## Thoughts & Stories

Beginning in the early 1970s my colleagues and I at Deere developed a variety of mathematical models and simulations to investigate power hop, a type of dynamic instability that can occur in tractors operating with moderate to high draft loads in the field. Although these models could predict the phenomenon, the results were so complicated and volumunous that we were unable to grasp a general understanding. Then in April of 1989 we had a breakthrough and decided to reformulate the problem as a dynamic stability investigation. I had purchased a copy of Mathematica in late 1988 and was intrigued with its capabilities, so we decided to build this new formuation as a series of Mathematica Notebooks. Within 2 weeks we were getting new results and displays that were easy to comprehend. These were expanded and utilized extensively over then next few years. Later we often remarked that we would not have been able to develop these results so quickly without Mathematica. Dr. Bernard Romig of the Deere & Company Technology Center did most of the Notebook development. More…

I first used *Mathematica* when a version came pre-installed on my NeXT cube. It was a revelation. In an industry where computers have increasingly become appliances, with programs dedicated to a single function and programming and flexibility relegated to developer environments, *Mathematica* remains an unbelievably powerful and general problem-solving tool. More…

A *Mathematica* memoir. It does sound fun, in a very geeky sort of way.

I think my best *Mathematica* presentation was with Craig Rollins when we introduced the geodesy group at the National Geospatial-Intelligence Agency to *Mathematica* at their GeoInt conference in St. Louis maybe six years ago. Peter Overmann and Joshua Martel also attended, as I recollect, as did some other Wolfram people.

Craig and I began the talk by adding 1/3 + 1/3 + 1/3 in a C program that, of course, did not return exactly one for the answer. The audience laughed, and we were off. More…

In the several decades of my theoretical physics research before *Mathematica*, I performed very few numerical calculations; numerics (mainly fighting with Fortran, which I found dreadful) was something I imposed on my students. By the mid-1980s I was starting to use BASIC, which was more friendly. But the instant I learned about *Mathematica* in 1988 (from John Guckenhimer), I realized that this software, together with my newly acquired Mac II computer, was exactly what I needed. More…

Stephen: Thank you for being THE *Mathematica* pioneer! I have used it more or less daily for 25 years, and it just keeps getting better. Congratulations on achieving this milestone.

It was the summer of 1988 when I first encountered *Mathematica*. I was a pre-freshman in Electrical Engineering. I was taking part in the summer preparatory program. As I was trying out different software programs in the computer lab, I came across *Mathematica*. I used *Mathematica* to help visualize various problems in my calculus class. Later, I stumbled upon *The Mathematica Book* and *The Mathematica Journal*. I was simply amazed by all of the applications and solutions that *Mathematica* and mathematics in general has to offer. (I was fortunate that I had learned *Mathematica* before I learned C because *Mathematica* allowed for elegant types of programs without using loops that I was able to master.) More…

I became aware of *Mathematica* as early as Version 1.2 (I believe this was in 1988 or 1989) and have been using the software in all versions ever since (currently Version 9). *Mathematica* has been an indispensable tool for many of my research activities, especially those devoted to theoretical mechanics of materials. More…

I cannot believe that it is already 25 years ago that I started using *Mathematica*. I have used it maybe daily since I became a *Mathematica* addict. More…

In 1989, when I was doing my undergraduate project at the Institute of Sound and Vibration Research at the University of Southampton, I gained access to the magical room that contained two Mac SEs and a Mac IIx (no Windows on PCs back then). The Mac IIx had a copy of *Mathematica* on it and I was enthralled, even though I didn’t need it for my project. More…

My life’s work is to be found in the book “Space-Time and the Elementary Particles.” This book is written in *Mathematica*. The work could not have been done without *Mathematica*.

I started using *Mathematica* 1.x on the NeXTstation in the math department’s computer lab at University of Wisconsin–Madison. It must have been 1990. I soon managed to get my own monostation bundled with *Mathematica*, and have been using it almost every day ever since, starting with classes then to data analysis and research and developing into a general repository of all kinds of ideas. It has become an important extension of my brain. Every once in a while I try to wean myself off it and try something else. But I always come back when I need to get real work done.

I knew of the existence of *Mathematica* for the first time in 1990. Then I started using *Mathematica* 2 on a NeXT computer. I think it was around 1992. Since then, I’ve been using *Mathematica* for acoustic simulation. I am amazed at the evolution of *Mathematica* to date. I need *Mathematica* more and more every time *Mathematica* is improved. Using *Mathematica* 9 now, I am going to start the calculation of the propagation of sound, including the effects of temperature and wind. I expect that the use of an acoustic field increases from now.

