There's a calculus to knitting. An untamed batch of wool gets twisted and fed into a spinning bicycle, a wooden contraption nigh equally high-tech as an abacus, that binds the fibers into a unmarried strand of yarn. That yarn, in plow, is woven into geometric designs comprised of equations: A certain number of rows combined with certain stitches yield something functional and cute. In the right easily, knitting produces a precise but almost magical alchemy–chaos into lodge.

You lot tin see why it would entreatment to Brenda Dietrich.

Dietrich, 47, runs the math sciences department at IBM's renowned Thomas J. Watson Research Middle–the height math manager at arguably the biggest and most of import math department in corporate America. She loves math's beauty and complication. Nevertheless she often spends conference calls and meetings spinning yarn on the wheel next to her ThinkPad. And she knits endlessly–a scarf, glaze, shawl, and hat in progress simultaneously. That exquisite blueish and purple cashmere shawl in her office? "This was last yr's inquiry software strategy meeting," she says. "I sat in the back row knitting for 3 days."

Dietrich, who has coauthored xiii patents and has twice been named one of IBM's top inventors, likes to make stuff–tangible stuff, non just theorems. As a mathematician, she has a rare power to travel betwixt ii very different worlds, says Paul Horn, head of IBM inquiry. She tin can mind to a customer describe the messy details of a business concern, and then interpret those specs into math problems for her squad to solve. And she thinks mathematicians should alive 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 piece of work with IBM consultants in the field.

These days, her team is, in fact, venturing out from years of backside-the-scenes, by and large theoretical research to tackle an impressive array of existent-world problems at IBM and beyond. How to assemble a project team from consultants dispersed around the world. How to fight vast forest fires more than effectively. How to place the best sales leads in the pipeline. OnTarget, sales-prediction software that grew out of math enquiry, generated $100 1000000 in new acquirement as a pilot program in Canada. Last year, it delivered about $500 million in worldwide use, a sum that makes Dietrich giggle every bit if she can't quite believe it.

Dietrich's 160 researchers are, in fact, increasingly among the nearly valuable trouble solvers at IBM. "Historically, the stars here accept been the physicists who made the technology that went into fries and systems, and so it was the reckoner scientists and engineers," Horn says. "Now nosotros'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 information technology, certainly, is a part of Dietrich's marketing and political savvy: A geek, merely 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 that, her section'southward growing impact reflects a bigger real-world shift. A generation ago, businesses called on mathematicians, at all-time, to optimize product lines and mayhap 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 plenty to crunch the numbers in time for execs to act on the assay. In the hands of talented mathematicians, data create an invaluable reward. 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 exist a computational mathematician."

A number-theory class at the University of Due north Carolina at Chapel Hill changed Dietrich'southward mind about becoming a doctor. Math was a revelation, like hearing music for the kickoff time. "In that location'south construction and symmetry and the about gorgeous theory," she says. "It made me believe in some underlying order in the world."

Dietrich, whose husband is an IBM software architect, joined the company in 1984 later on earning her PhD in operations enquiry and industrial engineering at Cornell, and she applied that "gorgeous theory" to designing more-efficient chip-manufacturing lines. Information technology was thrilling to meet how useful math could be. In the mid-1990s, she grew bored between projects–"a dangerous situation," she laughs–and pursued a new set of problems, spending six months in the field alongside IBM consultants and customers. "They couldn't tell you lot the dependent and independent variables," she says. But she could, and that ability to translate the practical into the theoretical (and dorsum) was powerful. In some ways, her feel was the basis for how her research department now operates.

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

Have the wood-burn project 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 especially devastating year, the federal government spent more than than $i billion and yet lost more than so 8 million acres. Its burn planners desire to reduce the cost and the damage through better coordination amongst the 5 agencies involved.

