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The Day the Earth Stood Still (1951)
Robert Wise (director) / Harry Bates (story) / Edmund H. North

Contributed by Christopher Wolfe

One must wonder how aliens might communicate with humans when and if they arrive on Earth. In the 1951 film The Day the Earth Stood Still, the extraterrestrial Klaatu (Michael Rennie) introduces himself to the genius Professor Barnhardt using the universal language of math. After sneaking into the professor's office and examining a chalkboard full of what appears to be very basic differentiation and integration, Klaatu pinpoints the professors flaw, corrects the equation, and waits for Barnhardt's response. Following the awkward introductions, Klaatu reveals his expertise in the equation on the board, since this very problem in “celestial mechanics” allowed him to travel to Earth.

The math is later set aside to reveal the true purpose of the story. Klaatu's mission is not to enlighten men with mathematics, but to warn them against nuclear programs. The primitive scientists have no need for such destructive weapons, so they must disarm in order to prevent the destruction of Earth.

There is really not much math in this movie, but the bit that is there is handled nicely. I like the reference to variation of parameters particularly:

(quoted from The Day the Earth Stood Still)

Copied from where the script seems to be available for free:

                         You wrote this?

                              (nodding easily)
                         It was a clumsy way to introduce 
                         myself -- but I understand you're a 
                         difficult man to see.
                              (glancing at the 
                         I thought you'd have the solution by 
                         this time.

                         Not yet. That's why I wanted to see 

               Klaatu glances at the work Barnhardt has been doing on the 
               board. Then he points to one of the expressions in an 

                         All you have to do now is substitute 
                         this expression--
                              (pointing to a specific 
                         --at this point.

               Impressed and interested, Barnhardt tugs at his chin as he 
               studies and weighs the results.

                              (slowly, thoughtfully)
                         Yes -- that will reproduce the first-
                         order terms. But what about the effect 
                         of the other terms?

                         Almost negligible... With variation 
                         of parameters, this is the answer.

                         How can you be so sure? Have you 
                         tested this theory?

                              (with a slight smile)
                         I find it works well enough to get 
                         me from one planet to another.

Contributed by Brett Wormley

I saw this movie as a young teenager, and thoroughly enjoyed it. I usually pay attention to details I don't understand, like new words or concepts. I mentally logged "variation of parameters" and wondered what it meant, but thought it was just fiction. Ten years later, in my ordinary differential equations class, I finally learned the technique, and told the professor I had been waiting for a decade to understand what Klaatu meant!

An anonymous contributor wrote to point out that Sam Jaffe, who plays the Einstein-like scientist in the film, actually worked as a math teacher prior to becoming an actor and may have played a role in formulating the equations on Barnhardt's blackboard. However, Peter Armstrong has reason to think otherwise:

Contributed by Peter Armstrong

I can shed some light on this. The equations on the blackboard were developed and written by Prof. Samuel Herrick of UCLA. He was hired by 20th Century for the then-sizeable sum of $75 per day to come up with something for the blackboard.

The book "Lab Coats in Hollywood: Science, Scientists and Cinema" tells quite a bit of Herrick's involvement. The author writes

    Herrick reasoned that an equation related to celestial mechanics would be most appropriate, specifically an equation related to his own work on the "three body problem" in astronavigation. The equation itself was so complex that Herrick provided the director with a list of 'confusable symbols'. Note in figure 4.4 the presence of signs saying "Don't Erase" and "Don't Touch." Once Herrick left the set there was no one who could put it back together outside of a scientist (or an alien intelligence).

I do not believe that actor Sam Jaffe had anything to do with the math on the blackboard.

Contributed by Anonymous

I took Astrodynamics @ UCLA, which he taught for many years ... later, with his own textbook. Herrick is credited with inventing the term 'astrodynamics' after World War II and was a major contributor to the field. His two-volume textbook on the subject (though now a bit dated) is considered a classic for its clarity and exposition ... rare in such a difficult field. The equations on the chalkboard LEAP OFF THE SCREEN (!) to anyone who has studied Astrodynamics, of course ... And you _thought_ you were only watching a Silly Science Fiction movie ... !

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Works Similar to The Day the Earth Stood Still
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Tau Zero by Poul Anderson
  2. Paint ‘Em Green by Burt Filer
  3. The Tale of a Comet by Spencer Edward
  4. Dalrymple’s Equation by Paul Fairman
  5. All the Universe in a Mason Jar by Joe Haldeman
  6. Archive (Travelers, Season 3 Episode 8) by Ken Kabatoff / Brad Wright
  7. Phase IV by Mayo Simon (writer) / Saul Bass (director)
  8. Torn Curtain by Alfred Hitchcock (Director)
  9. The 39 Steps by Alfred Hitchcock (director)
  10. The Unwilling Professor by Arthur Porges
Ratings for The Day the Earth Stood Still:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
2.2/5 (5 votes)
Literary Quality:
4.5/5 (6 votes)

GenreScience Fiction,
TopicAnalysis/Calculus/Differential, Mathematical Physics,
MediumFilms, Available Free Online,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)