More…

My first use of *Mathematica* was in the last months of 1988 when I was asked by my aerospace industry management to evaluate various mathematics software programs that could be used to help the company engineers increase their development productivity. After my evaluations were complete my view was that *Mathematica* (then in its very first release) was in a class of its own. It had no close competitors in terms of the huge breadth of capability the core unadorned *Mathematica* software package provided. More…

I began the use of *Mathematica* 2 in 1992. I can still remember my excitement when I began to realize the new possibilities that *Mathematica* opened for scientific calculation, mathematical research, and teaching mathematics. More…

So many memories!

In 1979 as a graduate student in mathematics at University of Washington (Seattle), I attempted to use SMP to do some calculations for my PhD thesis. I underestimated the difficulty of doing so and abandoned this effort. It wasn’t until many years later that I learned that SMP had been written by Stephan Wolfram at age 17.

The first time I met Stephen Wolfram and the first time I saw *Mathematica* in action was at the (First Annual) Conference on Technology in Collegiate Mathematics (ICTCM), held at Ohio State University in (I believe) October 1988. I was VERY impressed, and upon returning told my (mathematics) department chair, “This is what we’ve been waiting for.” More…

In the 1980s I began working on a general mathematical theory of self-organization in nature, which is now called Foundation Mechanics. While a visiting scientist at the now defunct MIT Information Mechanics Laboratory, I studied Stephen Wolfram’s work in digital physics. Simultaneously I was using Macsyma for my theoretical calculations. Following a discussion with Richard Stallman, whose office was in MIT LCS at the time, on what was happening to Macsyma by way of Symbolics, I switched to *Mathematica* as soon as it was released by Wolfram Research. I have used *Mathematica* ever since that time for 25 years and am considered a *Mathematica* “Jedi Grand Master” by those who have seen the results I produce with the system.

It was in 1995 that I saw the manual to *Mathematica* 2.2 in a bookshop. I realised it would make hours of pencil and paper calculation unnecessary, and allow us to explore chemical systems more easily. So, my boss provided the budget and soon we entered the CAS age. One of the first notebooks, apart from exercises needed to climb the steep learning curve, was a simple program to explore the combinatorics of chemical interesterification of triglycerides. But what most struck me (and helped me up the curve) was the quality of the online help file. More…

I was a graduate student in high energy theoretical physics at Stanford University when I first met Stephen Wolfram in either 1978 or 1979 (I don’t recall which). This was before *Mathematica* and he invited me to give a talk at Caltech and was my host for my visit. I have to say he made me feel welcome and did an excellent job. I was a little nervous since it was my first talk.

Of course in my field *Mathematica* has completely changed the way we work in high energy theory. It is an essential tool and I congratulate Stephen and the *Mathematica* team for the remarkable work you have done and the incredible product you produced. More…

I wish I could remember precisely when I purchased my first version of *Mathematica*. It was very early on, at the MacWorld Expo in San Francisco of either 1989 or 1990 or 1991. I purchased my copy right out of the exhibit booth, from a heavily bearded and highly enthusiastic individual.

My first professional use of the program was for analyzing the precision of a stepper motor driven mechanical stage, used in high end semiconductor processing equipment. More…

Congratulations to the staff of Wolfram Research on your 25th anniversary.

We were fortunate to see the editorial in the *New York Times* on the values of *Mathematica* in 1992.

The symbolic math capabilities caught our eye because we realized how important the MIT symbolic math service was. More…

I was born and I live in Spain. I had my first contact with *Mathematica* at the end of 1991, when I visited USA, and I was impressed by the program. I was in my thirties and worked as a manager of a company. I had left the academic world a few years before, but when I realized the power of *Mathematica*, I decided to earn my Ph.D. using it. More…

I honestly think that a lot of words are required when speaking of ordinary programs but very few are needed for a masterpiece such as *Mathematica*. I got in touch with it in 1991 and I was truly impressed by its scope, its logical construction and layout, and its outstanding documentation. More…

*Mathematica* came into my life in 1992 via a fourth-order equation for a 3D flow field. A colleague had the equation but couldn’t solve it. He had heard of *Mathematica* and recommended I try it, which I did. From the solution for the 3D field, the fluid dynamical strain rates and divergence on a certain 2D plane needed to be calculated and presented as contour plots. After I learned enough finally to formulate the computations correctly (even back then without too many lines of code), and with the PCs and *Mathematica* of that era, it took about 30 minutes to complete the calculations and render the plots. (In 2013 it takes a couple of seconds.) More…

