Dear Luther, I've been puzzling over your observation for nearly 15 years, and I also fail to understand why Mathematica/Wolfram Language gets dismissed by my colleagues so haphazardly. In discussions with my colleagues about this question, I tend to go in listening mode and don't advocate on one side or another. I'll try to summarize what they say below.

Some background:

I'm a professor at MIT in physical sciences and engineering. I've been teaching a course on mathematics and problem solving in materials science for about twelve years, and I use Mathematica extensively in my course. I can't judge the efficacy of my course objectively, but my students generally have very positive evaluations; I've been given MIT's highest institutional teaching awards, as well as the School of Engineering's. I believe that these awards reflect the quality of the Mathematica based course. I give nearly all of my research presentations using Mathematica and these are received well (however, such feedback tends to be biased towards positive)

The summary (I don't agree with many of these, and am still honing my counter arguments)

1) Mathematica is not as fast as X (X may or may not be a compiled language).

2) Mathematica's syntax creates too steep of a learning curve.

3) Our (particular) scientific community uses X; so there are many more routines and working examples in X

4) I am already using X, why should I change?

I believe most of the above are the result of "user inertia".

I don't hear the comment that Mathematica gives "bad results" so much now. I doubt if many faculty roll their own algorithms, but are probably thinking back to when they were postdocs or graduate students--however, there are happy exceptions to this

I believe that the best way forward is to offer students a choice; and hope that they will make an unfettered choice of a their preferred programming language. However, I am not so optimistic: a student who went to graduate school at a university down the street wrote to me saying, "I'm taking this class and they insist on using X and I asked if I could use Mathematica instead, and he said no. We were doing more advanced things in 3.016 ( the sophomore class I teach)."

I concur with your assessments and those of Park based on a more general exposure to technologists with particular preferences. I started with a blank slate in terms of exposure and preferences, since I had avoided programming at any level after my early pre-PC experiences with Fortran and Basic and more punch cards than any one graduate student should have to carry. I was never required to do much programming, starting with my first job at Michigan (we used a Wang with punch cards!!!) to Battelle, where I was fortunate to manage a talented group of scientists and technologists who loved programming. Now as I close in on my dotage, I am on my own.

I had to find a muscular program to work out some problems that had never been properly solved because all work on those problems stopped a hundred years ago. A reading of a basic paper showed that the author had not actually done what he said he was going to do and did something else because there were no tools like Mathematica available then.The author did what he could. I reread the paper and identified an asyllogistic conclusion and set out to test the author's methodology. I got results that contradicted the text books. However, I did not know if the fault was mine (mis-interpretation or mis-statement of the real problem) or whether the issue was Mathematica (again, was it my use of mathematica or something within Mathematica), or were the results true? So, after research that led to no resolution on any of the points, I asked.

The results of my consulting with several faculty were disappointing. Other than criticizing Mathematica and my methodology, I simply could not get anyone to actually read the statement of the problem as originally presented nor my interpretation and subsequent modeling using Mathematica. I had expected push back but not total out of hand rejection of my thesis, and the criticism of Mathematica seemed to be a way out for actually having to address the issues and possible consequences that the problem presented. I am, at this point, working down the list of criticism eliminate them. Hard slog.

Luther, why don't you write me at djmpark@comcast.net and tell me what your project is.

Hello Danny and Luther, That makes three of us who started with punch cards.

A bizarre as it might seem, I think punch cards were a beneficial way to learn to program. I spent so much more time thinking about the program and doing thoughtful debugging because submission of a job was so painful. I confess that I often do debugging now with less reflective thought because I can do dozens of haphazard experiments in minutes--this probably speeds the debugging process as often as it slows it down.

I was sold on symbolic computation (pre-wolfram-language) when I was able to solve classical mechanics homeworks faster and more accurately than my classmates. I remember that just being able to do a taylor expansion around a point and copy down the results and redraw crt-rendered plots into my homework felt like cheating.

I also remember my own "inertia" of switching from "symbolic-program-x" which was free at Berkeley (and had opaque syntax that I had learned moderately well) to Mathematica 1.

Craig

Ah, memories!

