We are so used to the notion that the US lags behind the rest of the world in mobile phone use that it is a shock to be told it is no longer true.

I am in San Francisco at the leadership conference of the American Association of Advertising Agencies (now formally re-branded as the 4As) and have been hearing some interesting statistics.

They were in a presentation by Cyriac Roeding, an entrepreneur-in-residence at Kleiner Perkins Caulfield & Byers, the venture capital firm, who used to be head of mobile for CBS, the television network.

Mr Roeding pointed out not only that the number of mobile phones in the US has grown rapidly as a proportion of the population but that the Apple iPhone has shifted the balance of mobile software development to Silicon Valley.

There are now 270m mobile phone users in the US, out of a population of 304m, compared with 223m internet users.

More surprisingly, Americans now send 110bn text messages a month, which has grown exponentially from an average of 48bn per month in 2007, 19bn in 2006, 10bn in 2005 and 5bn in 2004. In other words, the number has been doubling each year.

As a result, Americans now send an average of 400 messages a month each, which is four times the number sent by British mobile phone users, who used to be far heavier texters.

“That is an unbelievable catch-up. There is a fundamental shift going on and I believe that this (Silicon Valley) is now the centre of mobile innovation in the world,” said Mr Roeding, who was born in Germany.