"Long Live Walter Jameson" is the 24th episode of The Twilight Zone, and was first broadcast in March of 1960. It was written by Charles Beaumont, and starred Kevin McCarthy, and featured Estelle Winwood, who was 80 years old at the time, in a small role.
Walter Jameson is a history professor whose detailed descriptions of the past are so evocative that his students believe that he must have been there. And his colleague at the college where he teaches takes note of the fact that while they seemed to be the same age when they started, he is now getting older while Jameson appears the same age.
This episode is one of the more straightforward and clearly choreographed episodes of The Twilight Zone. There is no real "twist", and the theme and plot are set up almost from the title. I have to admit that there was not much in the premise or the execution of this episode that caught my eye: tales of immortality and its downside are well-worn, and there was nothing in this episode that caught my attention in that regard. If anything, the most memorable scene was where Walter Jameson's fiance, despite being in her late 20s and a Ph. D. candidate, is told be her father to do her homework before bed. This episode is about things that don't age: but the social mores of the 1950s are certainly not amongst them.
Somewhat amusingly given the subject matter, this episode also features Estelle Winwood, who was 77 at the time of filming, and who would later become, at age 101, the oldest actor ever to be in the Screen Actors Guild. Given that Estelle Winwood first acted professionally in 1903, and that Ron Howard, featured earlier in the season is still making movies, the first season of The Twilight Zone has already given us better than a century of span in its actor's careers. So perhaps this episode does have something to teach about timelessness.