Google's support page at http://support.google.com/accounts/bin/answer.py?hl=en&answer=185839 states that if I set up two-factor authentication from my Android device, it will offer me a chance to install Google Authenticator and set two-factor authentication up without needing to give a phone number.
However, when I try this on my Nexus 7, it tells me to use a computer — and that only offers me options of an SMS or a voice call, both of which require me to give Google my phone number.
I've run this account since gmail.com was launched without a phone number attached, and I don't want to give my number to one of the world's largest advertising companies!
The gmail account is not my primary email account, and nothing important or secret goes through it, but I still don't want it getting hijacked.
Is there a way around this that doesn't involve spending money on burner SIMs? (nb: I'm not in the US, so please don't suggest Google Voice :)