I had heard of it as a Planck quote, but I have also heard that it was a quote of a quote. It is like Newton's standing on the shoulders of giants. I think that is a quote of a quote, too. The more modern version of Planck's quote is about progress or acceptance occurring one funeral at a time. Planck's quote was kinder and about acceptance occurring through the younger generation being more familiar with whatever is new and novel and having grown up with it. I am always reminded of the idea of continental drift and how hard it was for the geologists of not so long ago to get their heads around the idea despite the circumstantial evidence. Alvarez's asteroid extinction hypothesis is still being tested...as it should be.

I can understand the push back if it were something truly novel, but in my case it was a redo using more advanced techniques available through Mathematica. The approach was simply a re-reading of something and realizing there was a disconnect between what was said and what was actually done. I am of the opinion that everything should be periodically revisited in light of newer findings, insights, and techniques.

When I started my career, I was performing contract R&D and we were selling applied physics and technology. I remember plowing though the journals to get ideas for applications, since I knew what my customers' problem areas were from a technology perspective. If something was novel, I tested it for applicability to various applications. Got some things so wrong, but got some very right, too. It was a fun time to get into the technology business.

The times were different. We took chances. Even a dumb idea might have a nugget of goodness buried somewhere inside.

"All of the manuals on how to use Mathematica have been written by people who know too much. Their work should be edited by someone like me who is trying to learn what the developers already know."

Luther, I find your basic thesis here by and large accurate. Mathematica does have a steep learning curve and to directly use the more advanced features (particularly the various programming paradigms) one has to think like Mathematica, which for me has not come naturally.

Like others here, I started off with FORTRAN punch cards in college and was simply amazed at what could be done with the "simple" Do Loop. Ten or so years later I stumbled upon Macsyma, anybody remember that ? It was a command line math tool that claimed it could do symbolic math, maybe it could but I did not find it useful. Then I noticed that our Technical Librarian had a copy of Mathematica sitting on her shelf, version 2.2. After inquiring about it I learned that one of the Chief Engineers owned it originally but returned it to her because he couldn't figure out how to use it. I convinced my company to purchase the Premier Support package which offers supurb technical support and over the years would amaze him (and myself) of what could be done with this tool. I also read a few Mathematica books which I enjoyed at the time but that didn't boost my usability knowledge as I had hoped. During and prior to these years I became somewhat proficient with FORTRAN, MathCad, Excel, BASIC, Minitab and Matlab. And from my experience only Matlab comes close to the power of Mathematica if various toolboxes were acquired. Out of the box, Mathematica was a clear winner for my technical computing and data processing needs. And when serious statistics were added (ver 8 I think) there was no need for any other tool.

Fast forward to today, I am still a clunky Mathematica user and I still rely on the basic Do Loop from yesteryear even though much more efficient programming techniques have been available in Mathematica for years. But I've done some pretty neat stuff that no one else in the company has been able to do.

I share the learning curve frustration but I will take a hard to use yet capable tool over an easy to use limited tool any day. And for my technical computing needs, Mathematica has never let me down in the sense that if I could conceive it, Mathematica could be coaxed to solve it; that is powerful.

On a practical note, the approach I have found very useful is to create and maintain a private library of "How To Notebooks" that describe a narrow task that you know you will be facing again in the future. The source material for these may come from the hard slugging and self-learning that you have produced, a call to Tech Support , the online Help, books, or the Mathematica StackExchange site. If I look at my "How To" Folder I see file names like

How to align entries nicely using TableForm.nb How to compute running averages.nb How to conditionally extract values from a list.nb How to convert time formatted strings to numerical values.nb How to control minor ticks on a log axis.nb How to create a 3-D surface plot.nb How to extract algebraic solutions produced by the Solve command.nb etc.

I find this is far more useful that trying to rely on the built-in Help which, in general, offers a very simple example or two (material that you already know) and then jumps to examples so complex that [literally] some Tech Support Engineers at Wolfram have had some difficulty with, and these guys are good !

Kudos to Stephen Wolfram and his team for inventing, enhancing and maintaining what I think is the strongest technical computing environment on the planet. The professors mentioned at the beginning of this discussion don't know what they are missing.

For an example, that I have put to use in my own work, Google and download the Sandia report Sample Sizes for Confidence Limits and Reliability, by J. Darby.

