What Is It What Only Mathematica Can Do?

This question arose when I read in WIRED's Blog This Day In Tech 12-Jan-92 or 97: HAL of a Computer1992: HAL 9000, the master computer aboard the Discovery spaceship in the novel and film '2001: A Space Odyssey', becomes operational. He will inspire millions of dreams — and some nightmares — of artificial intelligence.
An artificial intelligence that could think, talk, see, feel and occasionally go berserk? HAL - a fictional computer that is more advanced than any computer today?
From the The AI Revolution Is On one could summarize: systems in the forefront of artificial intelligence shall apply machine learning and  massive data management instead of emulation human intelligence.
And beyond new ways to program and compute are required.
What is It .. ?
  • Natural language input and in general the possibility to define any syntax and input form that generates programs that trigger anything from simple to complex computation. The strength of linguistic capabilities has been shown by, say, fuzzy logic, but its representation is restricted to rule-bases
  • More general the tight integration with Wolfram|Alpha
  • The capabilities to dancing with symbols and numbers in a way that allow for asymptotic math approaches supported by automated algorithm selection and adaptive precision control (symbolic parallelism, for example, saved us so much development and optimization efforts)
  • Pattern matching, let functions be applied to practically anything. It is indispensable if you want a program layer that describes in the language of mathematics
I might have missed other capabilities, but I think, this is a lot ....?