Tanya Barrett
Tanya Barrett is the main villainess from "Solve for X," episode 2.02 of Elementary.

She was played by Lynn Collins.

Tanya Barrett is a mathematics professor at TriBoro College, as well as the revealed murderous mastermind of a plot to steal billions of dollars. Her plan included the notorious unsolved problem, P vs NP, which--if solved--could crack cryptography systems from the world's banks, allowing the evil professor to rob them all.

Sherlock originally believed that Tanya was looking to solve the problem before math tutor Felix Soto and reclusive savant Cyril Nayer could. In actuality, Tanya solved it weeks ago, but she was looking to keep the solution a secret, or else the banks would change their systems. To do so, Tanya hunted down Soto and Nayer and killed both of them, doing so via gunshots.

Tanya's accomplice, Wayne Kaneshiro, worked on a computer code to implement the solution, and also tampered with the security video to make it appear that their meeting at a pub occurred during the murders. After her confrontation with Sherlock, Tanya was arrested and taken into government custody.