There'due south a calculus to knitting. An untamed batch of wool gets twisted and fed into a spinning cycle, a wooden contraption about equally 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 sure number of rows combined with certain stitches yield something functional and beautiful. In the right hands, knitting produces a precise merely near magical abracadabra–chaos into gild.

Yous tin see why information technology would appeal to Brenda Dietrich.

Dietrich, 47, runs the math sciences department at IBM's renowned Thomas J. Watson Enquiry Center–the top math director at arguably the biggest and virtually of import math department in corporate America. She loves math'south dazzler and complexity. Nonetheless she oft spends conference calls and meetings spinning yarn on the cycle adjacent to her ThinkPad. And she knits incessantly–a scarf, coat, shawl, and hat in progress simultaneously. That exquisite blue and royal cashmere shawl in her office? "This was last year's research software strategy meeting," she says. "I sat in the back row knitting for iii days."

Dietrich, who has coauthored thirteen patents and has twice been named one of IBM'south top inventors, likes to make stuff–tangible stuff, non just theorems. As a mathematician, she has a rare ability to travel between two very different worlds, says Paul Horn, caput of IBM inquiry. She can listen to a client describe the messy details of a business organization, then translate those specs into math issues 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 section in 2001, she encouraged researchers to venture outside Watson, which she calls "that lovely rock building on the colina," and work with IBM consultants in the field.

These days, her team is, in fact, venturing out from years of behind-the-scenes, more often than not theoretical research to tackle an impressive array of real-world issues at IBM and beyond. How to assemble a project squad from consultants dispersed effectually the globe. How to fight vast woods fires more than effectively. How to identify the all-time sales leads in the pipeline. OnTarget, sales-prediction software that grew out of math enquiry, generated $100 million in new revenue as a pilot plan in Canada. Last year, information technology delivered about $500 million in worldwide use, a sum that makes Dietrich giggle as if she tin'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 applied science that went into chips and systems, and then information technology was the computer scientists and engineers," Horn says. "At present 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 office of information technology, certainly, is a office of Dietrich'south marketing and political savvy: A geek, simply a far cry from the personality- challenged stereotype, she understands how to win attending and resources in an organisation of 330,000 people.

More than 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 mayhap to support pricing decisions. What more could they possibly contribute to the lesser line? Today, companies measure nearly every aspect of what they do, and computers are fast plenty to crisis 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' subconscious ownership patterns. Unabridged companies–think Google –are existence 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 smashing time," Dietrich says, "to be a computational mathematician."

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

Dietrich, whose hubby is an IBM software architect, joined the company in 1984 after earning her PhD in operations enquiry and industrial engineering science at Cornell, and she practical that "gorgeous theory" to designing more-efficient chip-manufacturing lines. It was thrilling to see how useful math could exist. In the mid-1990s, she grew bored between projects–"a dangerous state of affairs," she laughs–and pursued a new gear up of bug, spending 6 months in the field alongside IBM consultants and customers. "They couldn't tell you the dependent and independent variables," she says. Only she could, and that ability to interpret the applied into the theoretical (and back) was powerful. In some ways, her experience was the footing for how her enquiry department now operates.

If y'all're not a mathematician, the deep math that Dietrich and her team perform sounds utterly foreign–combinatorial auctions, integer programming, conditional logic, and and then on. Their whiteboard scribbles at Watson expect incomprehensible, like Farsi or Greek (then once more, many of the symbols are Greek). Simply these mysterious equations stand for the real globe and how it works. When mathematicians "model" a problem, they're creating a numerical snapshot of a dynamic system and its variables.

Take the wood-burn projection Dietrich and the researchers are working on. Extinguishing fast-spreading flames over tens of thousands of acres is an expensive and complicated undertaking. In 2000, a specially devastating year, the federal government spent more than $i billion and all the same lost more than and then 8 million acres. Its burn down planners want to reduce the cost and the damage through better coordination among the 5 agencies involved.

Armed with seven years of data, IBM's mathematicians are creating an enormous model that shows how the resource–every firefighter, truck, plane, etc.–accept been used in the by, how much each effort toll, and how many acres burned. The algorithms describe the likely costs and results for whatever number of strategies to combat a given fire. "How many bulldozers and buckets do y'all proceed in Yellowstone Park?" Dietrich asks. "And if you need to move them elsewhere, how much volition it price and how long volition it accept?" She's talking fast, describing the unruly variables that math makes sense of. "Information technology'south a nice project. Complicated, huh?"

