First aired April 26, 1993
Star Trek: The Next Generation Season Six - Stardate 46731.5
Lessons - The Chase - Frame of Mind

Richard Galen, Picard's old archaeology professor, visits the Enterprise and tells Picard that he's on brink of a monumental discovery in the field of microarchaeology and asks Picard to leave the Enterprise to help finish his research. Picard refuses and Professor Galen leaves on his shuttle only to be attacked by a Yridian destroyer. The Enterprise rescues the professor, destroying the Yridians, but Galen has taken a disrupter beam point-blank and dies. It's discovered that the Yridians had been trying to download data from the professor's computer.

LaForge and co. downloads what's left of the professor's memory banks (a bunch of numbers) and Picard sets a course for the planet where the professor had last been to see if they could find anything. They find no animal life on that planet.

Then they go to where the professor was planning on heading next only to find somebody has destroyed all life on that planet. Realizing that the numbers must have something to do with biology Picard and Crusher tell the computer to search only the biology databases and it finds a match, showing the numbers to be from the DNA of seventeen species from different planets, all matching in a way that they can be organised into an algorithm, though not a complete one.

Then Picard remembers that the gift Professor Galen gave him earlier was from a far away place and that he had said that he was "in the neighborhood". Picard and Crusher discover that there's a planet near there--Loren III--that may have another piece of the program and head there, only to find two Cardassian ships already there. While Picard is talking with the Cardassian captain, Gul Ocett, a Klingon Bird of Prey decloaks nearby.

Picard convinces the Klingon captain--Nu'Daq--and Gul Ocett to put all the pieces together 'cause they sure as hell aren't going to solve the puzzle otherwise.

(Nu'Daq, by the way, has weird shoes that curve up in a point at the toe.)

When they put the three pieces together it turns out that there's one piece missing. It takes several hours for the computer to extrapolate where that piece is and in the meantime the Gul Ocett plans to attack the Klingons and the Enterprise once they've found where the piece is. LaForge discovers this and Picard and Nu'Daq trick the Cardassians, having the computer show them a false location for the DNA and then having the ship appear hurt when the Cardassians attack. Once the Cardassians leave the system, Nu'Daq goes with Picard on the Enterprise, his own ship having been damaged, to the real planet.

When they get there they find the only place where there's life on the planet is a fossilised seabed. Picard, Crusher, Worf, and the Nu'Daq beam down to collect the DNA. Then Gul Ocett beams down. Then the Romulans beam down and explain that they had intercepted a transmission from the Yridians and while the Gul Ocett, Nu'Daq, and the Romulans are arguing, Crusher collects some DNA and Picard adds it to the program in his tricorder.

The program runs and causes the tricorder to emit a holographic projection of an alien female.

The projection explains that four billion years ago her race created the DNA strands on many planets in hopes that later the different species that would evolve from it would come together and solve the puzzle, as a monument on the old species' existence. (This episode is used as an explanation of why so many species in Star Trek are humanoid, the lady alien stating that that the DNA strand was designed to make the daughter species look like them.)

The Nu'Daq is disgusted, having hoped it was an ueberweapon, and Gul Ocett is disgusted that Cardassians could have anything in common with Klingons.

Later, just before the Romulans leave the system, the captain hails Picard and comments that it seems their species are not completely dissimilar. Maybe someday...

One of the coolest endings to a TNG episode.

Patrick Stewart as Jean-Luc Picard
Jonathan Frakes as William T. Riker
Brent Spiner as Commander Data
LeVar Burton as Geordi LaForge
Michael Dorn as Worf
Gates McFadden as Beverly Crusher
Marina Sirtis as Deanna Troi
John Cothran, Jr. as Nu'Daq
Linda Thorson as Gul Ocett
Norman Lloyd as Professor Richard Galen
Salome Jens as Humanoid
Maurice Roeves as Romulan Captain
Directed by Jonathan Frakes
Story by Ronald D. Moore & Joe Menosky
Teleplay by Joe Menosky