In the very long term, Mathematica needs an open-source equivalent. Someday Wolfram might open it; it would be a gift to humanity.

 It depends which parts of Mathematica you need.Python is an alternative, especially within the Sage package [0].Then there is also Maxima [1].
 I use Octave daily (in the last hour, will return to it when I finish my soup), but have never seen anything that matched Mathematica's symbolic/pure math functionality.Will check out Sage, haven't used Maxima since 2004. Thanks!Edit: Sage looks nifty, Maxima looks unchanged, at least at screenshot-level.
 SymPy (sympy.org) is a well-developed Python package that works with symbolic/analytical mathematics on a level comparable to Mathematica's.Octave is more of an open source Matlab equivalent. That is, mostly linear algebra.
 Indeed, there are plenty of open source solutions that can solve your particular problem, and many problems don't need any sort of symbolic tools. There's also Octave with a nice collection of packages on Octave-Forge, there's PARI (included in Sage), and there's LAPACK, and I'm sure there are others I'm either forgetting or haven't heard of.
 I too can attest to the extensive abilities of the Sage package. It's extremely powerful and easy to use given that it's based in Python. Even if you don't want to download it, give the notebook a try: http://www.sagenb.org/.
 > Mathematica needs an open-source equivalent.Mathematica _has_ open source equivalents. It has equivalents that predate Mathematica. Their libraries just aren't as extensive.
 It stretches the definition of equivalent but folks interested in an open-source version of the Mathematica language should see or contribute to http://www.mathics.org/
 I'm not sure what you can do in Mathematica that you couldn't do in R http://www.r-project.org
 It's been a long time since I used Mathematica, but I always used it for symbolic computations (e.g. "derivative of x^2 = 2x"), especially when I was learning calculus and differential equations. As far as I'm aware R doesn't even natively have a way of storing symbolic equations, let alone solving them (at the least, it's not its main use-case).But I could be wrong; I used mathematica and R for very different things so I may just be unaware of their similarities.
 In principle R language is equally potent than Mathematica's one (functional+self-modifying), so Mathematica clone can be done in R (and in fact there is a built-in function "D" which calculates derivatives of native expressions symbolically).Of course this won't ever happen because of the paradigm -- R is for data crunching and does this way better than Mathematica.
 https://code.google.com/p/ryacas/ to name one. It's not native but yet so aren't a lot of libraries in other languages.
 Hasn't been updated since 2007... math doesn't really change that often but that does not look promising...
 There's "can do" and then there's "is like."
 Hats of if you can do http://blog.wolfram.com/2012/10/23/calculating-the-energy-be... in R or, for that matter, about half of the other examples given in that blog.
 Mathematica provides symbolic computation, R does not.
 Sympy (written in python) also provides a number of features.
 Maybe we need an open-source Mathematica or Wolfram Alpha, but I don't think Wolfram would benefit of either being open-source.
 He'd be remembered as having given a gift to mankind, which he might like very much.
 Wasn't that NKS?Seriously though, he did seem open to the idea of at least partially open-sourcing Mathematica during a recent AmA: http://sx.reddit.com/r/IAmA/comments/qisot/im_stephen_wolfra...
 His very large book was the "gift" to the public. Now we just need to find the "rule" that explains the universe.

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