Short answers, pulled from the story.
Ken Keeler studied applied mathematics at Harvard University, graduating summa cum laude in 1983. He then earned a master's degree in electrical engineering from Stanford before returning to Harvard, where he completed a PhD in applied mathematics in 1990. His doctoral thesis was titled "Map Representations and Optimal Encoding for Image Segmentation."
Ken Keeler proved an original mathematical theorem to resolve the body-swapping plot of the Futurama episode "The Prisoner of Benda," which aired in 2010. The theorem demonstrates that any permutation of minds can be restored using a sufficient number of new participants in the swaps, given that the machine cannot swap the same two minds twice. According to David X. Cohen, Keeler proved it himself, and it appears written on a whiteboard within the episode.
Matt Groening refused to be credited on "A Star Is Burns," which aired in 1995, because he objected to The Simpsons crossing over with The Critic, a competing animated series. Keeler wrote the episode.
Ken Keeler wrote fourteen Futurama episodes, making him one of the show's most prolific writers. His credits include the original series finale "The Devil's Hands Are Idle Playthings" in 2003, the Writers Guild Award-winning episodes "Godfellas" and "The Prisoner of Benda," and the second series finale "Meanwhile" in 2013.
After earning his PhD from Harvard in 1990, Keeler joined the Performance Analysis Department at AT&T Bell Laboratories. He then left to write for David Letterman before moving into sitcoms, writing for Wings, The Critic, The PJs, The Simpsons, and Futurama.
Ken Keeler is a fan of the writer Harry Stephen Keeler but is of no relation to him. He won the fifth and twelfth annual Imitate Keeler Competitions, which challenge participants to mimic Harry Stephen Keeler's prose style. His Futurama episode "Time Keeps on Slippin'" from 2001 was partly inspired by Harry Stephen Keeler's short story "Strange Romance" from the novel Y. Cheung, Business Detective.