I feel obliged to defend my use of Mathematica. The obvious
reply to the remark that “hey! It’s free” is that sometimes you really do get
what you pay for. The density of bugs in Mathematica seems much lower than in
the social network packages that I’ve tried. Also, I’ve realized that sadly I’m
not as good at writing low level code (say in C) as are the professionals who
produce Mathematica (or MatLab for number crunching, SAS for standard
statistics). Of course, it all comes down to your own personal needs and
preferences, but here is what I like about Mathematica. Tell me you’re not blown
away by the following video:

http://www.wolfram.com/broadcast/screencasts/introducingmathematica7/

Mathematica has many graph theoretic graphing and analysis
functions. E.g. here are just the GraphData functions and predicates starting
with the letter “a”:

Acyclic, AdjacencyMatrix, AllImages, AllVertexCoordinates,
AlternateNames, AlternateStandardNames, AlternateVertexCoordinates, Andrasfai,
AntelopesTour, Antiprism, Apollonian, Archimedean, ArchimedeanDual,
ArcTransitive, ArcTransitivity, ArticulationVertices, Asymmetric,
AutomorphismCount, Automorphisms.

All are computed with the best known algorithms.

Like many program Mathematica can do numerical
integration, but it also does symbolic integration. For example, a problem from
Ramanujan' s notebooks can be
solved with the input,

Integrate[Log[(1
+ Sqrt[1 + 4 x])/2]/x, {x, 0, 1}]

giving the
exact, symbolic answer, Pi^2/15.

Finally, Mathematica because it takes me out of the narrow
confines of social networks and into the world of real math and science. It
makes me learn something new every time I use it. What is life about except
growth?

John Boyd

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