Sunday Funnies – X Marks the Spot

Bob says:  I found this article interesting and decided to share it with my readers.  I found it on the Smithsonian

A Brief History of the Letter ‘X,’ From Algebra to X-Mas to Elon Musk

A math historian explores how “x” came to stand in for an unknown quantity

ven though “x” is one of the least-used letters in the English alphabet, it appears throughout American culture, from Stan Lee’s X-Men superheroes to the television series “The X-Files.” The letter “x” often symbolizes something unknown, with an air of mystery that can be appealing. Just look at Elon Musk with SpaceXTesla’s Model X and now X as the new name of Twitter.

You might be most familiar with “x” from math class. Many algebra problems use “x” as a variable to stand in for an unknown quantity. But why is “x” the letter chosen for this role? When and where did this convention begin?

Math enthusiasts have proposed a few different explanations, with some citing translation and others pointing to a more typographic origin. Each theory has some merit, but historians of mathematics (like me) know it’s difficult to say for sure how “x” got its role in modern algebra.

Ancient unknowns

Today, algebra is a branch of math in which abstract symbols are manipulated, using arithmetic, to solve different kinds of equations. But many ancient societies had well-developed mathematical systems and knowledge with no symbolic notation.

All ancient algebra was rhetorical. Mathematical problems and solutions were completely written out in words as part of a little story, much like the word problems you might see today in elementary school.

Ancient Egyptian mathematicians, who are perhaps best known for their geometric advances, were skilled in solving simple algebraic problems. In the Rhind Mathematical Papyrus, the scribe Ahmes uses the hieroglyphics referred to as “aha” to denote the unknown quantity in his algebraic problems. For example, problem 24 asks for the value of aha if aha plus one-seventh of aha equals 19. “Aha” means something like “mass” or “heap.”

The ancient Babylonians of Mesopotamia used many different words for unknowns in their algebraic system—typically words meaning length, width, area or volume, even if the problem itself wasn’t geometric in nature. One ancient problem involved two unknowns termed the “first silver thing” and the “second silver thing.”

Mathematical know-how developed somewhat independently in many lands and in many languages. Limitations in communication prevented any immediate standardization of notation. But over time, some abbreviations crept in.

In a transitional syncopated phase, authors used some symbolic notation, but algebraic ideas were still presented mainly rhetorically. Diophantus of Alexandria used a syncopated algebra in his great work Arithmetica. He called the unknown “arithmos” and used an archaic Greek letter similar to “s” for the unknown.

Indian mathematicians made additional algebraic discoveries and developed what are essentially the modern symbols for each of the decimal digits. One especially influential Indian mathematician was Brahmagupta, whose algebraic techniques could handle any quadratic equation. Brahmagupta’s name for the unknown variable was yavattavat. When additional variables were required, he instead used the initial syllable of color names, like “ka” from kalaka (black), “ni” from nilaka (blue) and so on.

Islamic scholars translated and preserved a great deal of both Greek and Indian scholarship that has contributed immensely to the world’s mathematical, scientific and technical knowledge. The most famous Islamic mathematician was al-Khowarizmi, whose foundational text, The Compendious Book on Calculation by Completion and Balancing, is at the root of the modern word “algebra.” (Its Arabic name is abbreviated as “al-Jabr.”)

So, what about “x”?

One theory of the genesis of “x” as the unknown in modern algebra points to these Islamic roots. The theory contends that the Arabic word used for the quantity being sought was al-shayun, meaning “something,” which was shortened to the symbol for its first “sh” sound. When Spanish scholars translated the Arabic mathematical treatises, they lacked a letter for the “sh” sound and instead chose the “k” sound. They represented this sound by the Greek letter “χ,” which later became the Latin “x.”

It’s not unusual for a mathematical expression to come about through convoluted translations. The trigonometric word “sine” started as a Hindu word for a half-chord but, through a series of translations, ended up coming from the Latin word sinus, meaning bay. Still, some evidence casts doubt upon the theory that using “x” as an unknown is an artifact of Spanish translation.

The Spanish alphabet includes the letter “x,” and early Catalan involved several pronunciations of it depending on context, including a pronunciation akin to the modern “sh.” Though the sound’s pronunciation changed over time, there are still vestiges of the “sh” sound for “x” in Portuguese, as well as in Mexican Spanish and native place names. By this reasoning, Spanish translators conceivably could have used “x” without needing to resort first to the Greek “χ” and then to the Latin “x”.

