During the film opening, we see a man, presumably Einstein (Walter Mathau) playing a violin, as another man walks past a poster advertising Boyd's comet. We then see Catherine Boyd (Meg Ryan) with her fiance James Moreland (Stephen Fry). She's working on some math referring to the comet. He comments that she's babbling when she tries to tell him a story. The scene cuts back and forth with a group of elderly men arguing about whether time exists. Meg and James are in his convertible when it develops engine trouble. We see Einstein discussing with his friends (the elderly men), whether there are 'accidents' and he says, "I do not believe God plays dice with the universe."
Catherine and James pull into a garage, where Ed Walters (Tim Robbins) is arguing with his boss, Bob (Tony Shalhoub), about the car they hear coming into the shop, what make and model it is and what the trouble with it is, based on what they can hear. Bob sends out Ed to check because he sees the couple and assumes they're "college people" meaning they come from Princeton College. As soon as Ed sees Catherine, he falls for her.
James, obnoxiously asks if someone there can work on a British engine, and Ed says, "May I look under the bonnet?" James, reassured by the use of the word 'bonnet' consents. Ed looks at it, looks at Catherie and pronounces, "You have no spark." There's clearly a double meaning here, referring to her relationship with James. James insists, "But what's wrong with it?" and Ed adds, "My guess is that you have a short stroke and premature ignition." He turns to Meg Ryan and says, "Does it ever feel that way?" She replies, "I'm sure I don't know what you mean" but it's clear that she gets the double entendre. Ed says he'll go check with his boss about fixing it, and goes in to tell his boss that he's in love, that time and space stopped, that he could see himself kissing Catherine in the future. Ed tells Catherine that fixing the car will take days, and she uses his phone to call a cab, giving the cab company and Ed her address for the invoice. In the process, she leaves behind a pocket watch. There's a brief moment where you see a hand move the watch under some magazines, but whose hand? And is it an accident? Or deliberate? The theme of accident versus deliberate intervention occurs repeatedly in the film.
Ed goes to return the pocket watch and discovers that the address is the home of Albert Einstein, who is Catherine's uncle. Ed helps Einstein and his friends retrieve a badminton racket and in the process befriends them. It's clear to them that Ed likes Catherine. Einstein sees that his niece is unhappy with her fiance and wonders how to help Ed date her. She will only date a very intelligent man, and Ed is an auto mechanic. Ed says, "That's easy, lend me your brain for a couple of days." Einstein gets an idea.
Einstein and his three friends hatch a plot to make Catherine think that Ed has developed cold fusion as a way to power a rocket to reach the stars so she'll desire him. They help Ed appear hyper-intelligent, helping him present a paper on cold fusion at a symposium and then helping him pass an IQ test administered by Catherine's fiance. Catherine, as a mathematician, is trying to figure out "Ed's" theory on cold fusion, but she struggles with it. Ed wants to tell Catherine he's a fake, but he can't quite seem to. Einstein and his buddies interfere with Catherine's relationship with James, and encourage Ed. James is presented as a sadistic, sexually cold man who puts Catherine down subtly.
Of course, there's always a happily-ever-after ending, even though it takes President Eisenhower's appearance in the film, a convertible, a motorcycle, waltz music, engineered automotive troubles and a comet, to make it all come about.