I first used Macsyma over a 300 baud modem over the Arpanet from Caltech to MIT back in the mid 70s. And I found a bug. They had the general solution to the cubic entered incorrectly.

With the central claim for Mathematica being that it is the single tool needed for everything from jotting down mathematical notes to doing initial exploratory calculations to creating graphics to implementing entire sets of tools for a problem domain to writing and publishing papers and textbooks, I am surprised that I have not seen more published on how to carry out that last step. From the style of it, I am assuming that Ruskeepa's "Mathematica Navigator" was written almost entirely within Mathematica.

There was a thin little book published perhaps twenty years ago showing some of how, entirely within Mathematica, to create documents for publishing. I held a copy in my hands for a minute, but didn't buy it and have never been able to track down that title again. If you could find that book, even though it is old now, then it might help you get started. Perhaps someone else can recall that title.

On the larger question of reception, culture and attitude is far more powerful and persuasive than most might imagine. If you want to do another literature search, then look at the reception that automated theorem proving or even computer proof checking has received from the vast majority of the mathematics community over the last fifty years. Then you can compare and constrast that with the reception that Mathematica in particular and other computer algebra systems in general have received. Perhaps that would help you better understand what you are seeing.

Some have claimed that ideas which are rejected now will be embraced and adopted when the previous generation dies. But culture and attitude may be more persistent than that. If you are creating something new then choose your culture and attitude carefully because you will pay the price and live with the consequences of that forever. For example, if you happened to be around and watching during 1980s, when the culture and attitude was instilled into Mathematica, you might be better able to notice, and possibly even understand, some of the behavior of people inside and outside of Wolfram Inc. thirty years ago and, in some cases, unchanged today.

Lastly, I try to sense your attitude from what you have written above. You might contemplate that. It has a way of leaking out and there almost always seems to be a price to pay for that. I do realize my some of attitude has leaked out in what I have written here.

Dusty trails indeed, and in my case, of the handful of engineering companies I've worked for, if I wasn't the only Mathematica user, there may have been 2 or 3 others that let it collect, you guessed it . . . dust. For some reason Matlab/Simulink dominates the engineering world and Mathematica is more popular in science, education and maybe finance. One area of computation that is bound to continue to explode is medical research. I wonder if Mathematica played a role in cracking the human genome.

Macsyma over a 300 baud modem pre-dates me somewhat but nice job in catching that error. I do remember running test cases with it from my CRC Standard Math Tables handbook and having much difficulty interpreting the results that Macsyma produced on my bulky, heat producing Cathode Ray Tube. Of course Mathematica has FullSimplify and similar commands to push results into a more human readable form.

On the topic of supportive learning materials in the 90's I subscribed to Mathematica in Education and Research put out by Telos/Springer. I found this journal to be highly readable and useful as I don't have advanced degrees. It was full of plots, images and code. Thinking back, I learned quite a bit from that little journal as it was very practical in nature.

Does anyone know if this or similar journal is still in print ? I'm aware of the Mathematica Journal, but I've found that to be too theoretical and advanced for my needs.

"Just playing with Mathematica is a good strategy for staying young"

I tried that Craig and it doesn't work! Running very very fast might work in a relative sense.

More accurately, playing with Mathematica is a good strategy for maximizing the use of your time.

This is not intended to criticize Edward Tufte or diminish any of the fine work he has done. If you carefully study each of his books you might notice that there is one thing which has not been included. There is not a hint of uncertainty in any of the graphics that he presents. For one example, I cannot imagine in the fog of war in 1812 that Napoleon's march on Moscow was anywhere near as precise and tidy as the famous graphic leads our minds to believe. Yes, the graphic does round the numbers to thousands, but even that I suspect is a misrepresentation.

I spent time some years ago trying to get vendors to use all the new found compute power to demand from the user and then display the uncertainty associated with graphical presentations. Yes, Mathematica keeps track of the precision associated with some numeric quantities, but Plot does not then display graphics which are just fuzzy enough to force us to realize how much we don't know. I don't think the classic error bars are the answer, but fuzz might be.

