Web first
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Creative Commons: https://j.mp/1dPimfh
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I evangelised mobile first, and responsive web design for years now. Not that I'll stop, but I'll switch my primary focus on something even more important, something I'm calling web first!
I'm a big fan of giving a great experience to the users, and I know you are too. Unfortunately, that means native applications for many developers, startups, and companies. I agree that when it comes to mobile, HTML5 isn't quite there yet, and it's why we are developing Firefox OS at Mozilla, but still, the web is a strong platform, and you can give a decent to a very good experience to your customers.
Because native applications seems to give a better integrated experience for the users on their smartphones, why should you start with the browser experience first or web first as I wrote earlier? There are many reasons, but the most important one is that you will give access to your application to everybody with an internet connection! No discrimination about the OS or the device: everybody that have access to a web browser we'll be able to use your application.
Reaching more people, and building the foundation for native applications are also important advantages. If you really want to build a native application, do it after. If your web architecture was well done, you'll already have mostly everything you need to communicate between your server, and your native application if necessary (login, saving, processing...).
I feel that web first is so important, that I want to promote this a lot more: I even brought webfirst.org to create a small site with a manifesto about this (I'll need designers help)! So next time you want to build an application, think web first!