Well, it's Alpha, not the Wolfram Language.

But I don't think it takes much imagination to see how things like http://www.wolfram.com/language/gallery/visualize-celebrity-... or http://www.wolfram.com/language/gallery/plan-a-city-tour/ or http://www.wolfram.com/language/gallery/track-a-gps-equipped... or http://www.wolfram.com/language/gallery/email-freeze-alerts/ or http://www.wolfram.com/language/gallery/classify-images-as-d... could be the basis of something commercially valuable or publicly useful, especially given how easy they are to create. (edit: and those examples are not even designed for commercial appeal, just concision and cool factor).

And it still has glaring omissions. One thing it still can't do is group theory. I'm not a mathematician, but I occasionally need some group theory stuff at work. This is stuff that is either tabulated or can be calculated easily by a computer. Like "show me a matrix representation of SU(3)" or "decompositions of SU(5)" or "irreps of SU(10)" or something. Group theorists have these little equations with circled operators, like 1+8=3 (imagine numbers in bold and a circle around the plus. I just made up the numbers, but they're usually as wierd), that I can never wrap my head around no matter how often I've tried. But they are kind of important for particle physics, and I hope that wolfram alpha will eventually incorporate that stuff.

Actual particle physics is also lacking, everything besides simple queries like "mass of the top quark" is missing (and the mass it gives is not up-to-date). I would like it to have "decay modes of neutralino-1 at m0=1000, m12=1000, ..." or "higgs mass=126, particle-such-and-such-mass=1000, solve for parameter-x" and it would show me valid values for x resulting in these masses. This is all easily implementable, but I guess the market for it is too small (otoh, I don't know what the market for "dog vision" is...(

I tried replacing dog by cat, and it doesn't work. Why?

Also, for the inverse gamma function of complex numbers: gamma^-1(1+10i) works. gamma^-1(1-10i) confuses its parser (doesn't know how to interpret input, even though the previous and next one work). gamma^-1(1-10.0i) works again. Why?

No it really doesn't. Think about the underlying abstraction. The point is that somewhere, the engine knew how to define a transformation "dog vision" on a set of objects, namely photos.

Taking it further, it's possible that "dog" was a transformation on "vision" and other visions are available.

As a math major who used Wolfram alpha for the last 3 years of my undergrad some odd years ago, I have to say I had an overwhelmingly positive impression of the product.