in turn, is woven into geometric designs comprised of equations: A certain number of rows combined with certain stitches yield something functional and beautiful. In the right hands, knitting produces a precise but almost magical alchemy--chaos into order.

You can see why it would appeal to Brenda Dietrich.

Dietrich, 47, runs the math sciences department at IBM's renowned Thomas J. Watson Research Center--the top math manager at arguably the biggest and most important math department in corporate America. She loves math's beauty and complexity. Yet she often spends conference calls and meetings spinning yarn on the wheel next to her ThinkPad. And she knits incessantly--a scarf, coat, shawl, and hat in progress simultaneously. That exquisite blue and purple cashmere shawl in her office? "This was last year's research software strategy meeting," she says. "I sat in the back row knitting for three days."

Dietrich, who has coauthored 13 patents and has twice been named one of IBM's top inventors, likes to make stuff--tangible stuff, not just theorems. As a mathematician, she has a rare ability to travel between two very different worlds, says Paul Horn, head of IBM research. She can listen to a customer describe the messy details of a business, then translate those specs into math problems for her team to solve. And she thinks mathematicians should live in that real world, the world of customers. When she took over the math department in 2001, she encouraged researchers to venture outside Watson, which she calls "that lovely stone building on the hill," and work with IBM consultants in the field.

These days, her team is, in fact, venturing out from years of behind-the-scenes, mostly theoretical research to tackle an impressive array of real-world issues at IBM and beyond. How to assemble a project team from consultants dispersed around the world. How to fight vast forest fires more effectively. How to identify the best sales leads in the pipeline. OnTarget, sales-prediction software that grew out of math research, generated $100 million in new revenue as a pilot program in Canada. Last year, it delivered about $500 million in worldwide use, a sum that makes Dietrich giggle as if she can't quite believe it.

Dietrich's 160 researchers are, in fact, increasingly among the most valuable problem solvers at IBM. "Historically, the stars here have been the physicists who made the technology that went into chips and systems, and then it was the computer scientists and engineers," Horn says. "Now we're seeing the emergence of mathematicians. They're embedded everywhere." This is partly due to IBM's shift from hardware to software and services. And part of it, certainly, is a function of Dietrich's marketing and political savvy: A geek, but a far cry from the personality- challenged stereotype, she understands how to win attention and resources in an organization of 330,000 people.

More than that, her department's growing impact reflects a bigger real-world shift. A generation ago, businesses called on mathematicians, at best, to optimize production lines and maybe to support pricing decisions. What more could they possibly contribute to the bottom line? Today, companies measure nearly every aspect of what they do, and computers are fast enough to crunch the numbers in time for execs to act on the analysis. In the hands of talented mathematicians, data create an invaluable advantage. Elaborate algorithms reveal a company's inefficiencies and opportunities--unseen bottlenecks in the supply chain or customers' hidden buying patterns. Entire companies--think Google --are being built almost entirely around math. And others, like IBM, are integrating math into operations and decision making in ways never before seen. This is what the Industrial Age must have been like for mechanical engineers. "It's a great time," Dietrich says, "to be a computational mathematician."

A number-theory class at the University of North Carolina at Chapel Hill changed Dietrich's mind about becoming a doctor. Math was a revelation, like hearing music for the first time. "There's structure and symmetry and the most gorgeous theory," she says. "It made me believe in some underlying order in the world."