Uh, yeah. For years, mathematicians were and then focused on basic research that they wouldn't go near projects like this–and they weren't asked to, either. "It was like working at a university without even the load of education," says longtime researcher Baruch Schieber. "When you lot decided what to work on, the get-go consideration wasn't, how will this bear upon the visitor?" If researchers wanted to, they could close their office door and focus on the most esoteric research, uninterrupted–and isolated.

At offset, Horn says, putting math specialists in front end of clients fabricated everyone nervous, not least of all the clients. The researchers are undeniably brilliant, he says, chuckling, but "you wonder how some of them become home at night." Watson, located an hr due north of New York, has a laid-back, collegiate feel; sneakers and jeans, along with the occasional bushy beard and ponytail, are the norm. Opinionated, professorial types fit right in. Dietrich may seem genial and charmingly quirky, simply when she holds forth on the intricacies of math, she tin can exist intimidating. She doesn't suffer fools and relishes a good debate.

But Dietrich has learned to soften her approach to avoid undermining the consultants' relationships with clients. She helped create a class for researchers that explains the consulting process and culture. A mathematician's perfectionism has to give manner to deadlines. The smartest-person-in-the-room vibe is considered off-putting, rather than an invitation to match wits. "Instead of forcing an argument on logic, which we're trained to do–information technology'south a bit adversarial–you have to go along your mouth close and listen," she says. "And you've got to stay out of the technical muck."

Some longtime mathematicians initially worried that inquiry would suffer under Dietrich. Instead, they lead a double life. In fact, says researcher Robin Lougee- Heimer, projects like the one she is working on now, a nationwide distribution puzzle for a make-proper noun client, uncover fertile research topics. "I'm getting exposed to great problems," she says, "with nasty details and complexity."

It used to be that Schieber, a senior director in optimization, would hear well-nigh a project within IBM and occasionally reach out to consultants. They rarely returned his calls. Now, he says, "I am the one being selective."

"When we get-go started asking what resources consultants use on projects, they said every projection was different. That just drove me crazy."

The word is out: The math squad can help. Dietrich fields a few dozen requests a month, half of which she turns down because the problem has already been solved or is non challenging enough. "We desire to push the frontiers of what's solvable," she says. "Otherwise, what'southward the point?"

In a sense, Dietrich is doing what she enjoyed as a immature math whiz–solving word problems. Here's a doozy: After IBM's sales team signs a consulting contract, the company frequently has to assemble the project team on deadline–say, fifty Java developers in Chicago by the post-obit Mon. It tin choose from 190,000 consultants around the world with various skills, personalities, and availability. It must do this for thousands of projects a year for clients of all sizes in every imaginable industry. Meanwhile, the mix of projects and bachelor consultants is constantly changing.

"When we offset started asking what resources consultants use on projects, they said every project was unlike," says Dietrich. "That simply drove me crazy." By poring over two years of project data, the mathematicians identified which skills were nearly frequently applied in certain types of assignments. "You lot may not know exactly what the customer wants, merely now you take a rough idea who you need for a $5 million projection versus a $50 million project," says Dan Connors, optimization manager for the Workforce Management programme. That staffing-assay tool helped managers anticipate demand and schedule accordingly, boosting the consultants' productivity 7% and reducing travel expenses and the use of outside contractors. The savings exceeded $500 million. So exercise the math: Add in sales from the OnTarget forecasting tool, and that's a $one billion contribution past Dietrich's math whizzes.

The brainiacs are tackling another problem whose solution could be just every bit valuable: how to selection the all-time teams. Project managers tend to select the most talented developers and engineers available, or the ones they already know. That may work well for the project at hand, merely in the long run, information technology doesn't necessarily do good IBM equally a whole; better to spread the talent effectually. Researchers are besides creating a social- networking analysis that would assess trails of e-mail, instant messaging, and phone calls to place which teams operate as apartment organizations and which ones are hierarchical–who works well together and who doesn't.

But the trouble that's really grabbing Dietrich involves predicting the workforce of the future. Past analyzing population trends, employee demographics and skills, and demand for certain technologies, her researchers hope to identify labor shortages in various functions and professions before they happen.

That work, almost unthinkably complex and far-reaching, is nowhere near complete. Each respond generates new questions, and that's fine. That's practiced. Even mathematicians don't have all the answers. Dietrich won't get bored, and she'll turn out some lovely knitting. Eventually, she'll accept numbers that help united states call up differently almost the world and where it's headed–and IBM and its customers will hire or train employees accordingly.

Information technology may well plow out, of grade, that what they need are more than mathematicians.