In the John Adams Courthouse in Boston, Massachusetts, right outside the chambers of state Supreme Judicial Court Chief Justice Ralph D. Gants, there hangs a portrait of a distinguished-looking man. He’s got a widow’s peak, a large nose, and a yearning sort of look, and he’s wearing a high-collared shirt under a black jacket.

He’s been there for years, hobnobbing with portraits depicting the likes of Margaret H. Marshall and Oliver Wendell Holmes, Jr. And now, the court wants to know: Who the heck is he?

As the Boston Globe reports, officials have been trying to identify the portrait since at least 2005, when it was re-hung in the courthouse after a renovation. They’ve cross-referenced it with lists of former justices, and come up short. (Clifford Allen, the court’s director of education and public programs, even tried running it through the Google Arts & Culture App to see if it matched with any other paintings, he told the Associated Press.) At this point, they think he probably served as an associate justice during the late 18th or early 19th century, but that’s all they know.

The latest tactic was dreamed up by Gants, who, after all, has to look at the guy every day. “I basically said… why don’t we set loose the public to see if they can put on their Sherlock Holmes’s hats and help us to track down who this elusive and mysterious justice is?” he told the AP.

Would-be sleuths have their work cut out for them. “I hate to say it, but a lot of these guys do look alike,” historian Robert J. Allison told the Globe.

A visit to the court’s Public Information desk revealed that people have sent in some guesses, although thus far, none have come with instantly verifiable proof. Others have offered up less plausible theories in the form of comments and tweets. One speculated that someone got the portrait at an 1820s yard sale, and “decided to spruce up the spartan walls of the courthouse with anything distinguished looking.”

The John Adams Courthouse in Boston. Daderot/CC0 1.0

“He’s a time traveler from the year 2422 whose time machine broke when he arrived in Boston in 1812,” posited another, in the Globe’s comment section. “He was clever enough [to] erase all records of his existence (to preserve the space-time continuum) except for this portrait, which now echos [sic] through eternity.”

If you do figure it out, there’s a reward in store: According to a statement the SJC gave the Globe, whoever can provide proof of the subject’s identity will be invited to a ceremony in which Gants affixes an explanatory plaque to the portrait, solving this problem once and for all.