Oh boy! A topic from the area of the Internet where I actually spend my time and can add something to the conversation!
First, here's the best article on the subject. All quotes and insight are sourced first-hand via direct interview with Matt Mullenweg himself: poststatus.com/automattic-has-purc... -- I was present for parts of the conversation that formed this article. It was a special thing to witness!
The biggest questions that I've seen speculated, both here and elsewhere, are, "what are they going to do with it?" I think this article addresses that pretty well.
The most succinct summary:
Move infrastructure off Verizon.
Support same APIs on both WP.com and Tumblr.
[Eventually] Switch backend to be WP.
Open source [the] Tumblr.com client.
To address the title of this post, "how open-source will Tumblr become?" I believe the answer is "extremely." Automattic's most central tenet is the freedoms provided by open source.
This is a really beautiful acquisition that I think is going to work out extremely well for everyone on all sides. I can't remember the last time I felt that way about an acquisition, if ever. This one has so many upsides.
Cheers to everyone involved!
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