Michael Trott
The Science and Art of Mathematica
Self Interfering Wave on a Torus. Trott explains: “Imagine you are sitting on the ocean and the water is very flat and you throw a stone in the middle. You will see little waves going out from the stone to infinity and because of friction at one point they end. Now let’s say you could take two parallel sides of a pool and join them along with the inner rim and the outer rim to create a torus and then throw the same stone in the middle.” This is the resulting interfering waves in an object you couldn’t experiment with in the real world.
Fifteen years ago, Michael Trott, a theoretical physicist at a small university in Germany, carried his department’s only available computer, a Macintosh IIfx, from his office to the lecture hall every week to share knowledge about Stephen Wolfram’s groundbreaking mathematics application, Mathematica. He recorded reams of notes on applying Mathematica to theoretical physics and stacked them into hundreds of pages of formalized data. The value of his research on untapped areas of the application was immediately clear to Mathematica’s creator when Trott passed along his 800-page notebook to him. Wolfram promptly asked, “Why don’t you come work with us?”
Trott took Wolfram up on his offer. Today, comfortably sitting in front of his Power Mac, he works as a senior Mathematica developer at Wolfram Research’s headquarters in Champaign, Illinois. Over the years his visualizations of complex mathematical expressions have become the “face” of Mathematica. Almost every Mathematica logo, product brief, or cover comes from Trott’s use of the application to create phenomenal visual representations of mathematics. His Mathematica Guidebooks are essential reading for learning each facet of the application.
The paramount importance of accurately communicating mathematical principles through visual representation requires the right tools for the job. While Mathematica is available on a wide variety of computing platforms, for Trott and many of his colleagues Mac OS X is their platform of choice.
“Mathematicians and physicists don’t want to spend time hacking some UNIX or Linux interface together — they just want to use the programs that are vital to do their science. Mac is the ideal platform to do this.”
“It seems in the mathematics and physics community there is a much larger section of Mac users,” Trott says. “Most scientists prefer Macs because they are convenient. Mathematicians and physicists don’t want to spend time hacking some UNIX or Linux interface together — they just want to use the programs that are vital to do their science. Mac is the ideal platform to do this.”
Wolfram Research and Mathematica
Wolfram Research, Inc.’s stated goal is “pushing the envelope of technical computing.” Their primary product, Mathematica, is a general computational system used for a huge variety of purposes in both academic research and commercial applications. For the unfamiliar, Mathematica could be summarized as the world’s best calculator — but such a statement is a massive oversimplification of Mathematica’s varied strengths. It’s used in every field where math plays a role, including traditional sciences such as physics and biology, and emerging fields such as computational analysis of complex financial derivatives. The core components include a numeric and symbolic computational engine, a graphics system, a full-fledged programming language with an application development environment, and a document-creation environment. Everything is tied together with one of the most versatile user interfaces in scientific computing, one that can be used for everything from writing Mathematica code to typesetting press-ready technical documents.
Mathematica has supported the Mac since its inception. The same close attention paid to the fusion between a powerful computing platform and a fluid user experience makes Mathematica and Mac OS X natural companions. Trott says, “Mac is an exceptionally good platform for Mathematica users. I relish using it; it is particularly convenient. Some of our main developers use Mac, which is a very positive influence on the quality of Mathematica.”
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