I was working on my PhD at the University of Gainesville, Florida, in 1986 when I first started working with a Symbolic Manipulation Program called SMP (Wolfram’s own) on a VT terminal at the Physics Department. It was truly useful but soon afterwards I bought my first Mac II, and started working from home wishing that I could do some of that on it. Fortunately, I read in a Mac journal the announcement of the first version of *Mathematica* for the Mac, and I requested immediately a grant from the Luso American Foundation under the Fulbright program for its acquisition, and I’ve been using it ever since on Mac, NeXT, and Linux workstations. More…

Congratulations on your upcoming 5^{2} anniversary! Claire and I gave a talk at your 10th anniversary, which experience we remember fondly.

I want to thank you personally for supporting my mathematical sculpture in the form of giving me free versions of *Mathematica* over the years. More…

I started using *Mathematica* as soon as it was released in Australia, and pretty soon my colleagues and I were using it for our collective research efforts.

One funny incident occurred soon thereafter, when I was on study leave from Sydney at the University of Bath. I wanted to put *Mathematica* on a computer in the laboratory there, More…

Ten years before the end of the last millennium (~1990 depending on whether indexing begins at 0 or 1) a friend of mine who was a Professor of Mathematics showed me his revolutionary NeXT computer—and the star of it was *Mathematica*. The immediate impact was its versatility and the ability to easily visualize computational results with the variety of plots. More…

I used to like showing it off by putting in `2^2^2^2^2`

. That would take a fair part of a minute to calculate on my Mac IIfx.

I got *Mathematica* with my new NeXTstation when I started as a faculty member at Northwestern in 1991. I was soon happily using it across the network from my DECstation at Fermilab. I did many of the design calculations for the D0 experiment at Fermilab on that first machine. The NeXTstation is long gone but I still use *Mathematica*—to produce diagrams for my lectures and to add up my travel receipts!

I have a personal reason for brand loyalty as well. In 1981, as a beginning graduate student, I made a preliminary measurement of kaon production in *e*^{+}*e*^{–} scattering. Unknown to me, there was a bug in a simulation code which mixed up energy and momentum in a correction. A Caltech physicist named Stephen Wolfram probably wasted several months trying to explain the erroneous result. So I owe him. Sorry about that.

In 1988 I was head of the math & computer department at Brescia University and purchased a copy of *Mathematica* to enhance calculus and stats classes. I continued to use *Mathematica* until my partial retirement in 2004. In 1990 I wrote a book for my calculus students using many of the *Mathematica* functions. We also purchased a site license for our lab. In 1991 we added a one-credit-hour requirement to the calculus course using *Mathematica*. About the same time I started using *Mathematica* in other math classes, from college algebra to operations research.

I still teach part time and still have a set of floppy discs with *Mathematica* on them….

[*Mathematica*] was an obvious breakthrough for the “common mathematician.”

I attended the 1991 *Mathematica* Conference in San Francisco, and was converted on the spot when Stephen Wolfram played the bifurcation function with *Mathematica*—audio from mathematics on a computer! More…

*Mathematica in Education and Research*

I have been a Professor of Applied Physics at the Delft University of Technology in The Netherlands since 1981. As one of the first in our department to be “vigilant” for software packages that could contribute significantly to our research and teaching–I came across Numerical Recipes in 1987–I was delighted when I stumbled across *Mathematica* a year later. That prompted the following letter on 30 November 1988 to every member of our faculty:

“While I was in California this summer I came across a new software package, *Mathematica*, that was written by a physicist (Stephen Wolfram) for physicists and civilians. This package represents a completely different approach to mathematics and–in my opinion–should be available to every researcher and every student in our department. I purchased *Mathematica* this summer for $690 and have been using it since on my Macintosh II computer. More…

Thanks a lot for giving me an opportunity to contribute to the *Mathematica* story. It was in the early 90’s. I was a regular visitor to the University of Illinois at Urbana-Champaign, and I did some work about the size of coefficients in polynomial decompositions which turned out to be useful in the algorithms used by *Mathematica*. More…

My PhD supervisor, Klaus Schulten, showed me *Mathematica* on his Macintosh computer back in 1989 and it was unbelievable! I had had no idea that something like this existed. A real WOW moment! More…

