The Short Answer
No one knows. Not conclusively, at any rate. Satoshi Nakamoto is the potentially pseudonymous name associated with the person or group of people who released the original Bitcoin white paper in 2008 and worked on the original Bitcoin software that was released in 2009. Since Satoshi's identity is tied up intricately with Bitcoin's history, it is helpful to understand Bitcoin's provenance. Bitcoin is one of the first digital currencies which use peer-to-peer technology to facilitate instant payments.
Time Line of Early Bitcoin Events
Aug. 18, 2008: The domain name bitcoin.org is registered. Today, at least, this domain is "WhoisGuard Protected," meaning the identity of the person who registered it is not public information.
Oct. 31, 2008: Someone using the name Satoshi Nakamoto makes an announcement on The Cryptography Mailing list at metzdowd.com: "I've been working on a new electronic cash system that's fully peer-to-peer, with no trusted third party. The paper is available at http://www.bitcoin.org/bitcoin.pdf." This link leads to the infamous white paper published on bitcoin.org entitled "Bitcoin: A Peer-to-Peer Electronic Cash System." This paper would become the Magna Carta for how Bitcoin operates today.
Jan. 3, 2009: The first Bitcoin block is mined, i.e. Block 0. This is also known as the "genesis block" and contains the text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks," perhaps as proof that the block was mined on or after that date, and perhaps also as relevant political commentary.
Jan. 8, 2009: The first version of the Bitcoin software is announced on The Cryptography Mailing list.
Jan. 9, 2009: Block 1 is mined, and Bitcoin mining commences in earnest.
Though it is tempting to believe the media's spin that Satoshi Nakamoto is a lone, quixotic genius who created Bitcoin out of thin air, history has taught us that such innovations do not happen in a vacuum. All major scientific discoveries, no matter how original-seeming, were built on previously existing research. Isaac Newton had been working toward a treatise on calculus, but fellow mathematician Gottfried Wilhelm Leibniz published first, resulting eventually in controversy over who should be credited as the inventor of calculus.
Einstein’s theory of special relativity - originally proposed in 1905 - was built on the experimental works of other physicists such as Albert Michelson and Edward Morley, who in 1887 ran an experiment that debunked the prevailing theory of the day, initiating a line of research that laid the groundwork for Einstein’s elegant theory. Similarly, there are precursors to Bitcoin: Adam Back’s Hashcash, invented in 1997, and subsequently Wei Dai’s b-money, Nick Szabo’s bit-gold and Hal Finney’s Reusable Proof of Work. The Bitcoin white paper itself cites Hashcash and b-money, as well as various other works spanning several research fields.
Why Be Anonymous?
There are two primary motivations for remaining anonymous. One is privacy. As Bitcoin has gained in popularity, indeed becoming a worldwide phenomenon, Satoshi Nakamoto, if a public figure, would likely garner a lot of attention from the media and from governments. By staying anonymous, Satoshi is able to remain out of the spotlight.
The other reason is safety. Looking at 2009 alone, in GMT time, 32,489 blocks were mined. Block rewards were 50 BTC throughout 2009, and thus the total payout in 2009 was 1,624,500 BTC, which at today’s prices is over $900 million. On the last block mined in 2009, the mining difficulty, which started at 1.0 and reflects the amount of computing power involved in mining, was only 1.18. Today the mining difficulty is over 4.24 billion. One may conclude that only Satoshi and perhaps a few other people were mining through 2009, and that they possess a majority of that $900 million worth of BTC. Someone in possession of that much BTC could become a target of criminals, especially since bitcoins are less like stocks and more like cash, where the private keys needed to authorize spending could literally be kept under a mattress. It would make sense, however, that the inventor of Bitcoin would take precautions to protect his/her bitcoins and make any extortion-induced transfers traceable. Nonetheless, remaining anonymous is a good way for Satoshi to limit exposure.
Numerous people have been suggested as possible Satoshi Nakamotos by major media outlets. On Oct. 10, 2011, the New Yorker published an article speculating that Nakamoto might be Irish cryptography student Michael Clear, or economic sociologist Vili Lehdonvirta. A day later, Fast Company suggested that Nakamoto could be a group of three people - Neal King, Vladimir Oksman and Charles Bry - who together appear on a patent related to secure communications that was filed two months before bitcoin.org was registered. A Vice article published in May 2013 added more suspects to the list, including Gavin Andresen, the Bitcoin project’s lead developer; Jed McCaleb, co-founder of now-defunct Bitcoin exchange Mt. Gox; and famed Japanese mathematician Shinichi Mochizuki.
In December, 2013, Techcrunch published an interview with researcher Skye Grey who claims textual analysis of published writings shows a link between Satoshi and bit-gold creator Nick Szabo. And perhaps most famously, in March 2014, Newsweek ran a cover article claiming that Satoshi is actually Satoshi Nakamoto, a 64-year-old Japanese American engineer living in California. The list of suspects is long, and in all cases, the alleged suspects deny being Satoshi.
What Proof is Needed to Positively Identify Satoshi?
All evidence presented thus far is circumstantial. To conclusively reveal Satoshi Nakamoto's identity, a definitive link would need to be made between his/her activity with Bitcoin and his/her real identity. That could come in the form of linking to the real identity behind the domain registration of bitcoin.org, email and forum accounts used by Satoshi Nakamoto, or ownership of some portion of the earliest mined bitcoins. It would seem even early collaborators on the project don’t have verifiable proof of Satoshi’s identity, and only time will tell if such proof will be uncovered or if Satoshi himself/herself will unveil his/her true identity. And even though the bitcoins Satoshi likely possesses are traceable on the blockchain, it seems he/she has yet to cash them out in a way that reveals his/her identity. If Satoshi were to move his/her bitcoins to an exchange today, this might attract attention, but it seems unlikely that a well-funded and successful exchange would betray a customer's privacy.
The Bottom Line
Despite the elapse of years since being first announced and an explosion in Bitcoin's popularity, with today's market cap for all BTC in circulation exceeding $7 billion, its inventor's identity remains unverified if not completely unknown. Satoshi built his/her ideas on top of previous work, citing many in the original white paper, but clearly valued anonymity, perhaps for privacy and/or security. While many news organizations have drawn attention to circumstantial evidence linking various suspects to Satoshi, no definitive proof has been presented, and all alleged suspects have denied being Satoshi.