He tried, a long time ago, and lost the primaries to Carter (twice... not sure why he bothered to enter the primary in 1980). He also lost a presidential primary in 1992 (Clinton).
If he ran again in 2020... well, it would be pretty fitting considering he's done his whole career path twice, but it's pretty crazy that it's not absolutely out of the question for someone who was on the national stage at the same time as Carter and Reagan to still be there.
His 1980 campaign was particularly weird in its combination of positions. It was during the height of his "Governor Moonbeam" reputation, and combined a grab-bag of left-wing and right-wing proposals, mostly culturally left but economically right-ish. Strategically this might've been an attempt to paint both Carter and Ted Kennedy (the other main primary candidate) as old-fashioned: Carter as staid and culturally conservative, and Kennedy (who had proposed a single-payer health plan) as the big-government, big-spending liberal, with Brown as a new modern kind of liberal who balanced budgets while advocating for acupuncture, solar energy, organic farming, and space travel. Very "California ideology", but it didn't really work nationally.
His 1976 campaign by contrast was oddly similar to his current persona, a kind of center-left, pragmatic technocrat. The conventional wisdom seems to be that he only lost because Carter figured out quicker how to campaign in the new primary system (1976 was the first year that primaries rather than state conventions dominated) and racked up a bunch of early delegates.
Jerry Brown has had a pretty nutty career. He's been governor for 4 terms (16 years), but that's split into two stints 30 years apart. He was first elected Governor in 1974, at which point he was not quite the youngest governor ever, but close. He's now the oldest governor ever.
I can't imagine what that first day back in 2011 must have been like. "Oh yeah, just like I left it... except now there's all these computers, those weren't here before..."
What was funny was that when he ran for governor in 2010. He went against Meg Whitman. She ran an ad praising the economy when she came to California - when Jerry Brown was governor