I was a beta tester for the first version of *Mathematica* in 1988, and have used *Mathematica* more or less daily for the last 25 years for teaching, research (mostly synchrotron radiation biophysics, X-ray spectroscopy), data analysis and modeling, instrument design, project management, administrative and financial modeling, sound and waveform synthesis, graphics and design, image processing, and many other things. It’s my single most essential tool, apart from email. More…

I’ve been in awe of *Mathematica*‘s power since I saw it demoed by Stephen Wolfram at BMUG (Berkeley Macintosh User’s Group) when it was first announced (mid 80’s?). Blew my mind to see pure mathematics represented correctly, beautiful typesetting and graphics, and with many powerful features ready to be explored.

In ~1987 I saw Stephen Wolfram present his ideas of *Mathematica* at Northwestern University, and I was completely struck by the beauty and usefulness of his vision. I began using *Mathematica* upon its release, and three years later I became a faculty member at Tulane University. In my opinion one of the most beneficial aspects is the ability to quickly create simulations of complex mathematical systems and graphically observe the behavior. This provides an exceptional ability to couple intuitive understanding with mathematical rigor. More…

I bought a NeXT computer primarily to get *Mathematica*. When I started to play with it, I was immediately captivated. It could do so many things! After learning the basics, I proceeded to develop a set of notebooks that illustrated the concepts in my textbook, Microeconomic Analysis. These were released in 1992 and are still available on the Wolfram website.

I went on to edit two books about how to use *Mathematica* for economic analysis.

At the beginning I was mostly using *Mathematica* to illustrate concepts in economic theory, but over the years I shifted to using it for statistics, data analysis, and visualization. I feel that *Mathematica* has contributed greatly to my work.

I have been using *Mathematica* since Version 2, but I really started using it in earnest with the introduction of the front end. For me this was a game changer. Now I could and do use *Mathematica* not only to carry out calculations, but to write them up as well. Over the years I have used *Mathematica* for research in acoustics, lidar, data analysis, and, now, general relativity. It is fair to say that without the help from *Mathematica*, neither my teaching nor my research would be where they are today. More…

Although a *Mathematica* user for over a decade, I moved to using R more recently, so I was pleased to discover *RLink* in Version 9, and I’ve started using *Mathematica* once more. And I do, of course, use Wolfram|Alpha routinely on my iPhone and iPad—a marvelous facility.

**Happy Silver Anniversary**

I started using *Mathematica* in my classes in 1989 because I believed then that this tool can help produce much better-trained scientists and engineers. I was never disappointed and it is simply amazing to see how much *Mathematica* has matured, from deep underlying mathematical routines to a beautiful and more and more useful front end. More…

Congrats on a job well done. Yeah, I remember using *Mathematica* when you had to use DOS. I guess it was in the early nineties; I used *Mathematica* in teaching calculus at the first-year level. I wrote many programs, such as finding the equation of a tangent line. One interesting program I wrote was a model of our Lotto 649 here in Canada; you pick 6 numbers out of 49. The probability is about 1 in 14 million. I ran the program “buying 140 million tickets”—I would win the jackpot about 10 times. A very good demonstration. More…

Actually my story begins back in the 70s, before the advent of *Mathematica*. I had formulated some mathematical conjectures. The experts were skeptical, but there was the possibility of checking examples by computer. I tried, but I couldn’t get it to work. Certain numbers were supposed to be rational, and I concluded that these numbers must have very large denominators. At the time, standard mathematical software for portable computers did trig and exponential functions to eight decimal precision, and it just didn’t seem adequate. I tried doing the computation on the big computer at the University of Chicago, but affordable computer time was only available in the middle of the night, and I rapidly tired of carrying my punch cards through the streets of Chicago after midnight. Finally I enlisted the help of a friend at [University of Illinois at Urbana-Champaign] who was really good on the computer. He wrote infinite precision software for the necessary functions. When we were all ready to try the calculation, we realized that there had been an error in the original program I had written, and that in addition the math had to be modified slightly to take into account “bad reduction.” With those two corrections, everything ran like a charm. Try as we might, we never found a denominator bigger than 5.

What is the link with *Mathematica*? Well, my understanding is that the infinite precision routines my friend wrote ended up in *Mathematica*! In any case, I’ve been using *Mathematica* now for 25 years, and I do not have to go out in the middle of the night with my punch cards any more.

