As you may remember, Watson stopped being a surgeon because a patient died under her care and she got sued for it. While she's out at the patient's grave, his son asks her out for coffee. He's dropped out of college, but he's got a great plan to buy a bar and all he needs is five thousand dollars. This is obviously a scam and the kid is just going to blow the money, but Watson still spends most of the episode waffling and asking Holmes for the money. At the end, she offers to pay four times as much for the kid to go back to college, but he doesn't go for it. Still, Holmes gets her to try to consider her mistake to be an accident that's best left in the past, which is nice.
Meanwhile, a mathematician has been murdered. And a mugger out in the alley has been shot, although no one thinks he's important. Holmes quickly reveals that what appears to be an empty room actually has walls covered in writing only visible under a blacklight. This writing is the kind of crazy-person mathematical doodling that you might remember from A Beautiful Mind, and it has to do with the "P versus NP" problem. In this show, solving that problem will have two immediate results: you'll win a million dollars and you'll also be able to crack any computer security or encryption in the world. So you can see how it's suspicious that someone who was working on that has been shot. Judging by the handwriting on the wall (har har) he had a partner, but no sooner does Holmes identify that person than that person turns out to have also been murdered. Oops!
The second dead person was being monitored by a security company that was concerned about the prospect of computer security suddenly being obsolete. But they had been assured that his solution was nowhere close to being done. And who assured them of that? Professor Tanya Barrett, who also helped out identify the partner in the first place. So she's obviously suspect number one, especially since her dog matches hairs found at the scene and she had a gun that matches the shootings. But she has an ironclad alibi, as shown by a restaurant's security footage and its embedded timecode. So maybe she was being framed by her ex-boyfriend, who sent threatening emails!
And then the mugger wakes up from his coma and pins the murder on Barrett. It turns out she had the solution to P versus NP all along, and she used her magical security-breaking powers to hack her boyfriend's emails and change the restaurant's timecode. She also stole hundreds of millions of dollars, but they don't really figure into the plot.
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