Armed with 7 years of data, IBM's mathematicians are creating an enormous model that shows how the resources–every fireman, truck, plane, etc.–have been used in the past, how much each endeavor cost, and how many acres burned. The algorithms draw the probable costs and results for any number of strategies to combat a given burn. "How many bulldozers and buckets do you keep in Yellowstone Park?" Dietrich asks. "And if yous need to move them elsewhere, how much will it price and how long will it accept?" She's talking fast, describing the unruly variables that math makes sense of. "It's a overnice projection. Complicated, huh?"

Uh, aye. For years, mathematicians were then focused on basic research that they wouldn't become near projects like this–and they weren't asked to, either. "It was like working at a university without even the load of teaching," says longtime researcher Baruch Schieber. "When you decided what to piece of work on, the first consideration wasn't, how will this impact the company?" If researchers wanted to, they could shut their office door and focus on the nigh esoteric research, uninterrupted–and isolated.

At commencement, Horn says, putting math specialists in front of clients made everyone nervous, not least of all the clients. The researchers are undeniably brilliant, he says, chuckling, but "yous wonder how some of them get home at night." Watson, located an hr due north of New York, has a laid-dorsum, collegiate experience; 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, but when she holds forth on the intricacies of math, she 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 course for researchers that explains the consulting process and culture. A mathematician's perfectionism has to requite way 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–it's a scrap adversarial–you have to keep your oral fissure shut and listen," she says. "And you've got to stay out of the technical muck."

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

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

"When we kickoff started request what resources consultants utilize on projects, they said every project was unlike. That just drove me crazy."

The word is out: The math team can help. Dietrich fields a few dozen requests a month, half of which she turns downwardly because the problem has already been solved or is not challenging enough. "We want to push the frontiers of what'southward solvable," she says. "Otherwise, what'southward the bespeak?"

In a sense, Dietrich is doing what she enjoyed as a immature math whiz–solving discussion bug. Here's a doozy: Subsequently IBM's sales squad signs a consulting contract, the company often has to assemble the project team on deadline–say, 50 Coffee developers in Chicago past the following Monday. Information technology can choose from 190,000 consultants effectually the earth with various skills, personalities, and availability. Information technology must do this for thousands of projects a yr for clients of all sizes in every imaginable industry. Meanwhile, the mix of projects and available consultants is constantly changing.

"When we commencement started asking what resources consultants apply on projects, they said every projection was different," says Dietrich. "That just drove me crazy." By poring over 2 years of project data, the mathematicians identified which skills were most oft applied in certain types of assignments. "Yous may not know exactly what the customer wants, but now you lot have a crude thought who you need for a $5 million project versus a $fifty one thousand thousand project," says Dan Connors, optimization manager for the Workforce Management program. That staffing-analysis tool helped managers anticipate need and schedule accordingly, boosting the consultants' productivity seven% and reducing travel expenses and the apply of exterior contractors. The savings exceeded $500 one thousand thousand. And then practise the math: Add in sales from the OnTarget forecasting tool, and that's a $1 billion contribution by Dietrich's math whizzes.

The brainiacs are tackling another problem whose solution could be merely as valuable: how to pick the best teams. Projection managers tend to select the nigh talented developers and engineers bachelor, or the ones they already know. That may work well for the project at paw, just in the long run, it doesn't necessarily benefit IBM as a whole; better to spread the talent around. Researchers are as well creating a social- networking analysis that would assess trails of email, instant messaging, and phone calls to identify which teams operate as flat organizations and which ones are hierarchical–who works well together and who doesn't.

But the problem that'due south really grabbing Dietrich involves predicting the workforce of the future. By analyzing population trends, employee demographics and skills, and demand for sure technologies, her researchers hope to identify labor shortages in diverse functions and professions before they happen.

That work, almost unthinkably complex and far-reaching, is nowhere near complete. Each answer generates new questions, and that'due south fine. That's good. Fifty-fifty mathematicians don't have all the answers. Dietrich won't get bored, and she'll turn out some lovely knitting. Eventually, she'll have numbers that help us think differently virtually the world and where information technology's headed–and IBM and its customers will hire or train employees appropriately.

It may well turn out, of grade, that what they need are more than mathematicians.