The second-ever episode of Saturday Night Live didn't mark Simon and Garfunkel's first reunion. Still, because of its nationally broadcast stage, their performance together on Oct. 18, 1975, is far better remembered that the Madison Square Garden fundraiser they played three years earlier for presidential candidate George McGovern.

They'd already recorded "My Little Town" together for Paul Simon's new solo album Still Crazy After All These Years, too. Still, seeing them perform that new song – it was the closing moment for this brief new live collaboration, following "The Boxer" and "Scarborough Fair" – served as tantalizingly brief example of what they could still accomplish together.

But the duo's 1970 breakup hadn't just ended their musical lives together. They'd subsequently drifted apart personally, as well. SNL ultimately wasn't the beginning of anything, only another reminder of what might have been.

That left Art Garfunkel to try to make sense of things. "Did you ever get married? Did you ever get divorced?" he once told Florida Today. "It's the same old stuff. The juice ran down. We got tired. Compatibility proved difficult, in the long run. We needed a rest. The rest turned into a longer rest than we anticipated. It's organic for things to come together and move apart."

Certainly, Simon and Garfunkel showed that the old magic could still conjured on this night. Yet, in a sign of what was to come, the broadcast also included solo segments for both Simon and Garfunkel. The reunion was as emotionally resonant for fans as it was brief for the participants.

Simon opened Saturday Night Live that evening by singing the title track from the gold-selling Still Crazy After All These Years, and also performed “Loves Me Like a Rock,” “American Tune” and “Gone at Last.” Garfunkel, meanwhile, sang "I Only Have Eyes For You" – a highlight of his then-current Top 10 hit album Breakaway.

It would be 1981 before they'd share the spotlight at an historic Central Park concert. Alas, there has been no more new music. Simon and Garfunkel consistently appeared together through 1983 – when Simon's decision to release Hearts and Bones without Garfunkel's shared vocal tracks soured things. They didn't tour again until the early '90s and, after some notable intersections in the 2000s, haven't appeared together since 2010.

At this point, however, jokes could still be made about their estrangement. Simon memorably welcomed Garfunkel to SNL that night by saying, "So, Artie, you’ve come crawling back."