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The new functions include, machine learning, geometric computation, geographic computation.
You may calculate the photograph of the Yorkshire Terrier ;-), quickly draw the map of France on a parabola, or solve differential equations with 100,000+ solutions (Mathematica 11 will raise it up to \(10^{500}\) solutions which will kill all the individuals screaming that the landscape is intractable).
There are huge new algorithmic capabilities in Mathematica 10 in graph theory, image processing, control theory and lots of other areas. And you may find hundreds of similar sentences in Wolfram's description. Each sentence corresponds to a googolplex of new functions and tricks that Mathematica 10 can do for you.
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