I've been using Macsyma/Maxima pretty much since Joel Moses developed it. It has had a very rocky career, and had the extreme misfortune to be developed prior to the open source movement. Even though I love Lisp, I have lots of complaints about Macsyma/Maxima, most of which stem from the fact that it is probably the least mathematical thing that a mathematician will ever have to deal with. For example, one is never quite sure what ring or field one is working in -- e.g., whether (x-a)/(x-a)=1 or not. A truly mathematical algebraic manipulation system would force the user to be very precise about all of these things, but this level of precision might range from being merely scolding to being unusably anal. An analogy with precise type-checking in computer languages is in order here; without some form of type inference, dealing with some strongly typed languages would be unbearable. Macsyma/Maxima never really got any kind of formal semantics, and Joel Moses's own discussions about "what is a variable" are quite hand-wavey. Nevertheless, Macsyma/Maxima remains an incredibly flexible tool in the right hands. I would personally like to see a mathematical algebra tool that could be tightened up (when desired) into a proof-checker for automatically verifying proofs. I have personally used Maxima to algebraically verify a number of proofs normally done with geometric reasoning, and it was painful, but very educational. At 03:53 PM 8/14/2014, Eugene Salamin via math-fun wrote:

Mathematica is unreadable. I simply ignore Mathematica code in the math-fun posts. I'll use Sage as far as possible, and would consider buying the student version of Maple. Now, Macsyma was a complete winner. But due to a very bad decision, it is now being held hostage, and no reasonable person would pay the ransom for its release.

-- Gene

...

________________________________ From: Dan Asimov <dasimov@earthlink.net> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Thursday, August 14, 2014 3:14 PM Subject: Mathematica

Is it just my imagination, or is Mathematica syntax between 5 and 100 times as clunky as it needs to be?

Sometimes I feel it's like programming with Cobol^Cobol.

--Dan