If you don't have an internet connection, you will not be able to play Super Mario Run. Mashable reports Mario creator Shigeru Miyamoto confirmed the news in a recent interview in which he said the following...

"For us, we view our software as being a very important asset for us. And also for consumers who are purchasing the game, we want to make sure that we're able to offer it to them in a way that the software is secure, and that they're able to play it in a stable environment."

Specifically, Nintendo wants to make sure no one pirates the game, and catch the people who do. Miyamoto does say their original intention was to make the story mode of the game offline compatible but says it was impossible due to the way the game is tied to other modes in the game. 

This has proven to be a deal breaker for many in the gaming community, who don't think it's right they should pay $9.99 for a game they can't play however they please. I tend to side with them, although there's rarely a time where I have my cell phone and don't have service. If the game was free to download I might be a bit more sympathetic, but it looks like Nintendo will shoot themselves in the foot once again with gamers due to greed. 

I don't expect this to affect the sales of Super Mario Run greatly, however. Mario has an appeal that has time and time again reached audiences beyond the core of the gaming community, and now that he's on a phone I expect crazy numbers of sales the day of launch. I do also imagine that eventually Nintendo will develop an offline mode if enough people spread the word and gripe...which is precisely why I'm writing this! Let's hope spreading the word encourages some change at Nintendo headquarters.