Contributed by
Vijay Fafat
Julius Corbett, a man of fortune, is in love with an extraordinary woman, Nell Morrison, who is an astronomer. She has a particular penchant for Mars, an in particular, is trying to solve the problem of communicating with the Martians. So great is her obsession with this issue that when Julius proposes marriage to her, she says,
(quoted from Love and a Triangle)
“Talk with the Martians,” said she, “and the next day I will become your wife!”

So a dispirited Julius seeks help from his friend, Marston, an Astronomy Professor at Univ. of Chicago. Marston’s idea is to use electricity and mathematics (“We must use that. And the figures must, of course, be geometrical. Geometry is the same throughout all the worlds that are or have been or ever will be.”). Thus do they end up in the great Pampas of Argentina where “illuminated figures two hundred miles each in their greatest measurement” were made, comprising “only the square, equilateral triangle, circle and rightangled triangle.”
Many months later, the observatories on earth see the startling reply from Mars, in the form of all the figures which the earthlings had made as well as a clear geometric figure of a rightangled triangle with squares drawn on each side, indicating knowledge of the Pythagoras Theorem. As the author exults:
(quoted from Love and a Triangle)
“Ah, it required no profound mathematician, no veteran astronomer, to answer such a question! A schoolboy would be equal to the task. The man of Mars might have no physical resemblance to the man of Earth, the people of Mars might resemble our elephants or have wings, but the eternal laws of mathematics and of logic must be the same throughout all space. Two and two make four, and a straight line is the shortest distance between two points throughout the universe. And by adding this figure to the others represented, the Martians had said to the people of Earth as plainly as could have been done in written words of one of our own languages:
’Yes, we understand. We know that you are trying to communicate with us, or with those upon some other world. We reply to you, and we show to you that we can reason by indicating that the square of the hypothenuse of a rightangled triangle is equivalent to the sum of the squares of the other two sides. Hope to hear from you further.’
There was the rightangled triangle, its lines reproduced in unbroken brilliancy, and there were the added lines used in the familiar demonstration, broken at intervals to indicate their use. The famous pons asinorum had become the bridge between two worlds.”

And that is how love and geometry launched an interplanetary discourse.

I am very grateful to Vijay Fafat for bringing this impressive classic science fiction to my attention.
The portrayal of a strong and intellectual female character is very unusual considering that it was originally published in the collection "The Wolf's Long Howl" in 1899.
This makes it one of the oldest work I know of in which humanity is initially able to communicate with extraterrestrial intelligences using the "universal language" of mathematics.
(See Old Faithful for another old one and From the Earth to the Moon which is the oldest I know so far.)
In January 2022, Vijay Fafat wrote me with information about another work of fiction that mentions the Pythagorean Theorem in the context of communication with aliens, which is being mentioned here but not given its own entry in the database:
Contributed by
Vijay Fafat
Pythagorean Theorem and mathematics as a means of alien communication is a device used as a side thought in another story, “Second Chance” by Walter Kubilius and Fletcher Pratt (Fantastic Story Magazine, Fall 1952), where Venusians who have arrived in earth’s orbit signal the Pythagoras theorem to the military men, as in the following: (the story itself is not really mathfiction but a warning on the dangers of internecine intercontinental wars):
(quoted from
Second Chance
)
“The screen gave another series of flashes. “We got a picture sequence. Here it comes,” said the speaker. Those in the room saw an outline of an equilateral triangle (note: This should have said rightangled triangle), apparently formed of narrow strips of metal standing on edge. An invisible hand placed a series of little blocks along each edge; then rapidly these detached themselves into two groups, one from the hypotenuse, one from the two sides.
“The Pythagorean theorem,” said Sanchez, smiling.
But Marechal Laporte frowned. “My General,” he said to Weinburger, “we shall never communicate with these beings on this level. I suggest that we have two or three stations flash them simple mathematical problems in systems of dots and dashes.”


Available Free Online at MathFiction.net: "Love and a Triangle" is available as a PDF from Vijay Fafat and Prof. Mythili Vutukuru's MathFiction.net website. 
