Mom-Farnsworth relationship

The relationship between Mom and Professor Farnsworth is a recurring theme on Futurama.

Q. T. McWhiskers incident
At around age 90, Farnsworth works for Mom's Friendly Robot Company, where he designs robots for the company as well as toys, such as Q. T. McWhiskers, but Mom's suggestion of turning the toy into a giant makes Farnsworth leave her, because she simply does not understand him. (2ACV14)

Global Warming situation
Farnsworth later returns to Mom's company to work on creating actual robots, but at this point, robots are stiff moving and not very efficient. However, when he sacrifices fuel efficiency, he succeeds. Unfortunately, this robot design also causes global warming. Why he leaves Mom this time remains unsettled, but it may be because he once again realises she is evil. (4ACV08)

The Wernstrom Affair
At a third account, Farnsworth is once again at the company with Mom, where he discovers the secret of Dark matter, around the time where Mom's sons, Walt and Larry, are born. When he finds out she has left him for Dr. Ogden Wernstrom, he leaves her once again. During this period in which Farnsworth is working for Mom, their relationship grows deeper, as Mom becomes pregnant with Igner. (Bender's Game)

Mother's Day
On Mother's Day, 3001, during the Robot Uprising, all rebels under the command of Mom. Mom's three sons go to get Farnsworth to make Mom happy, but the only way to make Mom happy again is for Farnsworth to return to her, or at least fake doing so in order to reach the remote control she keeps in her bra. The crew and the sons travel to Mom's cabin in the Bronx by means of a cart, meaning that Fry needs to re-invent the wheel. Once there, the Professor does his best to seduce Mom in order to get at the remote control, but then the situation gets out of control and he sleeps with Mom. As the crew grows impatient, especially with robots appearing and trying to kill them all, they flee into the cabin and search for Mom's bra with the remote, eventually locating it hanging on a fan. The fan refuses to give it back, as it too is robotic, when Bender and the Greeting Card crash the scene. Mom asks Bender to return the remote, and after his discussion with the Greeting Card, he manages to return the remote control in time to Mom, who ends the rebellion. Unfortunately, Mom finds out that the whole action was just a plan to get to her remote, and she breaks up with Farnsworth yet again. Even though they're broken up, Farnsworth breeds Albino Shouting Gorillas that scream his love for Mom from the rooftops.