I first started finding the need for symbolic algebra systems in 1989 while I was studying chaos in the attitude dynamics of spacecraft in pursuit of my Ph.D. in Engineering Mechanics at the University of Wisconsin-Madison. I was applying a technique called Melnikov’s method that required the evaluation of some integrals that, at the time, did not exist in any known table of integrals. I purchased Maple, which is a competing symbolic algebra system, to help evaluate these integrals, but it didn’t get my any further than integral tables had taken me. As I state in my thesis:

“On the other hand, the evaluation of these integrals can be accomplished, albeit rather arduously, via the residue theorem of complex variable theory. The integral J1 required the application of L’Hopital’s rule seven times in order to find the residue at one of the poles of the integrand.”

When I tried performing these calculations in 1989 using Maple on a Mac Plus, which was Maple’s first graphical user interface, it would not finish since it had the limitation that the size of the output could not exceed 32 KB. Again, from my thesis:

“The resulting expressions were over 200 pages long in Mathematica!”

Notice that I used Mathematica, which I believe was Version 1.1 or 1.2, for that calculation. Needless to say, the output was substantially greater than 32 KB and Mathematica was able to handle it with aplomb on a Mac Plus with its 4 MB of RAM and floppy disk drive.

Since becoming a professor of Engineering Science and Mechanics at Penn State University in 1994, I have used Mathematica in every part of my research and I have introduced thousands of students to Mathematica since I use it in every class I teach. I have even taught a special topics course on using Mathematica a few times. I have been a Mathematica user ever since I first tried it in 1989 and now run Mathematica 9 on my MacBook Pro with Retina display.