It's nearly as inevitable as death, taxes and the eventual descent of overvalued Internet stocks. In what has become a ritual of the American education system, at some point during every elementary or high school mathematics class, one bewildered student will utter that timeless lament: "It's not like I'm ever going to use this stuff in real life."
While it's impossible to verify such a wager, it would be a relatively safe bet to assume that Steve Schwartz was never that student. To say that mathematics is the 49-year-old Schwartz's life work is almost an understatement, like referring to Howard Hughes as a neat freak or categorizing Bill Gates as being well off.
"I knew that I was going to be involved in math since I was 8 years old," Schwartz says. "My father was a mathematician. Math gave us a common language."
Although Schwartz spends a good deal of his free time working on a trio of equations that would give Will Hunting a headache, it is his day job that allows Schwartz to apply his considerable math skills to real life. He is the director of system architecture at IronBridge Networks, a start-up working on a supersized router for the Internet's backbone.
While the founders of most incipient hardware-based networking companies usually turn to engineers to anchor their original technical teams, Schwartz, who holds a computer science degree, was IronBridge's first employee. Heading a unique team of seven mathematicians, Schwartz's impact on both the design and construction of the Boston-based company's heavy-duty router is a reflection of the expanding demands on equipment that will play a major role in shuttling information across the Internet.
Designed to handle about 40 times the traffic that stresses the fastest routers available today, IronBridge's terabit-per-second device must be both powerful and agile enough to react to constant and sometimes dramatic fluctuations in traffic flows. By constructing complex mathematical models of hardware and software components long before a semiconductor hits the foundry or a line card rolls off the assembly line, IronBridge's resident math maven can provide system architects with an accurate blueprint for building a future-proof system.
"By understanding the nature of the traffic and the way to optimize networks, we can better design routers," Schwartz says. "We try to understand the way the Internet works and how to design routers that will accommodate it."
Schwartz's first job at IronBridge was to design the line card modules and switching fabric for the company's router, which is expected to be available sometime later this year. After helping the hardware side of the house build the system's guts, Schwartz and his teamed turned their attention to traffic engineering efforts.
Traffic engineering is essentially the science of figuring out the most efficient method of moving data from one point in the network to the next. Protocols designed to take the drudgery out of that process have been available for years, giving service providers the essential tools for managing capacity and traffic flow on their networks. As the Internet has grown in size, hosting traffic that is increasingly essential to consumers and businesses, traffic engineering has become as much art as science.
Not only are network pipes more congested, the traffic flowing over those pipes, such as voice and video, must be treated in a specific manner if it is to reach its destination on time and in one piece. All of this means that carriers must perform high-tech acrobatics to manage the timely flow of information across their networks. Network managers are constantly monitoring traffic conditions, jumping into action if a route becomes congested or mission-critical traffic is being held up by a router that is letting less important traffic, such as e-mail, pass through at will.
While it might be hard to imagine, given the size and complexity of public networks, a good deal of traffic engineering is done manually and on the fly.
Schwartz says, "It's called the 'stare-and-tweak' method. "You stare at the problem, and then you make tweaks."
While this is a perfectly reasonable and effective methodology for situations in which time is not of the essence, Schwartz says, it is inefficient in most public network settings. One of Schwartz's primary tasks at IronBridge was to create a mathematical system, or algorithm, that could detect changes in traffic conditions and initiate traffic engineering actions.
"We design optimisation algorithms to automate the process," Schwartz says. "These algorithms can do better than the human mind."
Although Schwartz's first love is pure mathematics and he prefers chalk dust to circuit boards, he's no stranger to the computer and networking industries. Long before "windows" meant anything more than what one opened to let air into the room - when "Mac" was simply a friendly appellation for a stranger - Schwartz was dabbling in the world of electronics.
"When I was young, I built things out of vacuum tubes," says Schwartz, who honed his skills on World War II surplus electronic gear supplied by his father. "There was a time when I knew the RCA receiver tube manual by heart."
After working on an advanced degree from Heriot-Watt University in Scotland, Schwartz settled in the Boston area, where he designed memory systems for mainframes, eventually designing microprocessor architecture for a mainframe manufacturer in the late 1980s. Before being recruited for IronBridge - which gets its name from a photograph Schwartz took of his favorite subject, a New England bridge - he was working as a consultant.
"I did consulting work for a number of large telephone companies, creating mathematical models of communications networks," Schwartz says. "It wasn't exactly routers, but it seemed related."
With IronBridge expected to put the finishing touches on its first router in a few months, Schwartz and his team are already working on their next project - a more advanced switching technology.
"Traffic engineering and traffic characterization is constantly evolving," Schwartz says. "And now optics is changing the playing field, and we need to know the best way to deploy these technologies. Mathematical models give us precision and certainty, and that's important when there's a lot of money at stake."
A direct correlation between mathematics and making money? Wait until those legions of frustrated math teachers, longing for a clever retort, hear about this.
