What is the best language to write mobile applications? Specifically for social networking, geographical location, spacial photos, videos, photos etc

Assuming you're talking about iOS mobile applications, your choices are Swift or Objective-C. Swift is the future on this platform. Objective-C will most likely be supported for many years but if you're just starting, I would go Swift at this point.

Right now, the broadest support for those examples, I believe, is likely to be via Obj-C - Swift is still new and resources outright might be constrained if you're looking for working examples, etc.

If you're asking which to learn, I'd say both, depending on how fast you expect to put something in the store. If in no hurry, Swift is your friend, I think.

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As mentioned - you have 2 choices, (Obj-C, and Swift). So, the choice of language, for me, is largely based the design of the App... is it Dynamically Driven, or Static. What I mean - is all of the backend ... (where you fetch your data), well defined? can/does it change? How often, etc... This Dynamic app is best dealt with a Runtime Architecture like Objective-C. Swift, which is Compile Time Architecture is great for the well defined static type of App.

With Objective-C, you can use 'Introspection', and other runtime API's to analyse the type data, to create Objects, with properties & methods on the fly... to process, and display data ... that was not 'expected'... thats very powerfull.

Also, while Swift is now ready for 'Prime Time', the push to use it by Apple has beenSpeed... basically the argument went, that a Compiled Time Architecture is faster'... this is true, if you your App did not depend on UI, (They failed to mention that at WWDC 2014). Thats because, all of the UI is created/built on top of Objective-C, (basically traffic flow problem...'You can move only as fast as the slowest car in front of you'). That being said, however... the speed difference is not likely to be noticed by anybody. The real benefit in using Swift, is the time to development should be shorter... especially with the use of Playgrounds. This is NOT a little thing, as one who writes up to 10 apps a year, (me and the team I work with), the time it takes to develop the App is Significant.

Anyway, just some food for thought ... hope it helps.