# Meet an Inventor Who Makes Complex Calculus Simple

**Gautam Naik, The Wall Street Journal, September 25, 1996.**

Ever wonder why certain shampoos have just the right consistency, so they flow from the bottle but not through your fingers? Or why a particular soft drink seems to hit the spot, while another may not? Or how cyclists could shatter 21 speed records at Atlanta's Summer Olympic Games?

The answer in each case: mathematics.

Or, more precisely, *Mathematica*, an obscure and high-powered software
program that lets computer novices crunch mind-numbing technical computations
with the ease of using a calculator. For the program's creator, Stephen Wolfram,
a physics whiz who got bored of academia and reinvented himself as a software
salesman, converting the complicated into the simple has yielded a handsome
business opportunity.

Most ordinary Americans may hate doing math, but they are increasingly subject
to its influence, whether they know it or not. Experts in a growing number of
fields are relying on calculation rather than estimation. Some textile designers
use geometry to create pleasing new designs. Many companies have discarded rule
of thumb in favor of sophisticated statistical tools to decide what products
to place on supermarket shelves. Even musicians use math equations to generate
inventive new sounds. *Mathematica* has been used in each of these cases.

Mr. Wolfram, 37 years old, has sold a million copies of the program, at about $1,300 apiece, since 1988. Now he hopes to push his program to a far broader audience—financial analysts, doctors and even high-school students—aiming to give them access to computational power that only programmers had previously.

Whether such neophytes are ready for it is the big question. Wolfram Research
Inc., Champaign, Ill., is about to launch a souped-up version of the product,
*Mathematica* 3.0. Next week, the company will start distributing free
samples to new users and hundreds of schools and colleges. Two "MathMobiles"—Dodge
Rams, painted in colorful *Mathematica*-generated graphics and equipped
with several computers—will embark on cross-country promotional tours in the
U.S. and Europe. A new and related application, *Technical Trader*, is
aimed at technical analysts who try to predict stock-price movement by using
sophisticated models.

If the new stuff can appeal beyond a core market of four million scientists and engineers, Mr. Wolfram, already a rare example of a millionaire scientist, could become a much wealthier man. "We'd better get it right," he mutters as he taps away on a computer, trying to fix a bug. "Or all the world's going to get its arithmetic wrong."

Mr. Wolfram is widely described as one of the world's smartest researchers, an intensely focused man who has never been known to suffer fools gladly. Despite his growing business, he is ever the eccentric scientist, often working all night and waking at noon. Running his company via cell-phone, pager and e-mail, he spends most of his time in Chicago along with his mathematician wife and nine-month-old son. But his freewheeling days as an academic are gone: He no longer picks vacation destinations by simply showing up at the airport and buying a ticket to whichever destination appears at the top line of the departure board.

Born in England, Mr. Wolfram attended Eton and Oxford but was so far ahead of his peers that he never bothered to graduate from either. That didn't stop him from receiving a Ph.D. in physics—in one year—from the California Institute of Technology at the age of 20, or from winning a MacArthur "genius" award at 21, the youngest-ever recipient. After a stint at the Institute for Advanced Study in Princeton, N.J., he founded a research center at the University of Illinois, Urbana-Champaign. Its main purpose was to unravel a hotly pursued question: Can complex patterns in nature be traced to a few simple—but still elusive—rules?

Mr. Wolfram created *Mathematica* to help him search for an answer. (He says
he has found it and is writing a book on his discovery.) But he hated
academia. It was "the worst of both worlds," he says: Unlike business, it
was often "aimless," and even good discoveries were likely to end up unread
in obscure research papers. So Mr. Wolfram founded his own company in 1988
to sell his tools to fellow scientists.

*Mathematica* does have some dazzling powers. It can spit out
the first 2,550 places of pi in a split second. It took a
mathematician working at Wolfram Research two hours and five pages of
computation to solve one calculus equation: *Mathematica* solved
it in one-twentieth of a second. And the program can generate
elaborate three-dimensional graphics that are easy to manipulate in
hundreds of ways, a claim rival products can't match.

These features prompted scientists at Helene Curtis Industries Inc. to use
*Mathematica* to understand how shampoo molecules interact so that the liquid
would have the right consistency. Flow is dictated by molecules' shape
(long, thin chains are best), and *Mathematica* was able to model their
optimal geometry. Chemical engineers at International Flavors & Fragrances
Inc. build math models with the program to predict the interaction among
chemicals, helping them pinpoint a pleasing food flavor. And Dun &
Bradstreet Corp. relies on the software to calculate its Nielsen ratings
for television shows.

*Mathematica* was also used to design the Atlanta Olympics cycling arena
entirely on a computer. About 235 massive chunks of steel, each with a
unique shape, were built to snap together and come apart just as
easily—essentially, a transportable velodrome. "Previously engineers would
use a trial-and-error method" to plot curves and slopes that would yield
the highest speeds, notes Chris Nadovich, chief engineer for the Atlanta
project. He used *Mathematica* and a complex algorithm it crunches—called
Fresnel Integrals—to design a 3-D version of the structure on the computer
screen "down to every nut and screw." The mathematical precision yielded a
surface ideal for record-breaking speed.

Seth Chandler, a law professor at the University of Houston, uses
*Mathematica* to represent, and then solve, insurance-law scenarios on drunk
driving that are so complex they can be described only mathematically. It
lets him manipulate a wide range of variables—driver experience, age,
seat-belt usage, time of day, and still others—to calculate the optimum
exposure an insurer should bear in hundreds of different situations.

Calculus problems occur everywhere, Prof. Chandler says: "Did you know that
the amortization of a home mortgage is actually the solution to a
differential equation—and one that *Mathematica* can solve in the blink of
an eye?"

Jerry Uhl, a math professor at the University of Illinois, teaches calculus
to 2,500 students spread across the country; the entire course, including
text, is written for students with *Mathematica*, and shipped over the
Internet. Many old-line calculus teachers decry this trend. They lament
that *Mathematica* yields answers without requiring students to crunch the
numbers themselves, much as a pocket calculator lets a grade schooler get
answers without having to learn long division.

"It's a silly controversy. I never learned long division, and look at me," Mr. Wolfram says contemptuously. "If you start off doing everything by hand, you'll never get anywhere."