The Spanish alphabet includes the letter “x,” and early Catalan involved several pronunciations of it depending on context, including a pronunciation akin to the modern “sh.” Though the sound’s pronunciation changed over time, there are still vestiges of the “sh” sound for “x” in Portuguese, as well as in Mexican Spanish and native place names. By this reasoning, Spanish translators conceivably could have used “x” without needing to resort first to the Greek “χ” and then to the Latin “x”.

Moreover, although the letter “x” may have been used in mathematics during the Middle Ages sporadically, there is no consistent use of it dating back that far. Western mathematical texts over the next several centuries still used a variety of words, abbreviations and letters to represent the unknown.

For instance, a typical problem in the algebra book Sumario Compendioso, published by Juan Diez in Mexico in 1556, uses the word cosa, meaning “stuff” or “thing,” to stand in for the unknown.

The most plausible explanation is to credit the influential French scholar René Descartes for the modern use of “x.” In an appendix to his major 1637 treatise, Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences, Descartes introduced a version of analytic geometry, in which algebra is used to solve geometric problems. For unspecified constants, he chose the first few letters of the alphabet, and for variables, he chose the last letters in reverse order.

Scholars may never know for sure, but some theorize that Descartes chose to make the letter “x” appear often because his printer had a large cache of x’s in stock, as the letter is scarce in the French language. Whatever his reasons for choosing “x,” Descartes greatly influenced the development of mathematics, and his mathematical writings were widely circulated.

Xtending beyond algebra

Even if the origins of “x” in algebra are uncertain, there are some instances in which historians do know why “x” is used. The “x” in X-mas as an abbreviation for Christmas definitely comes from the Greek letter “χ.” The Greek word for Christ is Christos, written χριστοσ and meaning “anointed.” The “χ” monogram was used as shorthand for Christ in both Roman Catholic and Eastern Orthodox writings dating back as far as the 16th century.

There are some instances in which “x” was chosen specifically to indicate something unknown or extra, such as when the German physicist Wilhelm Röntgen accidentally discovered X-rays in 1895, while experimenting with cathode rays and glass.

But there are other cases in which scholars can only guess about the origins of the letter’s role, such as the phrase “X marks the spot.” As for Musk’s affinity for the letter, commentators have offered a range of explanations, from the entrepreneur’s status as a member of Generation X to the letter’s historical association with mystery and faith.

This article is republished from the Conversation under a Creative Commons license. Read the original article.

Peter Schumer is a mathematician at Middlebury College in Vermont. He is the author of two books, Introduction to Number Theory and Mathematical Journeysin addition to many articles in the fields of number theory and the history of mathematics.


Where Do Words Come From?

Caught this in my Facebook feed from my neighbors

Completely true or not, they are always fun to read:
In the old west a .45 cartridge for a six-gun cost 12 cents, so did a glass of whiskey. If a cowhand was low on cash, he would often give the bartender a cartridge in exchange for a drink. This became known as a “shot” of whiskey.
This is synonymous with dying. During WW1 soldiers were given life insurance policies worth $5,000. This was about the price of an average farm so if you died you “bought the farm” for your survivors.
To have an ironclad contract came about from the ironclad ships of the Civil War. It meant something so strong it could not be broken.
The Old English word for “spider” was “cob”, thus we get cobwebs.
Traveling by steamboat was considered the height of comfort. Passenger cabins on the boats were not numbered. Instead, they were named after states. To this day cabins on ships are called staterooms.
Early beds were made with a wooden frame. Ropes were tied across the frame in a crisscross pattern. A straw mattress was then put on top of the ropes. Over time the ropes stretched, causing the bed to sag. The owner would then tighten the ropes and say sleep tight.
In the days before CPR, a drowning victim would be placed face down over a barrel and the barrel would be rolled back and forth in an effort to empty the lungs of water. It was rarely effective. If you are over a barrel, you are in deep trouble.
Steamboats carried both people and animals. Since pigs smelled so bad they would be washed before being put on board. The mud and other filth that was washed off were considered useless “hog wash”.
The word “curfew” comes from the French phrase “couvre-feu”, which means “cover the fire”. It was used to describe the time of blowing out all lamps and candles.
As the paper goes through the rotary printing press friction causes it to heat up Therefore, if you grab the paper right off the press, it’s hot. The expression “hot off the press” means to get immediate information.


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