I well remember my first days with *Mathematica*. I was working on a paper about the Hausdorff dimension of continued fraction Cantor sets. The basic idea was to represent functions by power series and linear operators by their matrix with respect to the coefficients of the power series. But I wanted to demonstrate that the idea worked in practice, and for that, I had to have an algorithm and a machine on which to execute it.

Along came the NeXT computer, which came bundled with *Mathematica*. The machine was expensive and weak by today’s standards, but it was awesome by the standards of its own day and the coding was a breeze in *Mathematica* compared to what it would have been in some other language. More…

In late 1980s and early 1990s, there were many scientific papers published about so-called surface instabilities in rocks, since surface spalling in deep mines often results in death of miners and extensive physical damage. Even though the problem was theoretically and experimentally well understood, solutions of the instability problems were very difficult to obtain. A colleague of mine had obtained specific solutions, and at a conference he showed me the relevant derivations that were done by hand and filled up a whole notebook. Soon after that I found general solutions, using *Mathematica*, and my colleague’s solution was a very special case. More…

I am still a *Mathematica* user and, despite the fact that I have some complaints about its evolution, it has played and plays today an important part in my professional career. So, this is a good occasion to thank you for inspiring me indirectly on several occasions.

It was November 1990 and I was shopping for a workstation to work at home on my dissertation at TAMU. One of my advisors had some cool-looking black cube workstations that had intrigued me because of the user interface. I learned of a cheaper pizza box slab version that was being offered at the campus bookstore. I went shopping and found out there were several packages bundled with them and one of them was called *Mathematica*. More…

At NASA Goddard, we have many fond memories of the early days of *Mathematica*. One of them is Stephen Wolfram sitting at a computer at the front of the Friday Scientific Colloquium acting like the Wizard of Oz behind his curtain, putting *Mathematica* through is paces and dazzling us. Another is how those of us who were mathematically inclined would get together to ooh and ahh over *Mathematica*’s features, and share tips about plotting fractals and strange attractors. A final memory is very personal: the *Mathematica* book kept getting bigger and bigger, but I would always take it on vacations with me, to my wife’s chagrin and hoots and hollers from my kids. It finally got so heavy I couldn’t take it any more, and they were much relieved, although they kid me to this day: “Dad, where is your *Mathematica* book?”

I was working as a staff economist at the US Department of Justice, Antitrust Division when I purchased my first copy of *Mathematica*. We began by using it to construct more complex and realistic oligopoly models for research, but it quickly dawned on us that we could use these models to make enforcement decisions.

As I was beginning to play with *Mathematica* in the early nineties, a colleague of mine in the Mathematics Department and I were working on a problem that required us to look at some examples of graphs. We had essentially built a “machine” whose inputs were graphs of relatively small order, *n*, and the outputs were graphs of order approximately 2^{n}, very daunting to do by hand. I remember inputting the data in my Mac Classic early in the evening and finding the results waiting for me in the morning. More…

I have worked with *Mathematica* almost all the time from the beginning. While working for a division of Beloit Corporation (Paper-Making Machinery), I started using *Mathematica* a year or so before I had my own personal license.

….I utilize only a small portion of its capacity. As expected, this is typical of most sophisticated high-level programs. Everybody has their own needs. There is obviously a lot to choose from. There is everything that I need—and more! More…

My first introduction to *Mathematica* was with Version 2.0 back in the early ’90s as an undergrad in physics at the University of Washington in Seattle. I had occasion to use it from time to time to double-check my math and physics work. Then in my senior year I did an amazing one-on-one project class with one of the department’s more elder mathematical physicists. In the class I did various projects and simulations using *Mathematica*. As the term went on I began to suspect that I was not so much there to learn from the professor, but to teach him how to use this relatively new amazing application. More…

I started to tinker with *Mathematica* on a NeXT MC68030-based computer with a magneto-optical floppy drive, limited memory, and no HD. I think the year was 1989, with *Mathematica* Version 1 or 2. But it was very cool to use a few lines of Lisp to simplify some symbolic Laplace transforms. *Mathematica* is an amazing program! It has come a long way.

In 1990, I was contracted to develop MundoCart for the NeXT. Along the way, I came up with a geographic object kit that used *MathLink* to extend my Projection class directly into *Mathematica*. With this capability, map designers could test new projection functions directly from *Mathematica* with the data from MundoCart. The fact that every NeXT shipped with *Mathematica* made this an easy choice as all users would have access.

I still have a tape containing an early version of SMP (pre-version of *Mathematica* written in Fortran by S. Wolfram).

