Upon discovering the answer to a now-legendary problem, Archimedes famously yelled “Eureka!” (“I have found it!”), jumped out of his bath, and ran naked through the streets.

So “Eureka” seems like an appropriate name for the SyFy Channel’s quirky, well-written sci-fi series, all about a tiny town that brims over with geniuses and scientific breakthroughs. While it has the usual ups and downs of any long-running series, “Eureka: The Complete Series” is a charmingly eccentric little show that centers on the life of an ordinary law-forcement officer who just happens to live in a town full of oddball geniuses.

While dragging his delinquent daughter back to L.A., Marshal Jack Carter (Colin Ferguson) accidentally crashes the car. The only nearby place is the picture-perfect small-town of Eureka. But Jack starts to suspect that Eureka is a little odd — and his suspicions are confirmed when a tachyon accelerator starts ripping the seams out of the universe.

It turns out that Eureka is a town filled with geniuses, making groundbreaking scientific discoveries. After the local sheriff suffers a nasty accident, D.O.D. representative Allison Blake (Salli Richardson-Whitfield) makes Jack the new sheriff of Eureka. Now he has a new job, a “smart house” in an old nuclear bunker, and trigger-happy deputy Jo Lupo (Erica Cerra) who isn’t initially very happy to be working with him.

But life in Eureka is never peaceful, with countless scientific disasters threatening its people — and occasionally the whole world — and usually Sheriff Carter stumbles across some crimes and mishaps that just don’t seem to make sense. Some of them are more than mere technical problems: a mysterious Artifact that predates the universe, a boy with strange powers derived from said Artifact, a time jump that throws their lives out of balance by altering the past, a trip to Titan that goes horribly, horribly wrong, and the ever-present threat of government involvement.

“Eureka: The Complete Series” is a nearly ideal combination of gentle comedy and wild sci-fi, with the idea that leading experts in every scientific field imaginable (example: molecular gastronomy) have come to work in Eureka, in order to fully explore their fields. Unfortunately, most of these experts aren’t very good at the “being sensible” part of their job. So when there’s lots of genius and not enough common sense… well, let’s just say Carter’s everyman sensibility is required.

And the writers sprinkle it with funny scenarios (the whole town gets brainwashed into acting out the songs they listen to), bizarre problems (people are turned to stone) and funny dialogue (“I’m Sheriff Carter! I’m gonna save the day with my everyman logic, hahaha!”), which keep things from ever getting too serious. But there are moments of poignancy as well, such as the truly tragic loss of Henry Deacon’s first love, or the whole arc where the space crew is trapped in a virtual world that seems to have been set up to make them violently uncomfortable.

The biggest problem is that sometimes it feels like important plot threads are simply abandoned. The mysterious Artifact is held up as a cosmically inexplicable object that could change the way we see the universe… but it just sort of tapered off and was forgotten. And Allison’s ex-husband was eventually written out because the writers apparently couldn’t figure out what to do with him.

A lot of the show’s charm comes from the talented cast — Ferguson is particularly charming and slightly goofy as a guy so normal that he almost seems like a cliche. However, Carter is a lot smarter than he seems, and has a knack for figuring out the key to fixing these technical disasters. We also have a bunch of excellent actors like Cerra, Richardson-Whitfield, Ed Quinn, Niall Matter, Joe Morton and Neil Grayston. They play everything from nerds who push all the wrong buttons to super-genius mechanics, gun-toting sidekicks to charming bad-boys. Even the supporting cast is delightful, like Matt Frewer as an insane Aussie vet and Chris Gauthier as a feisty gay restauranteur.

Despite some dropped plot threads, “Eureka: The Complete Series” mixes equal measures of dramedy and sci-fi — where else can you find rage zombies, Egyptian bugs and brainwashing music? Clever, charming and well-written.