The Equality of Robert Recorde

Throughout their education, students will come across the most ubiquitous symbol in all of mathematics. It’s the symbol that defines all equations. It is the equal sign.  But where did it come from?

Robert Recorde (ca. 1512-1558) was a Welsh physician and mathematician. At the age of fifteen, he entered Oxford University, graduating in 1531. In the same year he was elected a Fellow of All Souls College. Moving to Cambridge University he obtained a degree in medicine in 1545. He is known as the founder of the English School of Mathematics and was the first person to write mathematical books in English. He also introduced, among other things, the idea of placing two hyphens in parallel to symbolize the balance of two expressions in a mathematical equation.

He wrote a math textbook with a most convoluted title: “The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers” (Published in 1557). You can find and download a digitized version of this textbook here at the Internet Archive. The book covers topics including whole numbers, the extraction of roots and irrational numbers as well as the execution of arithmetic operations.

This is the page in which he defines the familiar symbol:

“And to avoide the tedious repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a paire of paralleles, or gemowe lines of one length, thus: =, because noe. 2. thynges, can be moare equalle.”

He uses this symbol to subsequently express numerous equations, beginning at the bottom of this page. Thus, it can be said that the first math equation to be expressed using this modern notation is 14x + 15 = 71. Thankfully, by the time this symbol was consistently used in the 1700s, the two parallel lines (as well as other symbols he defined) were made more compact.

Robert Recorde is honored with a wall tablet at St. Mary’s Church. It is located in his birth town of Tenby, Pembrokeshire, Wales. It documents his achievements to mathematics:

“To his genius we owe the earliest important English treatises on algebra, arithmetic, astronomy, and geometry: He also invented the sign of equality, =, now universally adopted by the civilized world.”

There is also a display at the Tenby Museum & Art Gallery documenting the achievements of this Welsh mathematical pioneer.

Explore and enjoy!

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The Geometry of Flatland

Here is another literary reference to mathematics. In fact, this story has often been called mathematical fiction. It is the satirical novella “Flatland: A Romance of Many Dimensions,” (1884) which was written by Edwin Abbott Abbott (1838-1926), an English schoolmaster and theologian. This story explores the nature of dimensions from the point of view of a two-dimensional world of geometry. The narrator is the humble square, who ends up visiting the one-dimensional world of Lineland as well as the three-dimensional world of Spaceland.

He is even introduced to the world of Pointland. There are certainly some thought-provoking social elements to this geometry-filled story, and I recommend it to any math student who is studying geometry. Although the book was not ignored when it was published, it did not achieve great success. However, it experienced a surge in popularity when Albert Einstein’s Theory of General Relativity, and its introduction of the fourth dimension, was made known to the public. The text of the original books is made available to the public at WikiSource.
This story also inspired the making of a 30-minute animated movie, “Flatland: The Movie”. It was released and sold to the public as an educational edition DVD, private home-use DVD, and digital download in June, 2007. The educational edition is primarily intended for educators, teachers, schools and institutions that will use the movie as part of classes, lectures, and courses. Visit the movie’s website and watch the trailer. I found it to be a very contemporary and entertaining adaptation of this mathematical literary classic.  I hope you do too.

Can Alice do Addition?

John Tenniel (1820-1914) was a British illustrator, graphic humorist and political cartoonist. He achieved considerable fame as the illustrator of Alice. Tenniel drew ninety-two drawings for Lewis Carroll’s “Alice’s Adventures in Wonderland” (London: Macmillan, 1865) and “Through the Looking Glass” (London: Macmillan, 1871). There is an illustration to the ninth chapter of Through the Looking Glass and excerpt that touches upon the topic of recent blogs.

Illustration to the ninth chapter of “Through the Looking Glass” by John Tenniel. Wood-engraving by the Dalziels.

“Manners are not taught in lessons,” said Alice. “Lessons teach you to do sums, and things of that sort.”
“Can you do Addition?” the White Queen asked. “What’s one and one and one and one and one and one and one and one and one and one?”

“I don’t know,” said Alice. “I lost count.”
“She can’t do Addition,” the Red Queen interrupted..

The .pdf copy of this book was made available to the public by Lenny de Rooy at her website, Lenny’s Alice in Wonderland Site.