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. More…

When a colleague first suggested to me in 1991 that I consider using *Mathematica* in my classroom, we only had the DOS platform available, and all I saw was a “>_” blinking at me, not at all clear as to what I was supposed to do. The following year we got Windows 3.1, so I tried again, and I was hooked. The power was amazing, and every upgrade even more so. When web*Mathematica* appeared 10 years later, we immediately adopted it, and received the 2004 ICTCM Award for projects based on it, but those were next to nothing compared to the power of *Mathematica* today. These have been exciting times.

I have forgotten the names of the symbol manipulation programs I used before *Mathematica*. I have even tried some others since the launch of *Mathematica*, but none have ever compared. *Mathematica* has been an integral part of my research and contributed to classes that I have taught. Happy anniversary to *Mathematica*. I look forward to many more productive years.

As an early user of *Mathematica* it was with some excitement that I went to the Caltech campus many years ago to see Mr. Wolfram give a presentation on *Mathematica*. Before the lecture I was wandering close by the auditorium when a fella with a briefcase stopped to asked me where the Wolfram presentation was being held; more specifically, Beckman Auditorium. I directed him to the site. When the lecture began, I was amused to find out that the fella was Mr. Wolfram.

In the mid-1990s I started a hobby of collecting hymn music from various Lutheran hymnals. I used *Mathematica* to create, categorize, and organize the various MIDI, MP3, sheet music, guitar tabs, audio, and video files. The collection has grown to more than 4,400 hymns with 250,000 associated files. More…

Believe it or not I first used *Mathematica* for plotting results found with APL. I suppose I rather distrusted someone else’s methods for evaluation of functions.

After a while I found that Mathematica got the same results as my APL functions—and much more easily—so I turned over in total to *Mathematica*. More…

The Ball State University *Mathematica* computer lab in early 1991—four IBM RS6000 machines running *Mathematica* 2.0. I hadn’t used computers in earnest before that time. But my Calculus II prof had created *Mathematica* labs to accompany our regular curriculum. So there I was learning how to use computers as a college freshman. I credit *Mathematica* 2.0 with not only a deeper understanding and appreciation for applied math, but also for introducing me to what computers were capable of doing—a very, very exciting time in those early college formative years for me. More…

In the early 1990s I began using *Mathematica* to solve some difficult geometric constraint problems. Over time I developed a robust library of *Mathematica* functions for manipulating geometry.

*Exploring Analytic Geometry with Mathematica*

I likely started using *Mathematica* in about 1989 or 1990. A habit I developed early was to use, as my first command in any new notebook, the addition `1+1`

, and only when I got the expected outcome would I proceed with the actual problem I was examining. After more than 20 years of using *Mathematica*, I still follow the same routine: `1+1`

, `Enter`

.

I was introduced to *Mathematica* in 1989 by a colleague, Ulf Wostner. He invited me to his house where he introduced me simultaneously to his brand-new Macintosh II and to *Mathematica*. I was bowled over. More…

*Mathematica* enables the physics of nuclear magnetic resonance (NMR) to be illustrated through animations that are readily understood even by by persons with limited mathematical backgrounds.

I have used a variety of *Mathematica* animations over the years to teach various aspects of NMR to graduate students.

I first started to use *Mathematica* at Caltech when I was an undergraduate in physics there (1984-87), and Stephen was a young hotshot. I immediately fell in love with it, since it removed all the tedium from doing physics. Stephen might even have been my TA then. Little did I know that the system would not only evolve as it has, but become my core computing crutch to this day. For me, it is indispensable. Until I can create a model with *Mathematica*, I feel my understanding is fuzzy. Great work, and looking forward to the next set of developments. I “think in *Mathematica*”.

I was a graduate student at the University of Texas at Austin in electrical engineering in 1988 when *Mathematica* was released. I remember attending the presentation in which it was rolled out to the UT math department. Now, 25 years later, I am a patent attorney, and I used *Mathematica* recently to download and parse 1,000 patents from the US Patent and Trademark Office website—likely not a use that was envisioned in 1988!

It was Christmas 1989 when my fiancée handed me a box labeled *Mathematica* 2, the Student Version for DOS. She was a student at the time. That night I began to play with it; in no time I was using it to do a problem in tensor analysis. I had some experience with Maple prior to this, but I found *Mathematica* much easier to use. More…

*Mathematica* is a very beautiful software. The power of this software never ceases to amaze me.