Several simulation tool vendors will quietly admit that their calculations are really not as precise as their tool displays. One vendor even suggested that I diddle the coefficients a little each time, do ten runs, print all the results, tape them to a window and try to guess what the uncertainty really is.

I listened to an invited speaker years ago. He presented slide after slide of very impressive graphics showing the behavior of something. He was asked if it would be possible to include an indication of the uncertainty in his slides. He replied no, because if he did then it would be obvious that his results had no predictive power. I suspect even the audience members who already knew this still made incorrect assumptions when looking at the graphics.

Consider how many predictions we see for projects large and small. We almost never see the uncertainties of the inputs or outputs or any indication of the uncertainty associated with the project success or failure. The only use of uncertainty currently is to claim there is none if it my project or it is a stupid idea and we shouldn't do it if it is yours.

It seems that everyone wants to know "the number", nobody wants to hear there is any uncertainty. Everyone wants to see the graph with the spidery little line showing the economy is going smoothly off to infinity. There was a book not too long ago which talked about how everyone wants to be told the number, usually the mean, and how badly we make mistakes when we don't see and plan for the uncertainties. Ah! Found it! The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty by Sam Savage, Jeff Danziger and Harry Markowitz. This should not be license to now have to make up numbers for the uncertainties to go along with the numbers we made up for the predictions.

I considered writing a letter to Mr. Tufte asking him if in his next book he might introduce the world to the knowledge that nothing in the real world is precise, when we don't know the uncertainty that we reach false conclusions and we should all begin demanding credible uncertainty information be included in graphics. But the last word I heard is that he is deep into what will likely be his final book and I doubt that he could incorporate such a dramatic change in presentation now. If Mr. Tufte can't be the one to do this then perhaps someone else can.

Something that I learned years ago (very likely from Feynman or quoted about him to me by someone else) is that, when looking at a dataset in a presentation and listening to the presenter's description of the meaning of the data, in your mind drop the data points from the graph at its extremes and decide if the conclusions make sense. Why? The data at the extremes are often there because the experiment stopped being trustworthy at roughly near those limits so the strength of those points often would be in question....

Bill, your remarks are well put. I think that Tufte somewhere does have a maxim to Be Honest. And he does give several suggestions in Visual Explanations page 34. This might include multiple presentations based on different measures or viewpoints and textual explanation that might address various concerns. That's why I'm an advocate of literate notebooks that make a case and try to clarify and present a true picture. I would be very skeptical of any analysis summarized in a single presentation without extended discussion. In the final analysis it largely depends on the integrity of the person making or responsible for the analysis.

Mathematica probably has the tools to present uncertainty and risk. You just have to figure out how to put them together. With a dynamic presentation you can provide information in tooltips. You can provide information in numerical side reports, which may vary as you move a locator about the primary data representation. You might be able to toggle a presentation between various assumptions. And of course there are the old fashioned error bars and multiple presentations. Your suggestion of fuzzing the data representation might work very well. To go one step further, in a Mathematica notebook (or application) you can give the reader active tools for performing various types of data reduction and the actual data itself. I'm not knowledgeable about statistical analysis of data; I'm sure you can work out much better methods. The point is: Mathematica does give you better tools to present honest results.

The quintessential example that comes to mind for me is the Fleischmann–Pons claim of cold fusion.

http://en.wikipedia.org/wiki/Cold_fusion

Bill, that seems a bit off topic of whether academics are missing out by not making greater use of Mathematica. But maybe not completely. Because of their active and dynamic character, Mathematica provides the opportunity of presenting higher quality results with higher integrity. One can include, in the document, raw data and procedures for analyzing and representing the results. Others can check if they actually work or have entry points for exposing problems. If people want to lie about data I suppose they can but it's not quite as easy to get by with just plain sloppiness.

I once worked as a computer consultant for a group of biochemists. At one point I was asked to look at an experiment one of them was doing to measure the rate of some biochemical reaction. The person was very nice and very meticulous in his biochemistry. But when I looked at the reaction system and what he was measuring I discovered to my horror that it had no relation at all to the reaction rate he was trying to measure. Needless to say, he was not pleased with this. I left the group but later learned from someone who replaced me that they continued the experiment and analyzed it with a statistical program. The result was something like 1.0 +/- 10^6 millimole/minute - and they published it!