By Christopher Tse

In the world of computing, people refer to software packages whose introduction redefines computing as "killer apps." A look back at the short history of personal computing will reveal that such "killer apps" are few and far between.

VisiCalc, one of the first spreadsheet programs for personal computers, was clearly one of the "killer apps" of the early PC era, almost single-handedly selling the idea of the personal computer as a business tool. While the informed reader may be able to come up several other examples of groundbreaking software that "revolutionize everything," few will come up with the name Mathematica.

To most people, Mathematica is just what its name implies: a program for doing math. According to Dr. Steven Wolfram, however, Mathematica is "a fully integrated environment for technical computing" which has done for physical science, engineering, and m athematics what spreadsheets did for business computing. Dr. Wolfram, Mathematica's creator, came to Columbia on October 10 to describe the "Vision of Mathematica" and demonstrate the newly released Mathematica 3.0.

Before the arrival of Mathematica in 1988, there were few tools for carrying out complex technical computations. While a lot of people used FORTRAN to construct the main algorithms, it is difficult to integrate the different program fragments into a worki ng whole.

Dr. Wolfram, himself an accomplished scientist (he received his Ph.D. in theoretical physics from Caltech by the age of 20), saw the need for developing a set computation tools based on "one big idea"-that everything can be represented as a symbolic expre ssion.

Transforming centuries of mathematics into a set of well-defined, text-based symbolic expressions requires the identification of some basic primitives. One solves problems by using those primitives as building blocks to construct more complex expressions.

Mathematica 3.0 promises to "extend the domain of programming," while at the same time "making things easy for people," proclaims Dr. Wolfram. For those familiar with an older version of Mathematica, the new version should be familiar.

There are, of course, enhancements. Normally plain-looking Mathematica Notebooks can now be spiced up with a new predefined style that adds color and font formatting to the Notebook. The new version's ability to let users add text to annotate particular ly complicated formulas will be welcomed by instructors who use Mathematica in class.

In addition, finished Mathematica notebooks can now be exported as HTML to be posted on the World Wide Web for millions of people to see. Since there are no standard HTML specifications of mathematical formulas, all the Mathematica expressions and graphic s are exported as a GIF image.

Besides the Web export ability, Mathematica 3.0 can also communicate with third party applications through an improved MathLink feature. MathLink allows "the exchange of symbolic expressions" between two programs in the same uniform way that Mathematica c ommunicates internally.

In his presentation, Dr. Wolfram recalled the time he tried to determine exactly how much faster than humans Mathematica computed integrals. He described how he asked the two Russian scientists who actually wrote the algorithm for integration used by Math ematica to compute a certain integral by hand. The solution generated pages upon pages of hand-written calculations and took several hours to compute. Using Mathematica, Dr. Wolfram was able to evaluate the integral in less than 15 seconds.

Today, Mathematica is used not only in technical fields such as physics and engineering, but also in applications as varied as finance, textile design, and computer art, where "the artist's brush is replace by formulae and algorithms," said Dr. Wolfram. " It brings a the human touch to Mathematica."

Mathematica 3.0 is available for Windows 95/NT (not, however, for Windows 3.1), Macintosh, and Unix systems. While it carries a list price of $1,295, full-time students can purchase an academic version for around $130. In addition, Columbia has purchase d a site license for the package, so it should be available on workstations on campus.

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