Their API is down too - started slowing down at 2016-11-07T05:44:52Z and went offline in earnest at 2016-11-07T05:47:37Z.
As you can imagine - we have a lot of analytics on this sort of stuff at Zapier. :-) Usually we know about API outages before any official status pages update (besides our own https://status.zapier.com/#app-status). Ironically Twitter's status page is also down... https://dev.twitter.com/overview/status (or maybe that is just their status API? hard to tell).
It is pretty rare for Twitter to go down - even for a moment.
Update - at 2016-11-07T06:12:55Z we're seeing some HTTP 200s...