Let's analyze John Nash's public and presentations activity to determine if could have been Satoshi Nakamoto.
@traincarswreck has pointed that removing "i am Nash" then remains 'sato' which is the most common name and 'koto' which means thing and is the national instrument in Japan, thus an implied meaning of Bitcoin is harmonious thing for the common people created by John Nash.
2001 Nov Presented ideal money in Tampa, FL.
2002 Apr Presented ideal money in Beijing, China.
2002 Oct Presented ideal money in Gamble lecture at UMass.
2003 Nov Starts research on Cooperation in Non-Cooperative Action in a Repeated Game Context (aka Agencies game theory research), for which I conjecture proof-of-work consensus is a specific case of incentives for agency cooperation wherein the Shapley value is a hashrate weighted Poisson process. He did some Mathematica programming.
This was presented at Penn State where he also presented his ideal money concept.
2004 Apr Presented ideal money at Georgetown University in Washington D.C..
2004 Oct/Nov Uploads utility programs for transferring files to hosts on the Internet.
2005 Jul Uploads more secure utility program for transferring files to hosts on the Internet.
2006 Apr Presented Agencies game theory at Lindau, Germany.
2006 Aug Presented Agencies game theory at the University of Northern Iowa in Cedar Falls.
2007 Feb Continuing his journey towards unifying quantum mechanics and Einstein's general relativity.
2007 Feb Presented ideal money in India.
2007 Jul Presented Agencies game theory at Stony Brook, Long Island.
2008 Feb Presented ideal money at NYU.
2008 May Uploads Symantec AntiVirus (SAV) for servers.
2008 May Presents his Agencies game theory research at ECCAD'08.
2008 May/Jun Presented ideal money in Russia.
2008 Aug Presented ideal money at Nobel Laureates Meeting in Lindau, Germany.
2008 Sept Presented ideal money at Fordham University in New York.
2010 Feb Presented ideal money at "Campus for Finance" in Vallendar, Germany.
2010 Oct Presented ideal money at Lafayette College in Easton, Pennsylvania.
2011 Oct Presented ideal money in Hong Kong.
2012 Apr Published new results of research on Agencies game theory.
First notice the periods of relatively low or no public inactivity for Nash were from May 2004 to Feb 2006, and again Oct 2008 to Feb 2010. Also note how Nash shifted from ideal money focus before 2004 to Agencies game theory research focus and didn't return publicizing ideal money again until summer 2008 wherein he did it very intensively.
Note that Satoshi announced Bitcoin Oct. 31, 2008. And it is also noted that Satoshi basically stopped being involved as of of "mid-2010".
Add to this that Szabo (re-)published bit gold Dec 2005 which described how to make a Bitcoin, except Szabo hadn't solved the Agencies consensus game theory by employing the proof-of-work and had instead only offered Byzantine agreement (Szabo solved minting and greatest proof-of-work rule but not the Agencies consensus). Wei Dai had proposed in 1999 a flawed/inadequate solution to the Agencies game theory but which would hint as to how to combine with Szabo's design. So all Nash had to do was be aware of those and integrate it with his research on Agencies game theory and he would have easily seen the solution for Bitcoin. So it appears Nash was working very intensely on Bitcoin coding in 2006 and 2007, probably teaching himself to be proficient in C++.
This ability of Nash to combine the works of others in novel ways was noted by French mathematician Cedric Villani which @traincarswreck featured as a video in one of this blogs.
Satoshi often used British English and we should note that John Nash had previously left the USA and lived in the UK for many years. And the posting time of Satoshi (presuming he was sleeping when not posting) indicated he would be where Nash was located in the USA.
It all correlates well for Satoshi being Nash.
Nash's Agencies research was on Cooperation in Non-Cooperating Repeated Games, which is precisely what Satoshi's PoW is!